At the 2009 ChildLight USA Conference, I gave a presentation on mathematics. It was the first time I had ever studied what Charlotte Mason had written about math. Since I understood math, I neglected her writings and I now regret that because David would have benefited from her wisdom! Unlike other subjects in Mason's philosophy, mathematics depends upon the teacher. I let David down. I fell into the trap of many teachers of allowing reworking until the right answer magically appeared. I did not focus on reasoning like I should have because that is his weakness. I should asked for more explanations to assess his understanding. Even though he took precalculus with the Teacher of the Year, attended ACT prep classes, and studied an ACT study guide, his math scores were lower than we would have liked. Mea culpa! I have resolved not to do the same to Pamela.
At the conference, I asked parents and teachers what they were using for mathematics. The most passionate endorsements were for Singapore Math, RightStart, Algebra and Geometry by Harold Jacobs, and Living Math for supplementary resources. I researched reviews and commentary on these programs and the only glitch I saw was that NOBODY recommended Singapore past elementary school, even devoted Singapore fans. I studied the resources in RightStart's Intermediate Geometry (what they use for pre-algebra). I poured over their sampler, pilot program, dictionary, and tests. It reminded me of the math activities we tried to make Math-U-See more inquiry-based with opportunities for discovery last year. What a relief that someone out there has already invented the wheel!
In June, I ordered RigthStart's Starter Kit Geometric Approach for Pamela this year and Jacob's Algebra and Geometry for next year. Right about that time, my friend over at The Black Pearl Academy started blogging about doing RightStart Level B with her autism-spectrum daughter. They went through seventeen lessons together over the summer and it was exciting to see their confidence grow. At the end of the July, my friend asked her children what subjects they liked best. After careful consideration her daughter said, "I guess now it's math!" Another friend Queen Mum, a self-admitted math curriculum junkie, has RightStart among her other arithmetic paraphenalia.
Don't let these three books scare you! The idea behind Intermediate Geometry is to explore mathematical concepts students will learn in high school by drawing and building things. A friend had popped into visit the afternoon the kit arrived. I excitedly showed her what it was. She majored in graphic design and commented, "Wow! These are like some of the tools I used in college!" Pamela is taking a pottery class right now and we are making boxes out of different shapes to reduce the amount of pinching she has to do until she gets used to the feel of clay again. She made a rectangular box last week. To experiment with different possibilities before making a new box, Pamela and I explored the geometric panels pictured below. Her teacher, another math atheist, marveled over what we could do with them and said, "What a cool math program!"
The three books include the solution manual, the lesson guide that students read to work through a lesson, and the three-ringed notebook with work pages. Students remove a page or two for each lesson and tape it to the drawing board. When opportunities to focus on a formula arises, students study the patterns and develop an understanding of concepts before a formula is presented. Here are some of the tools and drawing tools that come in the starter kit:
These geometric panels are beyond what I was trying to imagine last year. I can see how much they will help Pamela understand surface area and volume of simple solids. Today, after we build them, we were working on our RDI objective (understanding that you can see different parts of an object depending upon your perspective). I sat opposite to her and, with the pentagonal prism, we had the same perspective no matter how we turned it. With the other solid, sometimes we shared the same perspective, but sometimes she saw four blue triangles while I saw a single yellow square, and vice versa.
I plan to do four 45-minute lessons a week (doing a total of 132 for the year) and to finish up the final 33 lessons (out of 165) next year along side Jacob's. If the schedule slips, I will start Jacob's regardless because RightStart recommends starting an algebra program about halfway through anyway.
All is not lost for David, a senior in public high school. After we received his ACT scores, we mapped out a game plan to work on reasoning problems in Jacob's Algebra and Geometry and retake the ACT in the fall. He has already knocked out three chapters and is explaining his understanding better because of the way the text is written and the kind of problems assigned. David likes the way Harold Jacobs presents mathematical ideas in fresh ways and is starting to succeed with some of the brain teaser problems. He told me, "Math-U-See doesn't teach you to think about what word problems actually mean in the real world. I could get by focusing on mechanics, but Jacob's does both. The Set IV problems are challenging me to tackle mathematics in the real world."
Here is an example of a typical problem that focuses on reasoning. Try this "magic trick" which always results the answer 5. Explain why it works:
Think if a number.
Subtract the original number.
From chapter to chapter, the mystery numbers thrown in occasionally become more complex. For example, solid circles represent negative numbers. After asking for an answer to word problems, the book asks what it means. Suppose you shoot an arrow up into the sky and then it falls to the ground. At two seconds, the answer is a positive velocity (speed). At 7 seconds, you get zero velocity. At 10 seconds, you have a negative velocity. What does zero velocity mean the arrow is doing? What does negative velocity means the arrow is doing?
Sniff, sniff . . . I have plagued you enough with math and have probably lost half my readers. Tomorrow, onward and upward to another subject in the knowledge of the universe: geography!
Do you feel better?