For More Information Visit the ACC-Angels Around the World website.
You may recall that last year in September Cindy Mauro Reisenauer and Alex Reisenauer, a mother/son duo, co-authored a very personal (electronic) book titled: Knowing Alex, about living life with Agenesis of the Corpus Callosum.
At that time it was only available as an e-book, with the hopes that a print version of the book would soon follow.
Well, I just received an e-mail this morning from Cindy who informed me that the print version of their book Knowing Alex: Life with Agenesis of the Corpus Callosum is now available (for those of you who prefer a print copy--a regular paperback book).
Buy the print version.
Plus, they have just created a brand new website with information about their book.
http://www.knowingalex.com/
Read Amazon reviews of the book.
Have a look inside the Kindle version of the book to view the Table of Contents and read an excerpt.
Note: At this time the book is only available in English.
P.S. The previous e-book versions of Knowing Alex are still available for purchase, too.
Many months ago, I was contacted by a writer, Daisy Yuhas, from Scientific American Mind magazine who was inquiring about connecting with an adult who has Agenesis of the Corpus Callosum, who would be interested in being interviewed by her for an article about ACC in their magazine. After carefully checking her credentials and exploring their magazine further, I sent out Daisy's request to the ACC Adults yahoo e-mail support group and was so excited to learn that there was an interest from not only one adult who has ACC (but from SEVERAL adults) who wanted to be interviewed for the article.
In our correspondence between then and now, it was revealed that Daisy hoped to be able to not only write an article about one adult, who has Agenesis of the Corpus Callosum, in the magazine but to also include a follow-up to the article where she could include several more stories about other adults with ACC (who she interviewed).
This morning I received an e-mail from Daisy Yuhas who informed me that the ACC article is finished and it will appear in the January/February 2013 issue of Scientific American Mind. The additional stories of adults with ACC was published today, December 20, 2012, and appears in their Scientific American Blog.
I am including Daisy's e-mail below, so you can read it for yourself:
"Dear Sandie,
I hope that you're doing well! I just wanted to share that the agenesis of the corpus callosum feature will appear in the January-February 2013 issue of Scientific American Mind (you can find a preview with a paragraph or two online—the issue will hit newsstands in the new year). In addition, Scienitfic American has run a blog post that shares a few additional stories. I realize I can't possibly do justice to the full range of experiences shared— but I want to thank you again for your help in putting me in touch with others who could share their stories. I truly believe that readers will find strength in reading these experiences.
All the best and very happy holidays,
-Daisy"
This is incredibly exciting news and, thanks to each one of the adults who have ACC who shared their stories (and who revealed personal insights about living life with Agenesis of the Corpus Callosum), as well as the people at Scientific American Mind, there is now an even greater awareness about ACC, which brings us one step further in helping other adults and children in the world who have this congenital brain anomaly.
I know that (as a mom myself of a child with Agenesis of the Corpus Callosum) I definitely plan to buy a copy of the January/February 2013 Scientific American Mind magazine for The Mystery of the Missed Connection article.
Alexandra Berube has written several guest blog articles here about her teaching experiences with her student who has Agenesis of the Corpus Callosum. She is a former Kindergarten teacher, who first taught the student in her Kindergarten class and she also tutors the student, who is currently in a regular 3rd grade mainstream class.
Her most recent article today is about Reading Comprehension. In our e-mail correspondence, Alexandra shared information with me that I am including here for you to see (with her permission) as a preface to her article:
Alexandra writes:
"Max came into Kindergarten already reading because his family had been working with him before he came to kindergarten. He already knew a lot of sight words and understood decoding and blending when we started working together. His speech skills were not strong so it was hard to understand him (and know he was reading the correct word) but he did speech therapy and that helped a lot."
GUEST BLOG POST
Reading Comprehension--Taking it to the Next Level by Alexandra Berube, bostontutoringservices.com
Max and I did not spend time working together during his second grade year, because he was receiving services through school. At the end of his second grade year, I began working with him again, picking up where we had left off the previous summer. His mother's goals were for him to improve his reading comprehension in the following three areas: making inferences, comparing and contrasting, and deciphering main idea/details in text. In my assessment of his reading comprehension at that point, I noticed that he didn't anticipate the next steps in a text based on the clues. For example, if a character is put into a situation and someone tells him not to move, *Max did not anticipate that the character would of course move, because that is standard literary practice. He didn't know how to anticipate these common literary themes that would help him make predictions in his reading. His predictions were usually completely unrelated to the story structure so far. I started reading books with him that all had a theme: the character did something bad at first, then did something good, and everybody likes the character in the end. We read books such as Walter the Farting Dog and Leo Lionni’s Frederick. I wanted him to learn of this story pattern, which is so common in literature (and movies). I also wanted him to be able to contrast and compare the way that the character interacted with the others in the book in the beginning (and how they treated the character in response), and how things changed at the end. This also related to cause and effect relationships, because the character acted a certain way and the effect was that the others related back to him in a certain way (first he was ‘bad’ and they didn’t like him, then he was ‘good’ and they did like him). We also did many text-to-self and self-to-text relationships to help him connect to what he was reading. We continued to practice reading stories with this literary theme so that he would improve in his ability to make predictions. Adults are used to so many classic story patterns that we can anticipate when a common literary theme is being used. But young students don't have this storage of knowledge, and I wanted him to get used to more and more of the literary themes he would encounter in his reading, so he would be able to make predictions and make connections between what he already knew and what he would read. Talking about the structure of the stories also helped focus on the main point, because the main point is a larger perspective of the story, not the details in the story specifically. Many students focus on the individual details and can't back up farther to get the main point, but when talking about patterns between one story to another, it's easier to step back and see the larger story structures at hand. The more you do this, the more they also begin to understand the order of events and the idea of cause and effect The more we did text-to-text relationships between the books we were reading with common story patterns (including many text-to-self relationships so he could relate personally to what was going on in the story), the more he was able to make predictions about the text, make inferences about what was going on, determine what the main point was, and figure out the cause and effect relationships. This study of a specific literary theme helped Max realize that there are patterns in stories that he can recognize. All stories will not have this literary theme of ‘character is unliked, does something good, is then liked by others,’ but all will have a main point, all will have cause-and-effect relationships, and all stories have a beginning, middle, and end so that you can compare and contrast what happens from one part of the story to the next. You can also connect stories to other stories and to yourself. You can make predictions based on what you have seen characters do in other stories, or based on what you would do in that situation (text-to-self relationships). Just the knowledge that all this is going on helped Max know to look for these clues, and to be an active reader (not just ingesting details, but seeking out broader answers). This is the goal of every teacher in instructing reading comprehension. *Name has been changed.
In my assessment of his reading comprehension at that point, I noticed that he didn't anticipate the next steps in a text based on the clues. For example, if a character is put into a situation and someone tells him not to move, *Max did not anticipate that the character would of course move, because that is standard literary practice. He didn't know how to anticipate these common literary themes that would help him make predictions in his reading. His predictions were usually completely unrelated to the story structure so far.
I started reading books with him that all had a theme: the character did something bad at first, then did something good, and everybody likes the character in the end. We read books such as Walter the Farting Dog and Leo Lionni’s Frederick. I wanted him to learn of this story pattern, which is so common in literature (and movies). I also wanted him to be able to contrast and compare the way that the character interacted with the others in the book in the beginning (and how they treated the character in response), and how things changed at the end. This also related to cause and effect relationships, because the character acted a certain way and the effect was that the others related back to him in a certain way (first he was ‘bad’ and they didn’t like him, then he was ‘good’ and they did like him). We also did many text-to-self and self-to-text relationships to help him connect to what he was reading.
