## Aspen and RightStart™ Mathematics Level A Lessons, Installment #4

Aspen has been doing great in her lessons, however is at times getting frustrated as she feels she is not learning fast enough. For example, when were were doing a lesson and using the AL Abacus to double check her addition, she thought she would be “cheating” if she used the abacus itself. I asked her why she felt it was cheating, and she replied that it made it easier, so it must be cheating. She’s really trying to use her mind’s eye, and it took some convincing that it’s perfectly fine to keep using the abacus for now, and for the next levels as she needs it.

Aspen is truly loving the lessons regarding the coins. She has made a game out of dumping out my purse so we can go through the coins to add. She struggles a bit with the dimes and the nickels. I have a feeling that the size confuses her a bit between the two coins, as she’s noted that the bigger one should be more. We’ll just have to keep playing with the money, as she has to add it together in order to put it into her piggy bank.

Aspen’s favorite game thus far has been the addition memory game. She absolutely loves it when she can say what she needs before asking for help or using the abacus. On occasion she still uses it, as she tends to get stuck on the 7′s and 8′s when coming up with the other addend to make 10. Now any normal memory game is a little boring to her without the added challenge of addition.

Partitioning for Aspen has been a bit challenging when using the Part-Whole Circle sets. She does well with the abacus, but when the circles continue to be brought into play, she seems to have a bit of a road-block when she looks at them. Eventually she gets it, but they do frustrate her. When having the two parts, she comes up with the whole easily, however, determining the part, when the whole and one part are given stumps her, and she takes a bit of time to come up with the answer. She tries to do it in her head, but quite often grabs her abacus to find the answer.

Aspen has been doing fairly well with telling time. She has been working on it, and loves to try to figure it out. She seems to really struggle with it, when she has to note if it’s bed time. Imagine that! If you tell her to note when it is time to go to the pool or somewhere fun, then she does seem to be at the top of her game.    She is pretty confident in the whole and half hours, but the other variations still cause her a bit of confusion.

Aspen was working with her dad doing the teens with her school work, and was getting really frustrated. I grabbed her abacus and we did the RightStart way of saying the teens, such as 1 Ten 3, then she was easily able to come up with the correct number, and quickly converted it to the conventional number way: 13. Her dad just looked at her, and was surprised by how she was able to come up with the correct answer going that route, as opposed to just knowing the convention number off the top of her head. He’s really noticing how well she is doing and is attributing it to her using RightStart in helping her advance in her math skills.

Aspen has been becoming a great cook’s helper, as she loves to help with the measuring and mixing. She gets to help find the correct measuring unit, either in the measuring cups or spoons to help create our kitchen masterpieces. (At least she things they are.) She is getting to be consistently correct, and going through the lesson on fractions was quite easy for her. She did extremely well when working on the second edition fraction lessons (as I had an advance copy). She didn’t call them the correct name, for example called the thirds “threes” instead, but after corrected, she flew through the lesson and found it to be so much fun. She is continuously playing with her Fraction Puzzle and Fraction Magnet we have located on our refrigerator.

## Snub Cube Pattern

A customer called yesterday with an interesting question. She and her son were working on Lesson 164 in RightStart™ Mathematics; A Hands-On Geometric Approach. They were making a snub cube using the RightStart™ Geometry Panels and couldn’t get the net to work out. She was wondering if there was an error.

For those of you that want to know the short answer and not the details: the lesson has it right. The net does, in fact, become the polyhedra shown above.

For those of you that want to know the long answer and hear the story, settle in, and let me tell you the fun we had!

First of all, what IS a snub cube? A snub cube is one of the 13 Archimedean solids. It is formed by adding extra triangles around the squares of a cube. Specifically, 32 triangles are added around each side and vertex (point where the lines meet) of the squares.

I had two of our summer helpers work on this problem. Katie is a very bright college student and Logan will be a high school senior and likely the valedictorian of his class. They put together the net (pictured above on the left) with ease. However, they struggled to get the floppy pieces to shape up into the snub cube.

I checked on their progress after a while. I only added to the confusion. It just wasn’t working, which is what our customer had experienced.

I told Katie and Logan to approach this from a different perspective. I said, “Let’s build this by looking at the shape and recreating it.” Given that we hadn’t made any success with first method, both were eager to try a new tactic.

We started with the square on the right side of the shape pictured above. I said, “See how each side of the square has a triangle attached? And each square corner has two triangle points coming into it?” OK, I should have said “vertex”, but I didn’t.

I continued, “Then, when you have the square and 12 triangles attached, rotate, attach a square in the right spot, then build the same 12 triangles around that new square….” Katie and Logan jumped in and began building.

There was a small problem in the construction because Katie and Logan didn’t realize that two triangle vertices meet at the square vertices. Yes, I had told them that, but they didn’t apply what they had heard. We’ll address that issue in a minute…. After a quick conference and discovery, they went away and, in practically no time whatsoever, came back with a perfect snub cube and smiles all around!

I then challenged them to make the left handed version of the snub cube building the net then assembling, just to see if they could do it. They went off and came back shortly with a newly constructed snub cube.

I asked why they had no problems with the second net when the first was nothing more than a tangled mess. Katie responded, “Once we knew the pattern of two triangle points touching the corner of the square, it was easy!” Logan added, “The first time we did it, we were randomly attaching triangles here and there, which didn’t work! ”

So what have we learned here? First, when someone tells you something, it isn’t as effective as discovering and doing it yourself. I told Katie and Logan that each square corner has two triangle points coming into it. They heard me, but didn’t understand until they discovered it themselves, applied it, then developed the understanding for future situations.

