Teaching Multiplication through Skip-Counting to a Student with Special Needs

I have a student with a rare condition: Agenesis of the Corpus Callosum (a complete or partial absence of the corpus callosum, the band connecting the two hemispheres in the brain). He struggles with mental math and memorizing facts, and benefits from a more visual and tactile approach. I don't specifically use Touch Math with him, but I do incorporate those concepts. Multiplication through memorization tends to be the main way that students are taught nowadays. They are given drill after drill, hoping that rote memorization will be enough to keep the facts grounded into their heads. But what if they don't understand why they're multiplying, and what multiplication really means?

It is very important to me that my students understand why a math concept works. I introduced multiplication to this student by expanding on what he knew about addition. If we have two of something, and then we have two groups of those, then we have 2×2. He adapted to the concept of multiplication very quickly, but it's another thing to then be able to multiply larger products.

We practiced with skip counting, the concept of 'counting-by,' such as counting by twos (2, 4, 6, 8). If we had one 2, and then we had another 2, we would have two 2s. If we added another 2, we would have three 2s. This looks like 2×2, 2×3, etc. We connected each sum to the concept of multiplication, until he grasped that counting by 2s would give him the multiples of two.

We then worked on 5s, because it's just easy for kids to count by five, and they've been practicing since kindergarten. Then he knew the multiples of five. Next came three, but that was harder for him. He's getting used to the multiples of three enough to memorize them somewhat, but what he tends to do is start at one number, count up three to the next number, and so on, using his fingers to guide him along the way. So he started with six, with his thumb pointed up, then counted up three until he got to nine on his pointer finger, counted up three until he got to 12 on his middle finger, and so on.

With fours, I introduced the idea of actually skip counting as he counted by twos. So this way he would count two, four, six, eight, and omit every other number. We practiced this by verbally counting by twos and whispering every other number while saying louder every other number (say 2 out loud, whisper 4, say 6 out loud, etc.). We also did this visually by writing out 2, 4, 6, 8 and then crossing out every other number. Once he has a better handle on his threes, we will be doing the same thing in order to master sixes (skip counting every other multiple).

When he gets to a multiplication problem, we have a strategy for when one of the two numbers is five or below (if both numbers are above five he has to draw it out--for 6×6 he draws six dots six times--not the most efficient strategy but we’re working our way up). He underlines the smaller number, knowing he's going to skip count by that number the amount of times indicated by the other number. So if it's 2×4, he would underline the two, and count by twos four times (2, 4, 6, 8).

Over time, he is memorizing more and more of the products, and the multiplication drills that he's doing at school will certainly benefit this as well. But it's so important that he understands why he's multiplying and has additional strategies for when memorization fails him. I'm sure all adults have gotten to a mental block at some point where we just can't remember a multiple of seven, or eight. Teaching multiplication through memorization should be a backdrop to a greater understanding of what the student is really doing.

Guest Blog by: Alexandra

Message from Alise- Looking for a High School Math Tutor

Dear Readers,


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Alise

Math Resources to Keep on Hand When Tutoring

                                  
                                 

Math can be quite difficult to teach, especially regarding the analytical process and mental manipulation that people tend to go through with each problem they encounter. If you are tutoring Math, make sure you have the following resources that can ensure a smooth math tutorial, especially as they help maintain smooth function of the tutorial session.

Calculators

Bringing calculators is a staple in Math subjects as you can use them to countercheck answers and to simplify long processes that are preliminary to a given topic but are not required to go over once the student understands the topic at hand.

Charts

You can bring different charts to represent the topic you are discussing. For example, you can have a table of formulas of areas and volumes of planes and solids for a Geometry tutorial or perhaps a table of integrals for a Calculus one. Use charts as visual aids to guide people.

Problem Sets

Math is all about practice, so make sure you have enough problem sets for your student to try out. This is one practical way for him or her to learn Math.

Board

Math can’t be read out loud or perhaps just simply shown on a PowerPoint presentation. It must be applied manually through the solving process, and that is what a board is for. Bringing a whiteboard and showing how the equation is solved can allow your student to grasp the material easily.

Teaching Math can be quite tough without the right materials. With these Math resources to consider, you can perform your tutoring session smoothly as you are allowed to optimize the resources you bring for that session.

Tackling Math Subjects--Tutoring Tips to Consider

Math isn’t easy, and it becomes a growing subject children need to be tutored in. Let’s face it, Algebra or Geometry aren’t easy to learn and even more difficult to teach. If you really want to help children out with the math subjects, then here’s what you need to do, here are some considerations you should check out before starting the tutorial session.

Read Over the Material

Learn how the book approaches the material. Math is cumulative, so you should ask yourself: is there need to review a previous concept? This will allow you to modify your approach in order to allow the child being tutored to learn the material and even more future topics using the same strategy. If they introduce calculations before concepts, then try to work around that by formulating that session by writing it down for reference later.

Work Away From the Material

Once you’ve read it, it’s time to add some unique flavor to the teaching style. Math can be boring for those that aren’t interested, so spice things up. Add a little game to the tutoring session to keep children interested. Don’t stick to book-bound concepts because it tends to tire them out. Math can be a very tiring subject to learn, so keep in mind the short attention span most children have.

Explanation before Application

Kids want to know why something happens before they can see it for themselves. It gives them that expectation when they solve a problem or do an operation. Explain why the process goes that way in order to give the child the perspective of how math really works. After that, give them a problem to do, and once they get the process right, the answer comes smoothly.

Math is a difficult subject to teach, especially when the child isn’t interested. Understand the focus and scope of the lesson beforehand and work from there to make math a fun subject to teach. Always remember to give an overview of the process by showing him or her how it’s done so they learn actively.