We continued to practice reading stories with this literary theme so that he would improve in his ability to make predictions. Adults are used to so many classic story patterns that we can anticipate when a common literary theme is being used. But young students don't have this storage of knowledge, and I wanted him to get used to more and more of the literary themes he would encounter in his reading, so he would be able to make predictions and make connections between what he already knew and what he would read.
Talking about the structure of the stories also helped focus on the main point, because the main point is a larger perspective of the story, not the details in the story specifically. Many students focus on the individual details and can't back up farther to get the main point, but when talking about patterns between one story to another, it's easier to step back and see the larger story structures at hand. The more you do this, the more they also begin to understand the order of events and the idea of cause and effect
The more we did text-to-text relationships between the books we were reading with common story patterns (including many text-to-self relationships so he could relate personally to what was going on in the story), the more he was able to make predictions about the text, make inferences about what was going on, determine what the main point was, and figure out the cause and effect relationships.
This study of a specific literary theme helped Max realize that there are patterns in stories that he can recognize. All stories will not have this literary theme of ‘character is unliked, does something good, is then liked by others,’ but all will have a main point, all will have cause-and-effect relationships, and all stories have a beginning, middle, and end so that you can compare and contrast what happens from one part of the story to the next. You can also connect stories to other stories and to yourself. You can make predictions based on what you have seen characters do in other stories, or based on what you would do in that situation (text-to-self relationships). Just the knowledge that all this is going on helped Max know to look for these clues, and to be an active reader (not just ingesting details, but seeking out broader answers). This is the goal of every teacher in instructing reading comprehension.
*Name has been changed.
Hint: don't forget to check your local library when looking for the books mentioned here (or other books).
About Alexandra Berube
Alexandra is the Managing Director of Boston Tutoring Services, a tutoring company that offers one-to-one in-home tutoring in Massachusetts. She is also a former Kindergarten teacher who also tutors students in grades K-8, in all subject areas, including test preparation.
--click below for printable version of this article--
Reading Comprehension--Taking it to the Next Level - printable version
Watch for an upcoming guest blog post here in the near future from Teacher/Tutor, Alexandra Berube.
As a teacher and professional tutor, Alexandra plans to share more future guest blog posts here--where she will reveal additional insight into her student who has Agenesis of the Corpus Callosum and how it affects the student's education, and she will also be sharing teaching strategies that have helped her student.**
**Note: Agenesis of the Corpus Callosum has a very wide range of effects--ranging anywhere from no symptoms--or mild learning disabilities--to severe mental and/or physical challenges. It can sometimes also be seen with other medical conditions, genetic syndromes, chromosomal anomalies and more. Every person with ACC can present differently in terms of their development, cognitive abilities and educational needs.
Each child who has ACC is a unique individual with their own abilities, weaknesses, challenges, motivations, strengths, as well as their own style of learning.
Alexandra Berube, the former Kindergarten teacher, who taught a student with Agenesis of the Corpus Callosum (and who also tutors the student - who is currently in 3rd grade), has written several guest blog articles here about her teaching experiences.
Alexandra welcomes questions from you--if you might have a question.
The second question for Alexandra comes from the parent of an 8 year old child who has ACC, after the parent read Alexandra's previous Multiplication article.
The parent writes:
"This article came at the perfect time as my daughter is now working on multiplication. This is just what I needed to help her as she is struggling with it. Now if we can figure out how to help her find the key words to do word problems. Whatever math concept she did on the regular problems, she just automatically assumes it is what she does on the word problems, not realizing it could be different."
GUEST BLOG POST - Reply to Question
Mathematics from the Beginning (Struggles Overcome in Kindergarten) by Alexandra Berube, bostontutoringservices.com
In Kindergarten, it seemed at first that *Max did not have a strong understanding of one-to-one correspondence (he would count something twice or recount something). With more practice, however, it seemed that he may have been having difficulty with the task of physically counting objects with his hand and remembering how many objects he had touched. The combination of tasks—physically touching and cognitively counting—may have been challenging for him, rather than the concept of one-to-one correspondence itself. We found that drawing a dot for each time he counted worked better, because he was in control of each mark he was putting down, which helped him retain that he had counted the number, versus just touching an object. We have used dot-drawing ever since over physical manipulatives. The concept that Max struggled with the most was patterns. He had difficulty continuing patterns that had already been generated, or recognizing a set pattern. For example, the children played a game in which one child made a pattern and covered up the last four objects with cups. The other child had to guess which colors the objects under the cups were, based on continuing the pattern that they could see. This was called ‘breaking a pattern’ to find a ‘unit’ of a pattern. This was rather challenging for Max; although he understood the concept of a pattern, and was usually able to create his own patterns using math manipulatives, he had difficulty making more complex patterns and breaking patterns into units. When it was his turn to generate a pattern for his partner, he was able to build very simple patterns (like ABAB patterns), but he clearly understood what a pattern was. He just couldn’t ‘see’ a ‘unit’ of a ready-made pattern very well. With practice building his own patterns, the skills transferred over so he could recognize already-made patterns better over time. He needed to keep doing the skill on his own terms in order to recognize the skill in other students and out in the world, wherever patterns are found. Abstract story problems are the hardest for most children, and for Max they have always been a struggle to ascertain what the problem was asking. A big piece of story problems that is challenging is when it states something like, “Bob has 5 more carrots than Kate. Bob has 8 carrots. How many carrots does Kate have?” It’s hard for children to understand that this means they need to subtract. The wording on these problems is confusing, but having Max draw dots for each sentence helped a lot. If the first sentence doesn’t tell us a specific number, we know we need to work backwards and start with the second sentence. Draw 8 carrots for Bob. This is 5 more than Kate. Does Kate have less than Bob? He has more than Kate, so she has less than him. How many less does she have? She has 5 less. Cross off 5 dots. How many does she have? 3. It really takes a lot of repetition and using dots or objects to make these concepts more solid and less abstract. The more I talked through it, the more the logic came together. We worked backwards through problems over and over again. I had one lesson where I would draw dots on notecards--3 dots on one card, 4 dots on another card, and 5 dots on another card. I would say, “Kate makes two cakes. Her friend makes 3 more cakes than her. Which of these [point to the 3 notecards] is her friend?” So the card with 5 dots on it is Kate’s friend. We’d do that in many ways. “Kate has 4 cats. She has two more cats than her friend. Which of these is her friend?” So the card with 2 dots is her friend. This is far more intuitive than trying to memorize if you need to subtract or add based on the wording of the problem. They will see the numbers visually and they will know (over time and practice) if they need to add or subtract. Children understand addition and subtraction on an abstract level before they understand what the operation ‘addition’ means. They know that 2 more than 3 is five before they know that 2+3=5, if they see this with actual visual representation. Getting it visual versus through wording is key. *Name has been changed.
The concept that Max struggled with the most was patterns. He had difficulty continuing patterns that had already been generated, or recognizing a set pattern. For example, the children played a game in which one child made a pattern and covered up the last four objects with cups. The other child had to guess which colors the objects under the cups were, based on continuing the pattern that they could see. This was called ‘breaking a pattern’ to find a ‘unit’ of a pattern.