Dr. Joan A. Cotter says, “What one discovers and understands is remembered better than anything learned by rote.” This knowledge made the second snub cube a breeze.

A second thing learned is patterns! Logan said, “It was easy going when we knew the pattern.” Once a pattern becomes evident, the randomness of a situation becomes organized and manageable. This can be applied to other polyhedras, to math in general, and to life as a whole.

P.S. Look at the polyhedras shown above. See any special patterns with the dark triangles? They share vertices with three squares and share edges with only other triangles. The lighter triangles share an edge with a square. Hmmmmm…..

## RightStart™ Mathematics; A Hands-On Geometric Approach

We received this comment from a Geometry Approach curriculum user: “I’m finding myself very frustrated because there are no explanations of how the answers are obtained. Is there no teacher manual in addition to the answer book? The answer book is nice but it doesn’t tell us how you got the answer if we are confused.”

This is a good point. The RightStart™ Mathematics; A Hands-On Geometric Approach level is a different format than the prior RS levels. Geometric Approach is set up more as exploration of math, which, of course, is more like your child’s future learning.

In high school and college, it is expected that the student will “read between the lines” and extract information that’s not quite specifically stated. My high school senior and three college kids get so very frustrated with this, but that’s the way it works!

Real life is this way too. Think of a baby running a fever. There is no manual that specifically states the answer or provides the steps to the cure. Instead, we need to run with trial and error. Sometimes Tylenol brings the fever down. Sometimes a cool bath. Maybe both are needed. Sometimes it’s a trip to the doctor for antibiotics!

So, how do we help you and your child work through these lessons? Well, two things will help.

First, read (or re-read) the “Hints on Tutoring” found in the front of the lesson book and attached below. A critical excerpt from this page reads “If a paragraph is unclear, the student should reread the paragraph, keeping in mind that sometimes more is explained in the following paragraph. No one learns mathematics by reading the text only once.”

I personally find not rereading the lesson is my greatest error when working through the Geometric Approach. My second most common error is reading too quickly, then jumping to conclusions, which mostly are wrong.

Second, ask us a specific question and we will get an answer to you. Have your student send an email to either info@RightStartMath.com or to JoanCotter@RightStartMath.com, put “Math Student” in the subject line, and we’ll get an answer to you as quickly as humanly possible. You may call us at 888-272-3291 and talk through the question with one of our competent people.

Also, have you and your child watched the “How To Teach” recorded webinar? This will give both of you a firmer foundation in which to work through the program.

Remember, if we did have a teacher’s manual, it would be so tempting to following the instructions item by item, which may stifle true learning. So, although I understand and agree with some of the frustration, think of this as a change in your child’s thinking and learning. It’s now time to explore and think through situations, rather than just follow a rigid algorithm.

Finally, remember to email and/or call us. We are here to help you and your child be the best you can be with your mathematics and with your future learning.

## Four-Year-Old Aspen and RightStart™ Mathematics Level A Lessons, Installment #2

Maren has continued to work with her daughter, Aspen. Let’s hear how it’s been progressing…..

January 25, 2012

Aspen has been showing great understanding of organizing items by size in Level A. She is able to take any type of items and organize them both smallest to largest and in reverse. She continues to beg to go through her lessons each night and rarely gets frustrated with anything we’ve encountered thus far. She continues to want to “count items” using her AL Abacus. She wanders around the house and totals up her findings then has to verify that she is correct. When asked if a certain quantity has been added or subtracted, she has been stellar in her grasping of the concept and rarely gets them incorrect. I’m finding that the lessons are clear and concise and that it’s been quite easy to give the instructions to her to follow.

February 22, 2012

Aspen has been flourishing with her Level A lessons. She’s still so very excited when we work a lesson. We were working on parallels and about a week following the lesson as we were driving down the highway, Aspen kept asking to play the “pallellell game”. She definitely has a slight problem pronouncing it, however I was racking my mind trying to figure out what she was talking about. It finally came to me that she wanted to play a game to see if items were or were not parallel. We play our new game now whenever we have a drive, as well as when we are at home. She continues to verify with me if she’s correct when she judges if any two items are parallel or not. Math has been becoming one game after another with her, and it’s such a joy to see her enjoying herself and her new knowledge she’s acquiring.

March 27, 2012

Things are progressing nicely for Aspen, as she continues to enjoy her math. She loves working with the Abacus, and continues to play with it to work on her skills even when we’re not doing a lesson. She’s been working diligently on identifying numbers of items with her tally sticks, abacus and her fingers, and for the most part, she’s been successful. She still struggles with the 7, 8 and 9, but is getting more successful with those all the time. She still has a tendency to try to count those out when she thinks I’m not looking. She was working on them the other night, when her big brother, who’s 18, was watching. She was given an “8″ and she was looking at the abacus to figure out the appropriate beads to move, when her brother said, “Aspen just count them out on your fingers”, in which Aspen replied: “Bohdey, we don’t do it that way, we have to think about it.” He just looked at her and grinned. Maybe a little of this will eventually rub off on him, as he didn’t have the opportunity to take advantage of this product and he struggled all the way through school with his math classes. A mom can always be hopeful!