Right-Brained Math: Concepts to Facts

Building and math have pattern discovery in common.

I was asked to speak about a section in my book, The Right Side of Normal, that I’ll share here:

First, a definition from Chapter Twelve, “Building the Road to Math Competency:”

There’s a difference between arithmetic and mathematics. Here’s how I differentiate the two in this book. Arithmetic is the act of manipulating quantities (facts); mathematics is the science of finding patterns, coming up with theories about it, and proving its existence (concepts). Elementary schools primarily focus on arithmetic. Learning one’s “math facts” is arithmetic. Even most of high school “math” would be considered arithmetic because of how it’s presented (formulas to be plugged into problems). Right-brained learners are natural mathematicians. Left-brained learners are most comfortable with arithmetic. One way to tell if you’re right-brained or left-brained is to ask: Did I do better at geometry or algebra? If geometry, then you’re most likely right-brained; if algebra, then you’re most likely left-brained.

Then, a section from Chapter Seven: “The ‘Right’ Time for Learning:”

Arithmetic to Mathematics―The Left-Brained Way

 Let’s look at the timing difference with the goal of learning algebra in high school if each learner’s early year strengths are utilized. The left-brained learner does well with the current sequential progression of learning numbers, then addition/subtraction, then multiplication/division, and so forth until it’s time to apply these concepts to algebra later. At that time, left-brained learners use their foundation with number manipulation (arithmetic) to begin understanding the bigger concepts of negative/positive numbers, variables, math patterns, equality, and so forth (mathematics).

  Mathematics to Arithmetic―The Right-Brained Way

 For the right-brained child, the learning pattern is opposite but just as viable. In the early years, the right-brained learner needs to explore global concepts that can be visualized, such as negative/positive numbers, variables, math patterns, equality, and so forth (mathematics) so he can build the understanding necessary to be ready to learn algebra later. At that time, right-brained learners use their foundation with math concepts to begin understanding the reason to learn math facts, such as addition/subtraction, multiplication/division, and so forth (arithmetic).

As you can see, the goal remains the same―algebra for all in the high school years. But when the strengths of each type of learner are applied, the foundational knowledge needed before algebra begins requires different approaches. The left-brained learner excels at the symbolic sequential manipulation of facts in the early years while the right-brained learner easily visualizes abstract global concepts. It’s important to remember that both integrate the other ability later, but each works from a foundation based on their respective strengths in math processing.

Okay, so let’s talk about what the foundational strengths of a right-brained math learner would be: either visual-related or kinesthetic-related. Throughout my math chapter, I differentiate between these two input types. Let’s start with visual-related math learners.

My oldest artist son strongly identified with this in the math department. He often would enjoy talking over problem-solving math ideas (i.e., oral story problems, but more real-life than some of the concocted problems you can traditionally see in math books).  He also liked playing around with numbers in his head when I helped him discover different ideas. Visually seeing patterns was another way he picked up on number relations. There weren’t really a lot of living math books back then, but I think he would have liked them. Here are a few resources that did or would have worked for this type of visual math learner in the early years:

Now let’s talk about kinesthetic math learners in the early years. My builder son strongly identified  with the spatial or kinesthetic learner. It makes sense when you know that building with materials requires hands-on interactions. He loved anything that was math manipulative-oriented. He loved to problem-solve with these objects, so getting books that had challenges inside based on math manipulatives such as tangrams, geoboards, or pentominoes were always a high interest activity. He would have also enjoyed anything that had to do with math hands-on “projects” such as found in a couple of the resources below. Finally, board games, card games, dice games, or even things like dominoes were always favorites for my builder son. Here are a few resources that did or would have worked for this type of kinesthetic math learner in the early years:

I think one of the hardest things for us to do is be able to shift our perspective enough to view math non-sequentially. It might help you to do this if you put math in the same department as science for kinesthetic learners and history for visual learners in the early years. Usually, most teachers I know in the early grades don’t have a need to do a sequential science program, but are more than willing to be experiment or project-based. Think about math in the same way for your kinesthetic math learner. Pick 2 or 3 projects each week, whether it be a board game one day, something with math manipulatives another day, and a project another day.

Many teachers I know are willing to present history in different ways, such as a good story from someone in the era, or a project centered in another era, or having some good discussions about why history happened. So, think of each of the living books as a good story about an “era,” or area of math. Or a project on one style of concept (visual patterns) can be exploring all the patterns in the hundred’s board activity book. Or talk about how numbers interrelate with some mental math “conversations.”