This was rather challenging for Max; although he understood the concept of a pattern, and was usually able to create his own patterns using math manipulatives, he had difficulty making more complex patterns and breaking patterns into units. When it was his turn to generate a pattern for his partner, he was able to build very simple patterns (like ABAB patterns), but he clearly understood what a pattern was. He just couldn’t ‘see’ a ‘unit’ of a ready-made pattern very well. With practice building his own patterns, the skills transferred over so he could recognize already-made patterns better over time. He needed to keep doing the skill on his own terms in order to recognize the skill in other students and out in the world, wherever patterns are found.
Abstract story problems are the hardest for most children, and for Max they have always been a struggle to ascertain what the problem was asking. A big piece of story problems that is challenging is when it states something like, “Bob has 5 more carrots than Kate. Bob has 8 carrots. How many carrots does Kate have?” It’s hard for children to understand that this means they need to subtract. The wording on these problems is confusing, but having Max draw dots for each sentence helped a lot. If the first sentence doesn’t tell us a specific number, we know we need to work backwards and start with the second sentence. Draw 8 carrots for Bob. This is 5 more than Kate. Does Kate have less than Bob? He has more than Kate, so she has less than him. How many less does she have? She has 5 less. Cross off 5 dots. How many does she have? 3.
It really takes a lot of repetition and using dots or objects to make these concepts more solid and less abstract. The more I talked through it, the more the logic came together. We worked backwards through problems over and over again. I had one lesson where I would draw dots on notecards--3 dots on one card, 4 dots on another card, and 5 dots on another card. I would say, “Kate makes two cakes. Her friend makes 3 more cakes than her. Which of these [point to the 3 notecards] is her friend?” So the card with 5 dots on it is Kate’s friend.
We’d do that in many ways. “Kate has 4 cats. She has two more cats than her friend. Which of these is her friend?” So the card with 2 dots is her friend. This is far more intuitive than trying to memorize if you need to subtract or add based on the wording of the problem. They will see the numbers visually and they will know (over time and practice) if they need to add or subtract. Children understand addition and subtraction on an abstract level before they understand what the operation ‘addition’ means. They know that 2 more than 3 is five before they know that 2+3=5, if they see this with actual visual representation. Getting it visual versus through wording is key.
Mathematics from the Beginning (Struggles Overcome in Kindergarten) - printable version
Watch for an upcoming guest blog post here soon from Teacher/Tutor, Alexandra Berube.
ADDITIONAL INPUT FROM PARENTS OF KIDS WITH ACC:
Parent of 8 year old with ACC, Third Grade, writes: "In regards to your ACC article on Word story problems for ACCers, I noticed that my son has done so much better in Math in general, and especially word problems, if the problem(s) are separated into boxes. Our Math teacher separates my son's problems on graph paper, because we know that his mind has a hard time separating and organizing too much information on paper. We have also enlarged the font, as he has severe eye problems. This enlargement has made all the difference in the world. We also have done away with any timed tests, as it raised the anxiety and he often just stopped writing after a few minutes. He told me his "mind got stuck". We have also had enormous success with an iPad. My son absolutely loves practicing Math and doing Math on his iPad. The applications are so fun and endless." ******************************************************************************** If you would like to share input about Math Story Problems and your child who has ACC, please send me an e-mail and I will be glad to include it here. And, if you would like to recommend a specific Math "app" for the iPad that your child or student who has ACC uses, please click on the link above and let me know so I can include it here as a resource for others. Thank you very much. ********************************************************************************
"In regards to your ACC article on Word story problems for ACCers, I noticed that my son has done so much better in Math in general, and especially word problems, if the problem(s) are separated into boxes. Our Math teacher separates my son's problems on graph paper, because we know that his mind has a hard time separating and organizing too much information on paper.
We have also enlarged the font, as he has severe eye problems. This enlargement has made all the difference in the world.
We also have done away with any timed tests, as it raised the anxiety and he often just stopped writing after a few minutes. He told me his "mind got stuck".
We have also had enormous success with an iPad. My son absolutely loves practicing Math and doing Math on his iPad. The applications are so fun and endless."
********************************************************************************
If you would like to share input about Math Story Problems and your child who has ACC, please send me an e-mail and I will be glad to include it here.
And, if you would like to recommend a specific Math "app" for the iPad that your child or student who has ACC uses, please click on the link above and let me know so I can include it here as a resource for others. Thank you very much. ********************************************************************************
Do you have a QUESTION for Alexandra?
If while reading Alexandra's articles, about teaching and tutoring her student with Agenesis of the Corpus Callosum, you have a question -- she welcomes you to ask her a question.
She also generously answered questions (that I had). Plus, Alexandra informed me that she welcomes questions from you--if you might have a question.
With that being said, I received a question for Alexandra from an aide who is working with a student who has ACC.
With permission I am able to share the aide's question here:
"Hello!
Thank you SO SO much for your articles. They have been such a blessing! I just started working as an aide to a 5 year old girl with Agenesis of the Corpus Callosum. She is in a mainstream Kindergarten classroom but we also do lots of one-on-one sessions with other Special Service therapists. She is a very joyful little girl and a social butterfly. She loves people!
Kindergarten is a full day. Most days she is very, very compliant but lately, we've had a lot of discipline issues in the afternoon. We have a 'Star System' (you receive a star for good behavior or we take away a star for bad behavior) but this doesn't entice her either way. Do you have any suggestions on what you did for discipline with Max?
The afternoons are the hardest because she's so tired. And when she gets tired, she gets frustrated. I'm trying to be proactive by thinking of things that entice her so she'll want to do her work.
