In general math is taught by focusing on the steps. Conduct a Google search for solving equations and you will see the steps presented (below). You need a video to help your student understand solving and you typically get a presenter standing at the board talking through the examples. (I’ve posted on my approach to solving equations.)

When the math is taught through the skill approach the student may be able to follow the steps but often does not understand why the steps work (below). The brain wants information to be meaningful in order to process and store it effectively.

To help flesh this situation out consider the definitions of concept and skills (below). Concept: An idea of what something is or how it works – WHY. Skill: “Ability” to execute or perform “tasks” – DOING.

Here is how the concept first approach can play out. One consultation I provided involved an intelligent 10th grader who was perpetually stuck in the basic skills cycle of math (the notion that a student can’t move on without a foundation of basic skills). He was working on worksheet after worksheet on order of operations. I explained down and monthly payments then posed a situation shown at the top of the photo below. I prompted him to figure out the answer on his own. He originally forgot to pay the down-payment but then self-corrected. Then I showed him the “mathy” way of doing the problem. This allowed him to connect the steps in solving with the steps he understood intuitively, e.g. pay the $1,000 down payment first which is why the 1000 is subtracted first. Based on my evaluation the team immediately changed the focus of this math services to support algebra as they realized he was indeed capable of doing higher level math.

[…] explain steps in great detail to students but often omit the underlying concept. The topic of adding or subtracting fractions with unlike denominators is an example of […]

[…] is an example of instruction for unit rates to help a student conceptually understand (pretend that gas price shown on this pump is $2 per gallon). Say you pumped 3 gallons and it cost […]

[…] entry point to word problems should be a focus on the underlying concepts. For example, present the word problem with cutouts of the actual cookies and physically […]

[…] Often education and special education focuses solely on content. In turn, the content may focus only on steps and facts to memorize as opposed to ideas and concepts. […]

[…] student be presented problems with visuals but then use a calculator to compute. This can develop conceptual understanding and also address the working memory and other related issues that undermine learning math […]

[…] was called in by a district to help a 10th grader who was not grasping the basic math or pre-algebra that was presented for months. He was showing significant task avoidance. The postsecondary education goal was for him to attend […]

[…] explain steps in great detail to students but often omit the underlying concept. The topic of adding or subtracting fractions with unlike denominators is an example of […]

[…] is an example of instruction for unit rates to help a student conceptually understand (pretend that gas price shown on this pump is $2 per gallon). Say you pumped 3 gallons and it cost […]

[…] entry point to word problems should be a focus on the underlying concepts. For example, present the word problem with cutouts of the actual cookies and physically […]

[…] Concepts vs Skills […]

[…] Often education and special education focuses solely on content. In turn, the content may focus only on steps and facts to memorize as opposed to ideas and concepts. […]

[…] student be presented problems with visuals but then use a calculator to compute. This can develop conceptual understanding and also address the working memory and other related issues that undermine learning math […]

[…] was called in by a district to help a 10th grader who was not grasping the basic math or pre-algebra that was presented for months. He was showing significant task avoidance. The postsecondary education goal was for him to attend […]

[…] first step in presenting a new topic is meaning making. For scientific notation, the underlying idea is NOTATION – “the act, process, method, […]