Tuesday, September 23, 2014

Beyond Common Core – Math for Advanced Learners

Our 7 year old daughter has demonstrated high aptitude for math since she was a preschooler. In this post I would like to share how we help her go beyond her school curriculum in math.
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We live in California, and we got lucky because our district started transitioning to Common Core when our daughter was in kindergarten. At least she didn’t have to go from one system of learning to another. While I certainly heard a lot of arguments against Common Core math, I personally don’t think it’s inherently bad. In fact, in many ways Common Core is closer to “European math” both my husband and I learned in our schools. At least "in theory" of Common Core, math is not supposed to be treated not as a collection of recipes which you need to follow just so to arrive to the result. Instead, the goal is to teach you to cook “from scratch” fully understanding “ingredients” that go into formulas and calculations. We also like the focus on proving your work. The challenge, however, that many interpretations of Common Core (and our language-focused second grade teacher) think that proving your work means writing an essay about your thinking every time the proof is required. Luckily, in the first grade and now in the third grade we were blessed with better math teachers, and, after all, any curriculum only as good as the teacher who teaches it.
There is one thing, however, that worries me somewhat about Common Core math – a lack of differentiation between stronger and weaker students. Last year our Common Core-obsessed second grade teacher told us that Common Core is able to support differentiation for the strongest with different level of tasks, but we haven’t seen it at all. This year we see it more – again, I think ability to differentiate depends more on the teacher and on their stash of materials than on particular curriculum. Anyway, we learned from our last year's experience not to rely too much on school to challenge our little mathematician, and here is what we are doing at home to take math deeper and further.

Going Deeper in Math

Even though our daughter “works ahead” in math, we are not on a mission to accelerate her, because we want her to enjoy her childhood. This is why we want to “slow her down” in terms of getting into more and more complex math topics and go deeper instead strengthening her ability to think logically, apply creativity to math challenges, and solve multi-step problems. Here are a few resources to do that:

Math Books

There are workbooks, and then there are “math books”. The big difference between those is if the focus is on repetition or on challenging students to go deeper in their understanding of math concepts. Here are a few math books that I particularly liked.
Math Detectivea book that exercises reading comprehension, logic, and math. Every long word problem is presented in a story and then a set of questions is given to a student. Smarty did this particular book (it's a series) in grades 1 and 2, but it's targeted towards 3 and 4.
Think a Minute. I love this one, because the tasks require creative and lateral thinking and also challenge spatial skills. The one we have (B1) is for grades 4-5 and most tasks are “appropriately hard” for our third grader.
Mind BendersClassic logic word problems which already come “prewired” with “logic matrix” that we eventually learned to construct for logic problems in grade 8 or so. Smarty really enjoys them but requires a bit of handholding/scaffolding to help her reason out the answers.
Primary Grade Challenge MathI’d say that this one is my favorite, because every chapter introduces a way to solve the problems presented later in a chapter, and each chapter has 4 levels of difficulty, so the book is appropriate for students of different strengths. We are finishing this book now, and I am getting ready to get the next one in the series – Upper Elementary Challenge Math.

Math Games

Math is not only about solving problems on paper. Many board games really hone “think ahead” skills needed for math. Check out my post Board Games for Brainy Kids for our favorite math games.

Other great recommendations for board games:

Computer Animation

Another way to deepen your child’s dive into math, especially into geometry, is getting them interested in computer animation and game design. Both of these things require a lot of math and spatial skills. We tried to get our 7 year old into learning some computer animation through Khan Academy that teaches computer animation principles with JavaScript-like language, but so far this proved to be too hard for her. We might revisit our approach with a different online learning tool during winter break - some of the options listed in 15 ways teaching students to code might work better for Smarty.

Have a favorite math resource to share? Please feel free to recommend it in the comments.

More Math?

Follow my Pinterest board Math. Follow Natalie Planet Smarty Pants's board Math on Pinterest.

jeannine said...

I like how you describe math as "cooking from scratch" rather than just memorization. We want children to be flexible in their thinking and in their problem solving applications. I also like how you included problem solving type games. Games are often over looked; however, a good game can really challenge your thinking.

Ticia said...

I think that's where I'm against Common Core, many of the theories behind it or individual aspects sound good, but it's when you get into the nuts and bolts and the program as a whole that I disagree with it.

I'm with you though, the Critical Thinking Company has some truly awesome books for encouraging thinking. I really need to get some for my kids.

I forget did you ever pick up any Life of Fred books for Smarty? It seems like it would hit two things she enjoys. Puzzles/solving math problems and reading.

maryanne @ mama smiles said...

Thanks for these recommendations! Emma enjoyed reading the Life of Fred series this summer, and she has reread the earlier books several times so far (I think some of the later ones are too advanced for her at this point, beyond her initial skim read).

min said...

The teachers are taught that the new testing will require written explanations. The new teachers probably try to prepare them for a change in testing. The idea is that we are moving away from simple computation and moving towards conceptual understanding as well as communication in mathematics (using correct terms). The old schooled teachers probably just do what they've been doing. I always thought the new testing would lower second language learners' scores even though their mathematical understanding might be superior. I am not sure how the children will be tested but I imagine it will be multiple choices with the convenience of technology. I doubt that much writing would be required because it requires the teachers to interpret through the chicken scratch which is time consuming. This might be a good question to ask.

shelah moss said...

I have a few students who are gifted in math. Thanks for the resources, it will be really helpful.

Mathy Mom said...

Check out Art of Problem Solving! I think they started as a resource for competitive math but they are well into developing their own math curriculum that emphasizes depth over speed and they believe that bright kids learn best by trying to figure things out on their own first.

They have real-time, discussion-based, online classes (pre-algebra through calculus and group theory as well as computer programming) that use their own textbooks. They are actually accredited by the Western Association of Schools and Colleges and on the University of California a-g Approval list in case your Smarty finds herself too far ahead of her classmates.

You can also buy their text books to use on your own (grades 3 & 4 and soon 5 in addition to pre-algebra, "grade 6ish", through calculus), they all have lots of practice problems and complete answer keys (not just odd numbered problems) with both hints and complete solutions (not just answers). The books cost more than grocery store workbooks or even the math books you show in your photo, but they offer "broader, deeper, and more challenging instruction" and are designed to be comprehensive, not supplemental. (At this writing, a year equivalent set of elementary books will cost just over \$100. Middle school/high school book sets run \$40 - \$65 per set and are the equivalent of 1 semester to 2 years of public school coursework.)

They also have something vaguely similar to Khan Academy called Alcumus that is used in conjunction with their classes (pre-alg through geometry) and as such can be directly linked to provide additional support for a self-learner utilizing their textbooks, but it is free and can be used independently as well.