Thanks for any info you can provide! I've really appreciated your insights this far" :)
Motivation, Positive Reinforcement, and Reward Systems (and When they Don’t Work) by Alexandra Berube, bostontutoringservices.com
When *Max was in Kindergarten, our classroom had a sticker chart, and you would receive a sticker for each academic block that you conducted to the best of your abilities. There were four academic blocks each day, with a maximum of four stickers that you could receive per day. I would not remove a sticker for poor behavior, because I do not believe in negative reinforcement. You would either receive a sticker for positive behavior, or not receive a sticker at all. Once you received 30 stickers, you got a prize from the prize bag (filled with items I purchased from the dollar store). The sticker chart worked really well for most of the students, especially those for whom positive reinforcement made a huge difference. They would gather around the sticker chart eagerly to see how many stickers they had received that day, and it even became a math activity where they would count up to see how many stickers they still needed to get to 30 (this utilizes both addition and subtraction concepts). For Max, the sticker chart worked sometimes. It worked when he was slightly struggling with an academic task that I knew he was capable of doing, and this extra motivation could propel him towards finishing the goal of completing that task. But it did not do much for behavior modification. If Max found the task too challenging or too boring, a sticker on his chart was not enough compensation for him to want to work on the task at hand. He would roll off his chair onto the ground, toss his pencil, or find any other way to avoid physically doing the task. I still found the sticker chart worthwhile, because for those skills that I knew he was at the cusp of mastering, it just took a bit more incentive to keep him motivated. But there was always that tipping point where he just wasn't motivated enough by a sticker to actually work. In cases where the sticker didn't work, it became a game of how much can I change the activity so that it still meets its goal while framing it in a more approachable way for Max? Could I change the topic so that it was still testing the same skill but using a topic that he loved? Now when we work on triple-digit addition and subtraction, multiplication, geometry, etc., I always frame the activity around a topic that he enjoys. If there are two chicken houses, and three chickens in each chicken house, how many chickens are there? When we were doing story problems for addition and subtraction, where he had to write his own story problems, the problem became about bear attacks: "If three people are attacked by bears, and then four more people are attacked by bears, how many people are attacked by bears altogether?" When we focused on geometry, addition, and multiplication recently and worked with a floor plan of a home, I mentioned how Max was drawing doors on all of the rooms, and how that would be so great if there were zombies attacking, because there would be so many ways to escape. He started drawing doors all over the place and I asked him each time he drew a door what the measurements would be, and then what the area of that door would be, and then what the perimeter would be. This way he could enter his own world of the interests and topics that excite him, integrating the skills at hand almost so that he does not notice he is learning. He said the doors were 2 feet by 2 feet (small enough that we could escape through them but the zombies would be too tall and wouldn’t know to duck down), and then said, the area is 4! He just multiplied it spontaneously without my asking. The learning became part of the creativity. Behavior modification in the form of shaping your lessons around the topics that interest your child is usually the most motivating way to keep them on task. Of course, this means altering your curriculum when you're in a larger classroom. But you're just not going to be able to keep a kid on task if they have no connection to the material. Stickers will not be enough to entice them. You can try rewards at the end of the lesson, such as, once you finish this worksheet we will...(Fill in the blank), but this level of forethought is going to be challenging for younger students. They're not going to be able to keep that goal in mind long enough to keep going on the immediate task. The intense frustration around working on a concept that they do not enjoy will overpower that forethought. As children get older, they will be able to push through this frustration more and more, but for very young children where the behavior modification strategies of sticker charts and positive reinforcement don't do enough, it's best to try to mask an activity by wrapping a favorable interest around it. These children want to learn, and they are so excited when they get to focus on something they are interested in, that with that added effort on the part of the teacher or tutor, they will be able to tackle tasks that should be more challenging than they would normally be able to do. They will push through their frustration in a surprising way and surge forward in their capacity to develop these skills. *Name has been changed.
The sticker chart worked really well for most of the students, especially those for whom positive reinforcement made a huge difference. They would gather around the sticker chart eagerly to see how many stickers they had received that day, and it even became a math activity where they would count up to see how many stickers they still needed to get to 30 (this utilizes both addition and subtraction concepts).
For Max, the sticker chart worked sometimes. It worked when he was slightly struggling with an academic task that I knew he was capable of doing, and this extra motivation could propel him towards finishing the goal of completing that task. But it did not do much for behavior modification. If Max found the task too challenging or too boring, a sticker on his chart was not enough compensation for him to want to work on the task at hand. He would roll off his chair onto the ground, toss his pencil, or find any other way to avoid physically doing the task.
I still found the sticker chart worthwhile, because for those skills that I knew he was at the cusp of mastering, it just took a bit more incentive to keep him motivated. But there was always that tipping point where he just wasn't motivated enough by a sticker to actually work.
In cases where the sticker didn't work, it became a game of how much can I change the activity so that it still meets its goal while framing it in a more approachable way for Max? Could I change the topic so that it was still testing the same skill but using a topic that he loved?
Now when we work on triple-digit addition and subtraction, multiplication, geometry, etc., I always frame the activity around a topic that he enjoys. If there are two chicken houses, and three chickens in each chicken house, how many chickens are there? When we were doing story problems for addition and subtraction, where he had to write his own story problems, the problem became about bear attacks: "If three people are attacked by bears, and then four more people are attacked by bears, how many people are attacked by bears altogether?"
When we focused on geometry, addition, and multiplication recently and worked with a floor plan of a home, I mentioned how Max was drawing doors on all of the rooms, and how that would be so great if there were zombies attacking, because there would be so many ways to escape. He started drawing doors all over the place and I asked him each time he drew a door what the measurements would be, and then what the area of that door would be, and then what the perimeter would be. This way he could enter his own world of the interests and topics that excite him, integrating the skills at hand almost so that he does not notice he is learning. He said the doors were 2 feet by 2 feet (small enough that we could escape through them but the zombies would be too tall and wouldn’t know to duck down), and then said, the area is 4! He just multiplied it spontaneously without my asking. The learning became part of the creativity.
Behavior modification in the form of shaping your lessons around the topics that interest your child is usually the most motivating way to keep them on task. Of course, this means altering your curriculum when you're in a larger classroom. But you're just not going to be able to keep a kid on task if they have no connection to the material. Stickers will not be enough to entice them. You can try rewards at the end of the lesson, such as, once you finish this worksheet we will...(Fill in the blank), but this level of forethought is going to be challenging for younger students. They're not going to be able to keep that goal in mind long enough to keep going on the immediate task. The intense frustration around working on a concept that they do not enjoy will overpower that forethought.
As children get older, they will be able to push through this frustration more and more, but for very young children where the behavior modification strategies of sticker charts and positive reinforcement don't do enough, it's best to try to mask an activity by wrapping a favorable interest around it. These children want to learn, and they are so excited when they get to focus on something they are interested in, that with that added effort on the part of the teacher or tutor, they will be able to tackle tasks that should be more challenging than they would normally be able to do. They will push through their frustration in a surprising way and surge forward in their capacity to develop these skills.
Motivation, Positive Reinforcement, and Reward Systems (and When they Don’t Work) - printable version
GUEST BLOG POST Literacy and Communication Skills in Kindergarten (Back to the Beginning) by Alexandra Berube, bostontutoringservices.com
Max worked very hard in the first few months of Kindergarten to make strides in his ability to communicate verbally. As I mentioned previously, Max’s ability to communicate his needs was an area in which we put in a great deal of work. At times, when he got overwhelmed, he would shut down and choose not to listen to teachers who are trying to help him. When upset, *Max would become inconsolable, and have trouble recovering from setbacks. Especially in social situations, such as if someone broke a building of his, he retreated into self-consoling behaviors such as crying and rocking. He would growl or snarl at a peer if he or she upset Max in this way. I think this is why some behaviors of Agenesis of the Corpus Callosum may be confused with Autism. It looks like the student can’t express themselves, as they regress to either younger behaviors or more ‘primitive’ behaviors like snarling. But they can learn behaviors that will serve them better in social and academic situations, and it’s often up to them to decide if they want to respond or not. As I wrote before, Max would act out, or refuse to communicate or do activities, but he could do them. They were not beyond his capacity. I certainly wouldn’t want to put any blame on a child by saying they ‘choose’ not to respond, but by that I mean, they do have the capacity, it just takes time and a strong sense of trust and comfort level to make them want to do so (as well as emotional maturity, of course). I can only use my experience to state my opinions on this matter, of course--I would not want to generalize onto any students with more limited capacities. I just think that students need time to see what they can do, and it shouldn’t be assumed that something is beyond their ability. This goes for all students. Moving onto literacy, we practiced a great deal with rhymes, because Max had difficulty recognizing rhymes aurally and generating rhymes orally. He performed much better when asked to match pictures of rhyming objects, because the visual cue allowed him to better process the information. I had small phonics objects, and would use them to give him a visual clue (a cat and a hat, a ship and a clip, etc). This helped quite a bit, and when we did word family activities with pictures of objects (match everything in the ‘at’ family, match everything in the ‘um’ family), he was able to do much better than with just the aural clues. I wanted him to continue to improve in his ability to aurally recognize rhymes, as I had thought that this skill would help him in his reading. But it didn’t work that way. I had been taught in Graduate School that you needed phonological and phonemic awareness to be able to read. I was concerned his lack of rhyming ability would hold him back. But it didn’t, at all. His reading improved much faster than his aural rhyming skills. Max came into Kindergarten knowing all of his letters and letter sounds, with a solid foundation of how to sound out and decode words. He knew that he had to break down a word and sound out each part in order to read the word. So his reading skills improved rapidly. In turn, the more he learned word families, the more he ‘knew’ what rhymed. His ability to aurally detect rhyme only increased as he learned word families through visual clues and from reading words. He could rhyme once he could read. In writing skills, with the work Max had been regularly doing with his OT [Occupational Therapist], along with much practice, Max gained the ability to express himself with words and pictures. In September, when asked to write any letter, Max said he could not do it, and did not try. I would have him trace my letters or make lines from one dot to the next in order to form letters. A large part of this was that it is physically challenging for him to use a writing tool, and therefore it is understandable that he would resist the work. By December of Kindergarten, Max was forming letters on his own in order to write words. Similarly, when we began Kindergarten I could not get him to draw any representational figures. He would draw squiggles and circles all over the page, saying he could not draw anything. By December he regularly created representational images on his work. This huge leap shows in some ways that he had the ability all along, and just needed a way to get it out of him. Once he got that from the OT, it was like breaking open a shell so that we could see what had been inside him all along. *Name has been changed.