Here’s the deal: we’re just not used to thinking about math in this way. It only seems disjointed because we feel safe in the known sequence. But, just like science and history in the early years, it’s about getting excited and exploring thinking mathematically. Someone on my Homeschooling Creatively list pointed us in the direction of the Benezet study that I reference in my book. A teacher wanted to see if he focused on other areas of mathematical thinking, if students would still end up being able to do arithmetic later. This teacher played around with and talked about problem-solving and number relationships until the students were 11 years old, and then within 2 years, they were able to outperform their sequentially-taught math peers. Access to the full study is here. A breakdown of what he taught his students by grade is found here. It may help you come up with ideas for how to create a similar positive relationship with math for your own children/students.

What are some math resources that you’ve found that works for your right-brained child(ren)? Why do you think they work?

15 Responses to Right-Brained Math: Concepts to Facts

  1. I know you’ve heard me mention it before, but Math on the Level does almost exactly what you say in this article! It is a list of concepts that you can proceed through at your own pace, in whatever sequence. You can make it as structured or as unstructured as you want. And computation of facts is totally separate. I had one child (RB) decide to memorize facts around age 12, and one child (LB) who wanted to learn them at age 6. Either way was fine. I have loved MOTL so much that a friend and I started creating the same thing for grammar – a list of concepts, any sequence, fun ideas for learning them, and a tiny bit of written work for those who are ready for that step. It is here: http://lbleducation.blogspot.com/

  2. Thank you SO much for sharing, Robyn. You’re right, it’s a great idea to share a resource that has already been created to use as a spine for teaching math concepts globally. And how awesome of you to do the same thing for grammar! I think I need to start promoting certain types of products since I know so many really need the foundation, especially as they get started, or getting going on their shifting perspective ;-)

  3. Yes, I think you nailed it. As the comfort level increases, you start to branch off on your own … but at the beginning, it helps to have something tangible for reference, to make sure you aren’t “forgetting something.” :) Also, I have found it helpful when talking to doubtful family members (you know, the ones who constantly ask “what curriculum are you using?) to be able to say, “oh yes, for math we are using X as our curriculum.” If they are open to new ideas, you can elaborate … or not, if you don’t feel like going there!

  4. Thank you so much Cindy! This is exactly what my brain was needing, the visual. Your words give me reassurance. You’re SO right, I have no problem exploring other subject in this manner, I just needed to see what it looks like. My boys were oohing and awwing over the pictures of the book suggestions. It’s funny when my oldest was 5 he found a math picture book that explored multiplication, he went to it over and over again. He was telling me then what he needed. Wish I would of had the confidence to listen and follow then.

    • Isn’t that cool, Cassidy? How you can “see” it now that you can look back? This is an ah-ha moment for you…a shift begins with me moment…;-) I’ll bet you’ll notice more and more every day every time you get to make those connections.

      There are SO many types and styles of math resources now, it can become more like looking for various history items in the math department. It used to be that math resources were limited because it was assumed we all accept the sequential focus for math instruction. It’s awesome to see how we’re moving away from that simply from all the choices and styles of math resources we see around us today. Now, we just have to take advantage of it!

  5. Have you heard of Life of Fred for math? It seems to fit your description for exploring global concepts. I haven’t used it, but I would be interested in your take on it. http://www.stanleyschmidt.com/FredGauss/index2.html

  6. Yes, I’ve heard of it and have some! Unfortunately, my son who would have liked it the most, my artist, visual-based math child, was too old by the time I knew of it (or it may have not been out, either). I do mention it in my book in the math chapter as being a good choice for visual, verbal right-brained learners. I’ll be trying some of the younger versions on my youngest, though, to see if it would be a match for him. And yes, from what I know of Life of Fred, it seems to be global, concept-based, real world-oriented…all good for the right-brained math learner!

    I love how so many of you are already coming up with “matches” for right-brained children based on my descriptions of a good fit. That’s exactly what I wanted my book to provide. Although I do mention some specific products as examples of a good fit, I wanted to describe the type or style of resource that works well so that everyone can be on the look-out for similar products and resources, especially since new ones will come out all the time.

  7. I have a math unliking daughter. I have tried a vast assortment of stuff, including Math On The Level, Life Of Fred, Math-U-See, Math & Music, Oak Meadow. Here’s the problem for her as SHE states it: doing any kind of math makes her brain work in a way that overpowers the way she likes it to work. Like your autistic child who LIKES his autistic brain (and yes, she relates well to some people with autism). After doing math, it takes her several hours to reset her mind back to where she wants it. She HAS enjoyed the following, which we use from time to time: Story of Math from The teaching Company, and some of Visual Math from there as well). Picking and dipping out of Jacobs Geometry. Lewis Carroll’s Set Theory books. Books from amazon on “infinity” and “zero” (and time travel and chaos). Constructing The Universe. She liked John Holt’s Why Children Fail and said it clarified some things. I still haven’t come to a way of understanding her enough to make math work and I’ve kind of given up. She has learned enough to survive the CAT tests each year.

