A widespread problem at the secondary level is addressing basic skills deficiencies – gaps from elementary school. For example, I often encounter students in algebra 1 or even higher level math who cannot compute problems like 5÷2. Often the challenges arise from learned helplessness developed over time.

How do we address this in the time allotted to teach a full secondary level math course? We cannot devote class instruction time to teach division and decimals. If we simply allow calculator use we continue to reinforce the learned helplessness.

I offer a 2 part suggestion.

Periodically use chunks of class time allocated for differentiation. I provide a manilla folder to each student (below left) with an individualized agenda (below right, which shows 3 s agendas with names redacted at the top). Students identified through assessment as having deficits in basic skills can be provided related instruction, as scheduled in their agenda. Other students can work on identified gaps in the current course or work on SAT problems or other enrichment type of activities.

Provide instruction on basic skills that is meaningful and is also provided in a timely fashion. For example, I had an algebra 2 student who had to compute 5÷2 in a problem and immediately reached for his calculator. I stopped him and presented the following on the board (below). In a 30 second conversation he quickly computed 4 ÷ 2 and then 1 ÷ 2. He appeared to understand the answer and this was largely because it was in a context he intuitively understood. This also provided him immediate feedback on how to address his deficit (likely partially a learned behavior). The initial instruction in a differentiation setting would be similar.

This gap doesn’t just go back to grade school standards. In the secondary standards (grade 7) one finds, “Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.”

Estimation isn’t possible without command of basic math facts. Should 12.5% of $50 be closer to $5 or $10? Why estimate when you have a calculator on hand? Precisely so you know the “reasonableness” of your answer. For example if the answer you get from your calculator is $625 you should have a sense that it’s wrong. How can the calculator be wrong? If you put in the wrong input. How would you know that? By being able to estimate.

I am with you Doug. In fact, I suggest using estimation as an instructional strategy for learning new content. For example, if I am teaching a lesson on sales tax, I would start with estimating 10% of a given price and discuss what the sales tax is and why it exists. Then I explain to students that they will learn the steps for computing the tax. Typically the steps are introduced first, as more rote memorization.

Great post 🙂

This gap doesn’t just go back to grade school standards. In the secondary standards (grade 7) one finds, “Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.”

Estimation isn’t possible without command of basic math facts. Should 12.5% of $50 be closer to $5 or $10? Why estimate when you have a calculator on hand? Precisely so you know the “reasonableness” of your answer. For example if the answer you get from your calculator is $625 you should have a sense that it’s wrong. How can the calculator be wrong? If you put in the wrong input. How would you know that? By being able to estimate.

I am with you Doug. In fact, I suggest using estimation as an instructional strategy for learning new content. For example, if I am teaching a lesson on sales tax, I would start with estimating 10% of a given price and discuss what the sales tax is and why it exists. Then I explain to students that they will learn the steps for computing the tax. Typically the steps are introduced first, as more rote memorization.