I think this is why some behaviors of Agenesis of the Corpus Callosum may be confused with Autism. It looks like the student can’t express themselves, as they regress to either younger behaviors or more ‘primitive’ behaviors like snarling. But they can learn behaviors that will serve them better in social and academic situations, and it’s often up to them to decide if they want to respond or not. As I wrote before, Max would act out, or refuse to communicate or do activities, but he could do them. They were not beyond his capacity. I certainly wouldn’t want to put any blame on a child by saying they ‘choose’ not to respond, but by that I mean, they do have the capacity, it just takes time and a strong sense of trust and comfort level to make them want to do so (as well as emotional maturity, of course). I can only use my experience to state my opinions on this matter, of course--I would not want to generalize onto any students with more limited capacities. I just think that students need time to see what they can do, and it shouldn’t be assumed that something is beyond their ability. This goes for all students.
Moving onto literacy, we practiced a great deal with rhymes, because Max had difficulty recognizing rhymes aurally and generating rhymes orally. He performed much better when asked to match pictures of rhyming objects, because the visual cue allowed him to better process the information. I had small phonics objects, and would use them to give him a visual clue (a cat and a hat, a ship and a clip, etc). This helped quite a bit, and when we did word family activities with pictures of objects (match everything in the ‘at’ family, match everything in the ‘um’ family), he was able to do much better than with just the aural clues. I wanted him to continue to improve in his ability to aurally recognize rhymes, as I had thought that this skill would help him in his reading. But it didn’t work that way.
I had been taught in Graduate School that you needed phonological and phonemic awareness to be able to read. I was concerned his lack of rhyming ability would hold him back. But it didn’t, at all. His reading improved much faster than his aural rhyming skills. Max came into Kindergarten knowing all of his letters and letter sounds, with a solid foundation of how to sound out and decode words. He knew that he had to break down a word and sound out each part in order to read the word. So his reading skills improved rapidly. In turn, the more he learned word families, the more he ‘knew’ what rhymed. His ability to aurally detect rhyme only increased as he learned word families through visual clues and from reading words. He could rhyme once he could read.
In writing skills, with the work Max had been regularly doing with his OT [Occupational Therapist], along with much practice, Max gained the ability to express himself with words and pictures. In September, when asked to write any letter, Max said he could not do it, and did not try. I would have him trace my letters or make lines from one dot to the next in order to form letters. A large part of this was that it is physically challenging for him to use a writing tool, and therefore it is understandable that he would resist the work. By December of Kindergarten, Max was forming letters on his own in order to write words. Similarly, when we began Kindergarten I could not get him to draw any representational figures. He would draw squiggles and circles all over the page, saying he could not draw anything. By December he regularly created representational images on his work. This huge leap shows in some ways that he had the ability all along, and just needed a way to get it out of him. Once he got that from the OT, it was like breaking open a shell so that we could see what had been inside him all along.
Note: "aural"/"aurally" means: relating to the ear or to the sense of hearing.
Would you like to print a copy of this article?
Alexandra has given me permission to convert her article to a pdf format for printing, at the link below:
Literacy and Communication Skills in Kindergarten (Back to the Beginning) - printable version
please be advised: some children who have Agenesis of the Corpus Callosum are also diagnosed with Autism, Autism Spectrum Disorder (ASD) or Pervasive Developmental Disorder-Not Otherwise Specified (PDD-NOS).
ADDITIONAL INFORMATION AND RESOURCES:
Making a Rhyming Basket - Montessori video:
Rhyming Pictures Printable Game Note: to download free full-size printable version: 1. click on link above, 2. then on left-hand top of page, click on "File" 3. and then click on "Download" courtesy of the First Grade a la carte blog.
Or try this printable game with real photograph pictures: Rhyming Words/Photographs Printable Game
Tip: check out Pinterest for more rhyming words ideas (and other educational ideas, too). You could truly get lost exploring the awesome ideas on Pinterest!
And for activities to Match Word Families with Pictures, consider exploring this idea: Note: product appears to contain cards only and does not include the plastic pocket chart holder (as pictured).
In the ACC Reading and Comprehension document you can read about other children who have ACC. A few examples include:
Parent of 5 year old child writes:
"She does not get when we give her a list of words to pick out the one that rhymes, she will either pick the one with the same beginning sound or letter or pick a word at random that she knows. If we give her the word bat; a list of words such as cat, ball, dog, hand-she will pick ball because bat and ball go together."
Parent of 12 year old child writes:
"Lexie always struggled with reading. Our first sign of trouble was the fact that she never could rhyme. It was the strangest thing! But as school began I noticed she had such a hard time with those little books. Every single word was as if she had never seen it before...page after page. The same few words would repeat but she would not recognize them. So with each page she struggled just as much as the page before. By first grade we bought Hooked on Phonics.
It interested Lexie so she did it. Loved it. But still she really could not make the jump from the program to real books. Word families meant nothing to her. RAT CAT SAT........Lexie would say HOUSE.....Really? HOUSE???? Again, the rhyming thing never worked for her and that is what word families are. Second grade more of the same. She was reading, I guess. At about a Kindergarten level. No AR yet of course. We did dyslexia programs through the district. She would do FINE according to her dyslexia teacher. By 3rd grade she had graduated out of the program. I kept saying "But she really can't read!" The state assessment finally showed everyone how much she struggled. Of course she failed the state assessment. Her reading comprehension was/is terrible. She is in 6th grade. Reads about on a 3rd grade reading level. She is in regular classes with accommodations. Making straight A's."
Kathyrn Schilmoeller, Ph.D., in her September, 1999 article titled, Educational Suggestions For Children With ACC: A Beginning, wrote:
"People with ACC tend to absorb far more information than they can demonstrate to others in an educational setting by writing or verbalizing. Teachers need to be creative in finding ways for the child to show what he or she has learned. For example, a five-year-old child with ACC was asked to draw a picture of a man. He took a crayon and scribbled across the page. The teacher came to the conclusion that the child had no concept of what a person looked like. However, shortly afterwards when the child was provided different shapes of paper and pieces of masking tape, without prompting from an adult, that same child produced a face complete with eyes, nose, and mouth, and announced, "This is me." The child clearly understood what a face looked like. He simply could not manipulate a crayon well enough to demonstrate his knowledge. Similarly a few years later, this same child "wrote" "I LOVE YOU" with blocks without being prompted. His parents were startled by his skill in "writing" this message because at that point no one realized he could spell that well."