    • Hey Sheila,

      It sounds to me like your daughter is doing quite well with math! I can see she likes to think about it in its abstract form, definitely conceptual, and how it really relates with the universe. Kinda awesome really. I love how she’s able to verbalize that arithmetic (my assumption here) derails how her brain thinks. How fascinating and enlightening!

      In Chapter Eighteen in my book, at the conclusion, I talk about the idea that we expect a certain proficiency in certain subjects: reading and math being at the highest end of that expectation. But really? Why is it that we think every human will have a proficiency in those particular subjects? Is it possible to achieve 100% in anything? My daughter is a writer. She doesn’t think mathematically. As your daughter said, it would derail her. She is competent and unafraid of math in her regular life. She could even study enough for the ACT to achieve an average math score. But she in no way felt a need to press herself to reach some kind of minimum expectation with math courses. She went through pre-algebra in a series that was very concept-based. As she considered algebra, she went,, “No thanks, I’m a writer; I’m done with math.” And her logic was sound and I agreed with her declaration. She was 13 or 14.

      It sounds to me like your daughter has dabbled in enough areas of math understanding to also feel competent enough and unafraid, if we can keep society’s idea of a certain kind of math achievement out of our measuring toolbox :-)

  8. Fascinating! I had no idea that I’ve been using a “right-brained” approach to showing my children math.

    • Following your children’s leads and following your instincts have served you well, VIctoria! It’s kind of a validating experience when you translate what you’ve done and it matches what you discover has a name in the research that matches what you know about your child. Cool stuff! What approach were you using?

      • We are unschooling, but my inclination is to first build intuition as a foundation for conscious understanding. We read a lot of math fiction, play games, and just talk about math. If you are interested, you can take a peek at my math blog http://unschoolingmath.blogspot.ca/ . It’s just a collection of math things we do and my own reflections.

  9. Pingback: Honoring Both Math Minds | The Right Side of Normal

  10. Thank you for this! I just started reading your book tonight, knowing that I should have started it weeks ago. My husband and I have become so frustrated with my 8yo daughter’s seeming lack of math skills. (She loves to draw, build with Legos, play Minecraft, and knows more about animals than we do.) It feels like we’ve been stuck on learning addition facts with her for two years, to the point that we haven’t moved on to anything else. She hates math, and just saying that we need to do a math lesson brings grumbles and sometimes tears from her. My husband and I were both traditionally educated and keep thinking that she should be moving on to multiplication facts soon! This blog post and the comments give so many resources and ideas for me to try out or check into to make learning “math” more enjoyable and more based on what our daughter needs and is ready for. I will share this info with my husband and throw in extra doses of TRUST so that we can teach to our daughter’s strengths and not worry that she is “behind.” I am so grateful for your insights and research, Cindy!

    Jeni

  11. I cannot tell you how grateful I am for this website. I have struggled with math throughout my middle school and high school years. I have always been an artist-drawing, writing songs, stories & poetry, singing, acting, dance, modeling etc. I have also always excelled in language arts, literature, English and reading comprehension courses, earning “A” letter grades. However, in a world seemingly dominated by left brained executives and universities, it becomes difficult to not only get into a good university but to also complete university courses in order to earn a professional degree. I have attended several colleges and I have always stopped my studies when it came time for me to pass college level algebra. I just never conquered the concepts. I can recall my embarrassment at being placed in remedial college math courses and still not being able to understand the work. Those who are naturally left brained thinkers make you feel as though you are an idiot for not understanding something that comes easy to them. Now, as a full fledged adult, I have a very strong interest in earning several degrees. However, I know that in order to accomplish this, I must first conquer math. So, as I began to search “Google”, I put in “Why some people are bad at math” and it led me to “Brain Hemispheric Dominance”. I took the test and lo and behold, I am a right brained dominant thinker. Why does the mainstream U.S. curriculum not explore this phenomenon? I think that schools and universities should conduct tests to determine if a child is right or left brain dominant and base their learning curriculum on that. It would be so much easier for some children to grasp what they are learning and it would also improve self confidence and how they relate to others. Imagine how a right brained child must feel when their classmates understand certain things and they do not. I was one of those children. And now years later I am playing catch-up. Even in every day conversations with those who have degrees, I find that their way of thinking is sometimes different than my own. My intelligence is at times questioned and/or challenged. Although, because I have such high comprehension, they just assume that I have a degree. It is hard for left brained individuals to see things outside of the box or to conclude that the same conclusions can be drawn through the use of different means, just as it is difficult for right brained individuals to reach a conclusion through certain means. Even though I am behind, I’m grateful that the information is available now and that the next generation will be more enlightened than my own.

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