*Alexandra's article below reprinted with permission from Dr. Alicia Holland-Johnson, where it originally appeared as a guest blog posting on her Helping Tutors Become Their Best blog.
Introducing Multiplication to a Student with Different Learning Needs by Alexandra Berube, bostontutoringservices.com
The basis of my math instruction is always to move from one concept that the student firmly understands and then apply that concept to the next level of mathematic reasoning. In working with my favorite third grade student, I found the opportunity to introduce multiplication to him. This student was born with Agenesis of the Corpus Callosum (a complete or partial absence of the corpus callosum, the band connecting the two hemispheres in the brain), and I wrote about him in a previous blog post. He learns concepts in a completely different order than most people would expect. He is still solidifying his addition and subtraction facts, and adds and subtracts any amount, including one plus one, on his fingers. And yet I know that he is often ready for more advanced concepts, and that these advanced concepts will actually help solidify previous concepts that he is still working on mastering. In his third grade class, the student is working on geometry, including perimeter of squares. This was the perfect opportunity to introduce multiplication. In a square, all the sides are the same size. If he has a square with the side length of two, then he will do 2×4. I worked with him on this geometry concept for a while with different shapes such as pentagons, hexagons, and triangles: any shape that has sides of equal length. He quickly grasped this concept and then we moved on. I like to use a dry erase board in my instruction, because it's another form of media (‘media’ used loosely, I suppose) than pen and paper, and it allows the student to draw shapes and manipulate the written material in a new way. I had the student make shapes of his own, and we would see how many sides that shape had. We would give each side a length, and then see what the multiplication problem would be as a result. We then worked on the worksheet I've included a link to here, which shows pictures of groups of objects (for example, four triangles with three stars in each triangle). It asks the students to write an addition problem (so, in this case, three stars four times, so 3+3+3+3) and then the multiplication problem (3×4). He picked this up very quickly, and so we moved on to the last game of the session. Using a pair of dice, we played a game to visually show the amounts to be multiplied. First we rolled one die, and then drew the dots shown on the die on a piece of paper. We wrote the number value above the dots. Then we wrote a multiplication symbol, and then we rolled the other die, which would act as the 'multiplier.' The second die dictated how many times the first die would be multiplied by. So if the first die was a four, we drew four dots, put a four over it and then a multiplication symbol next to that. Then if the second die was a three, we wrote the number three next to the multiplication symbol, and then drew four dots two more times for a total of three sets of four dots. This way he could see why we were multiplying--we were adding the same number a multiple of times. He then added all of the dots on the dice and found out that 4X3=12. Below all the dots we wrote 4+4+4 (the addition problem like on the worksheet I just described), to further enforce that multiplication is an extension of addition. He'd already mastered adding groups of numbers, so this was the next logical step. He smoothly transitioned into a student who understands the basis of multiplication. Of course, he's not going to be memorizing his multiplication tables in the near future, but he understands what multiplication is now, and he grasps that it is an extension of addition that applies in real life.
In his third grade class, the student is working on geometry, including perimeter of squares. This was the perfect opportunity to introduce multiplication. In a square, all the sides are the same size. If he has a square with the side length of two, then he will do 2×4. I worked with him on this geometry concept for a while with different shapes such as pentagons, hexagons, and triangles: any shape that has sides of equal length. He quickly grasped this concept and then we moved on. I like to use a dry erase board in my instruction, because it's another form of media (‘media’ used loosely, I suppose) than pen and paper, and it allows the student to draw shapes and manipulate the written material in a new way. I had the student make shapes of his own, and we would see how many sides that shape had. We would give each side a length, and then see what the multiplication problem would be as a result.
We then worked on the worksheet I've included a link to here, which shows pictures of groups of objects (for example, four triangles with three stars in each triangle). It asks the students to write an addition problem (so, in this case, three stars four times, so 3+3+3+3) and then the multiplication problem (3×4). He picked this up very quickly, and so we moved on to the last game of the session.
Using a pair of dice, we played a game to visually show the amounts to be multiplied. First we rolled one die, and then drew the dots shown on the die on a piece of paper. We wrote the number value above the dots. Then we wrote a multiplication symbol, and then we rolled the other die, which would act as the 'multiplier.' The second die dictated how many times the first die would be multiplied by. So if the first die was a four, we drew four dots, put a four over it and then a multiplication symbol next to that. Then if the second die was a three, we wrote the number three next to the multiplication symbol, and then drew four dots two more times for a total of three sets of four dots. This way he could see why we were multiplying--we were adding the same number a multiple of times.
He then added all of the dots on the dice and found out that 4X3=12. Below all the dots we wrote 4+4+4 (the addition problem like on the worksheet I just described), to further enforce that multiplication is an extension of addition. He'd already mastered adding groups of numbers, so this was the next logical step. He smoothly transitioned into a student who understands the basis of multiplication. Of course, he's not going to be memorizing his multiplication tables in the near future, but he understands what multiplication is now, and he grasps that it is an extension of addition that applies in real life.
Alexandra has given me permission to convert her article to a pdf format for printing, which you can access by clicking on the link below (to share with your child's teacher):
Introducing Multiplication to a Student with Different Learning Needs - printable version
Multiplication Worksheet
Watch for a new guest blog post here next week from Teacher/Tutor, Alexandra Berube.
1. "My son learned the [multiplication] tables through Touch Math songs. He still struggles but I see him sort of singing the songs when stuck. Calculators are truly a kid's best friend!
Now about place value....."
Parent of child with ACC, 5th grade
Touch Math multiplication songs video - on Teacher Tube
http://teachertube.com/viewVideo.php?video_id=210943 ******************************************************************************** 2. "My son, 10 years old, PACC (and other things), has been learning his multiplication tables by making up songs to remember them by. He still struggles if it has been a while since he practiced, but the songs seem to help. He is in 4th grade, and is repeating the year mostly because he has struggled with the times tables, and other math, and logical thinking. We find that anything Kinetic that we can do to help him seems to help." Note: Kinetic or Kinesthetic Learners - learn through a tactile [touch] hands on, feeling, touching, manipulating objects, moving, doing, experiencing things approach. Parent of child with partial ACC, 4th grade ******************************************************************************** 3. "Concerning the use of songs, using familiar tunes and following the pattern of repetition of the words seemed to work well. We used the tune of Frere Jacques to memorize the 9 times table and it worked great. Each part of the verse is repeated twice so you get the following (original song words appear beneath the multiplication version so you can see how they match up): 9 times 1, 9 times 1; 1 times 9, 1 times 9 (“Frere Jacques, Frere Jacques; dorme vou, dorme vou?”) 9 is the answer; 9 is the answer (“Sonnez la matines; sonnez la matines”) 9 times 1; 1 times 9 (“Ding, ding, dong; ding, ding, dong”) But once used for the 9s, we couldn’t use it for another multiplication table because the words for the 9s were already tied to this tune in my child's head. Trying to associate the same tune to another multiplication table likely would have resulted in incorrect remembrances. And believe me, we needed to be able to illustrate that it doesn’t matter in what order the numbers appear, the answer will still be the same. 8 X 2 is 16 and 2 X 8 is 16. She learned the multiplication tables for 2, 5 and 10 fairly quickly. Most kids can count by twos, fives and tens. But she didn’t get the relationship that the answers in the 4 times tables were twice the answers in the 2 times table. So there was a slight disconnect there in terms of relating one set of multiples to another. She did eventually learn all of the multiplication tables (through 10 X 10), but it took a good deal of repetition...and I believe it was truly a rote learning experience. I think she would probably have to have to think pretty hard to explain that what is meant by 6 X 8 is 48 is that there are six groups which each contain 8 items and represent a total of 48 items. But she can pretty reliably give you the correct answer whenever you ask her “What is ‘this number’ times ‘that number’?” Parent of child with ACC, (in 8th grade now) ******************************************************************************** 4. "Multiplication and division are tricky. As they progress from learning the basic concept, it becomes necessary to memorize. Kids can "count on" on their fingers to do addition and subtraction, if need be, forever. Honestly, my child [who has partial ACC] was doing it still in algebra, but it was so subtle most people would not notice. It's quick and can be pretty efficient and accurate as well. Not so for multiplication (and its inverse, division). Counting on becomes tedious, and is far more likely to be erroneous for these operations. It needs lots of "drill and kill" for some kids, and not just those with learning problems. I found several things that worked well in my classroom; I used them for all my students, not just the ones who I suspected would have trouble. In that way, all of them had the same background, and nobody who needed them longer was seen as having to use a crutch. Here are some things that worked for me. Jewels Many programs that emphasize hands-on math use jewels. These are strings of plastic beads (they are attached to the strings) that can be cut apart into sets of ones, twos, threes, fours, and fives, each a different color. Kids can easily use them to visually represent multiples of each when beginning to multiply. strings of them are available at teacher stores and in math catalogs. The drawback to me is that there are only five colors, so you can only go to 5 X 5. This may be OK for first graders, and even some in second, but by third you need more. I solved this problem with Christmas garlands of plastic colored beads. If you can find four more colors besides the ones from the store (gold, silver, pink, purple, perhaps), you are set up to 9 X 9. Kids do have some problems losing place when they count them, but they are physically there so a recount is possible. These jewels are cheap, easy to store, and they reinforce the concept of multiplication as repeated addition. They are great for division as well. Using the margins When kids get older, they are expected to do multi-digit multiplication before some of them have their facts memorized. This often results in very slow work, with repeated, excruciating counting on. And it doesn't seem to stick from one time to another. So I taught them to utilize the margins of their papers to write vertical lists of the multiple they are working on, like this: 7 14 21 28 35 etc. Then, the next time they need a multiple of 7, it's either there, or they can easily extend the list to find it, not having to repeat the same feat again and again. There is usually enough room for 4 lists on each side of the page. I learned this just by chance, trying to help kids who had a terrible time multiplying. One by one, I noticed over time that fewer and fewer kids needed this technique, as they were realizing it was easier to just memorize facts than go to the trouble of listing. But in the meantime, they were not spending all their class time counting on their fingers. It had the added benefit of showing me instantly when someone had made an error, so I could point it out and help that student get it right. Some people use multiplication charts, but I prefer that the student at least do the computation him/herself at least once, and it seems to stick better when they do. (They can even do it on state tests, when manipulatives are not available.) Computer Software This is one area where a computer can really help. There were games available, even some really inexpensive ones, that filled the bill of "drill and kill" without any pain. I'm sure there are many more now. Some will even adapt to a child's level as s/he plays--I highly recommend those. I have been out of it for several years, but look online for some. I'm sure other teachers and other parents are also good sources. If you have the chance to play it before buying, do try it out. You want to make sure that a child can't "game" the system, by using something other than knowledge of facts to succeed at the game--like guessing. Math replacement units Marilyn Burns has a great set of math replacement units. These are books that give plans for units of study that cover one topic, such as money or probability, that teachers can use to replace (or supplement) the ones in their texts. I have used several of these at different grade levels, and I highly recommend them. I used the one on multiplication fairly often, especially when I had average or low third graders and high-achieving second graders, because it was easy to use with them altogether. It's intended for 3rd grade, but it can be used also as enrichment for younger kids and remediation or reinforcement for older ones. She explains a number of activities set up as one- and two-person games (an adult can play with a child) that give practice in the meaning of multiplication. Kids can go back to them again and again for reinforcement. Kind of pricey, I think around $30, but you can likely go to a teacher store and peruse its pages to see if you think it would help you. Tip: you can find the older out-of-print used version online titled: "Math by All Means: Multiplication, Grade 3" by Marilyn Burns through Amazon and other online sites. This is the version I used while teaching students. The newer updated version is titled: "Teaching Arithmetic: Lessons for Introducing Multiplication, Grade 3" and can be found at Math Solutions, a company founded by Marilyn Burns. It is also available (both new and used) through Amazon. My daughter (who has partial ACC) did have some trouble learning her multiplication facts, but we just practiced them relentlessly. At school she used jewels, and we used the software at home. I hadn't discovered Marilyn Burns or using the margins at that time. As I recall, memorizing multiplication facts was not as hard for her as addition was. Maybe because she was older. She did have problems remembering how to do multi-digit multiplying and long division, though. I decided she needed more practice. So I had her dad (she was a daddy's girl) write 3 or 4 problems, just for practice on the white board easel we kept in the kitchen, and she'd work on them while we made dinner. She just really needed a lot of practice, over and over, doing the same algorithm. And when she learned it, she needed lots of reinforcement for it to permanently stick." (Teacher) and Parent of daughter, 24, with partial ACC and septopreoptic holoprosencephaly ******************************************************************************** If you would like to share input about multiplication and your child who has ACC, please send me an e-mail and I will be glad to include it here. ******************************************************************************** RESOURCES - (for your consideration): For many kids who have ACC, learning through music is often times a helpful and successful method of teaching. Multiplication Mountain CD, by Hap Palmer - listen to sound clips of songs Singing Multiplication Tables CD, by Hap Palmer - listen to sound clips of songs Tip: check your local library (and online library system) to see if you might be able to borrow the multiplication music CDs by Hap Palmer to try with your child. **Please Note: Agenesis of the Corpus Callosum has a very wide range of effects--ranging anywhere from no symptoms--or mild learning disabilities--to severe mental and/or physical challenges. It can sometimes also be seen with other medical conditions, genetic syndromes, chromosomal anomalies and more. Every person with ACC can present differently in terms of their development, cognitive abilities and educational needs. Each child who has ACC is a unique individual with their own abilities, weaknesses, challenges, motivations, strengths, as well as their own style of learning.
2. "My son, 10 years old, PACC (and other things), has been learning his multiplication tables by making up songs to remember them by. He still struggles if it has been a while since he practiced, but the songs seem to help. He is in 4th grade, and is repeating the year mostly because he has struggled with the times tables, and other math, and logical thinking. We find that anything Kinetic that we can do to help him seems to help."
Note: Kinetic or Kinesthetic Learners - learn through a tactile [touch] hands on, feeling, touching, manipulating objects, moving, doing, experiencing things approach.
Parent of child with partial ACC, 4th grade ********************************************************************************
3. "Concerning the use of songs, using familiar tunes and following the pattern of repetition of the words seemed to work well. We used the tune of Frere Jacques to memorize the 9 times table and it worked great. Each part of the verse is repeated twice so you get the following (original song words appear beneath the multiplication version so you can see how they match up):
9 times 1, 9 times 1; 1 times 9, 1 times 9 (“Frere Jacques, Frere Jacques; dorme vou, dorme vou?”)
9 is the answer; 9 is the answer (“Sonnez la matines; sonnez la matines”)
9 times 1; 1 times 9 (“Ding, ding, dong; ding, ding, dong”)
But once used for the 9s, we couldn’t use it for another multiplication table because the words for the 9s were already tied to this tune in my child's head. Trying to associate the same tune to another multiplication table likely would have resulted in incorrect remembrances. And believe me, we needed to be able to illustrate that it doesn’t matter in what order the numbers appear, the answer will still be the same.
8 X 2 is 16 and 2 X 8 is 16.
She learned the multiplication tables for 2, 5 and 10 fairly quickly. Most kids can count by twos, fives and tens. But she didn’t get the relationship that the answers in the 4 times tables were twice the answers in the 2 times table. So there was a slight disconnect there in terms of relating one set of multiples to another. She did eventually learn all of the multiplication tables (through 10 X 10), but it took a good deal of repetition...and I believe it was truly a rote learning experience. I think she would probably have to have to think pretty hard to explain that what is meant by 6 X 8 is 48 is that there are six groups which each contain 8 items and represent a total of 48 items. But she can pretty reliably give you the correct answer whenever you ask her “What is ‘this number’ times ‘that number’?”
Parent of child with ACC, (in 8th grade now) ********************************************************************************
4. "Multiplication and division are tricky. As they progress from learning the basic concept, it becomes necessary to memorize. Kids can "count on" on their fingers to do addition and subtraction, if need be, forever. Honestly, my child [who has partial ACC] was doing it still in algebra, but it was so subtle most people would not notice. It's quick and can be pretty efficient and accurate as well.
Not so for multiplication (and its inverse, division). Counting on becomes tedious, and is far more likely to be erroneous for these operations. It needs lots of "drill and kill" for some kids, and not just those with learning problems. I found several things that worked well in my classroom; I used them for all my students, not just the ones who I suspected would have trouble. In that way, all of them had the same background, and nobody who needed them longer was seen as having to use a crutch. Here are some things that worked for me.
Jewels
Many programs that emphasize hands-on math use jewels. These are strings of plastic beads (they are attached to the strings) that can be cut apart into sets of ones, twos, threes, fours, and fives, each a different color. Kids can easily use them to visually represent multiples of each when beginning to multiply. strings of them are available at teacher stores and in math catalogs. The drawback to me is that there are only five colors, so you can only go to 5 X 5. This may be OK for first graders, and even some in second, but by third you need more.
I solved this problem with Christmas garlands of plastic colored beads. If you can find four more colors besides the ones from the store (gold, silver, pink, purple, perhaps), you are set up to 9 X 9. Kids do have some problems losing place when they count them, but they are physically there so a recount is possible. These jewels are cheap, easy to store, and they reinforce the concept of multiplication as repeated addition. They are great for division as well.
Using the margins
When kids get older, they are expected to do multi-digit multiplication before some of them have their facts memorized. This often results in very slow work, with repeated, excruciating counting on. And it doesn't seem to stick from one time to another. So I taught them to utilize the margins of their papers to write vertical lists of the multiple they are working on, like this:
7 14 21 28 35 etc.
Then, the next time they need a multiple of 7, it's either there, or they can easily extend the list to find it, not having to repeat the same feat again and again. There is usually enough room for 4 lists on each side of the page.
I learned this just by chance, trying to help kids who had a terrible time multiplying. One by one, I noticed over time that fewer and fewer kids needed this technique, as they were realizing it was easier to just memorize facts than go to the trouble of listing. But in the meantime, they were not spending all their class time counting on their fingers. It had the added benefit of showing me instantly when someone had made an error, so I could point it out and help that student get it right. Some people use multiplication charts, but I prefer that the student at least do the computation him/herself at least once, and it seems to stick better when they do. (They can even do it on state tests, when manipulatives are not available.)
Computer Software
This is one area where a computer can really help. There were games available, even some really inexpensive ones, that filled the bill of "drill and kill" without any pain. I'm sure there are many more now. Some will even adapt to a child's level as s/he plays--I highly recommend those. I have been out of it for several years, but look online for some. I'm sure other teachers and other parents are also good sources. If you have the chance to play it before buying, do try it out. You want to make sure that a child can't "game" the system, by using something other than knowledge of facts to succeed at the game--like guessing.
Math replacement units
Marilyn Burns has a great set of math replacement units. These are books that give plans for units of study that cover one topic, such as money or probability, that teachers can use to replace (or supplement) the ones in their texts. I have used several of these at different grade levels, and I highly recommend them.
I used the one on multiplication fairly often, especially when I had average or low third graders and high-achieving second graders, because it was easy to use with them altogether. It's intended for 3rd grade, but it can be used also as enrichment for younger kids and remediation or reinforcement for older ones. She explains a number of activities set up as one- and two-person games (an adult can play with a child) that give practice in the meaning of multiplication. Kids can go back to them again and again for reinforcement. Kind of pricey, I think around $30, but you can likely go to a teacher store and peruse its pages to see if you think it would help you.
Tip: you can find the older out-of-print used version online titled: "Math by All Means: Multiplication, Grade 3" by Marilyn Burns through Amazon and other online sites. This is the version I used while teaching students.
The newer updated version is titled: "Teaching Arithmetic: Lessons for Introducing Multiplication, Grade 3" and can be found at Math Solutions, a company founded by Marilyn Burns. It is also available (both new and used) through Amazon.
My daughter (who has partial ACC) did have some trouble learning her multiplication facts, but we just practiced them relentlessly. At school she used jewels, and we used the software at home. I hadn't discovered Marilyn Burns or using the margins at that time.
As I recall, memorizing multiplication facts was not as hard for her as addition was. Maybe because she was older. She did have problems remembering how to do multi-digit multiplying and long division, though. I decided she needed more practice. So I had her dad (she was a daddy's girl) write 3 or 4 problems, just for practice on the white board easel we kept in the kitchen, and she'd work on them while we made dinner. She just really needed a lot of practice, over and over, doing the same algorithm. And when she learned it, she needed lots of reinforcement for it to permanently stick."
(Teacher) and Parent of daughter, 24, with partial ACC and septopreoptic holoprosencephaly ********************************************************************************
If you would like to share input about multiplication and your child who has ACC, please send me an e-mail and I will be glad to include it here.
RESOURCES - (for your consideration):
For many kids who have ACC, learning through music is often times a helpful and successful method of teaching.
Multiplication Mountain CD, by Hap Palmer - listen to sound clips of songs
Singing Multiplication Tables CD, by Hap Palmer - listen to sound clips of songs
Tip: check your local library (and online library system) to see if you might be able to borrow the multiplication music CDs by Hap Palmer to try with your child.
**Please Note: Agenesis of the Corpus Callosum has a very wide range of effects--ranging anywhere from no symptoms--or mild learning disabilities--to severe mental and/or physical challenges. It can sometimes also be seen with other medical conditions, genetic syndromes, chromosomal anomalies and more. Every person with ACC can present differently in terms of their development, cognitive abilities and educational needs.
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