# Part 1: Math Methodology: Instruction

All teachers should consider the role of active or constructivist learning, as opposed to using only a lecture method. Active student involvement reinforces learning. This is not to minimize the role of direct instruction, however. Per Robert Coe, Cesare Aloisi, Steve Higgins, and Lee Elliot Major (2014, "...if you want students to remember something you have to get them to think about it. This might be achieved by being ‘active’ or ‘passive’ " (p. 24).

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Students should become active in the learning process immediately upon entering the classroom. Muschla, Muschla, and Muschla-Berry (2013) stated: "Classes in which students begin working from the minute they take their seats are usually more successful than those in which the first few minutes are lost as the students get settled" (p. 3). Losing just the first five minutes daily amounts to 25 lost minutes per week of instruction and could amount to a loss of 20 class periods of instruction per school year. Their solution is using a math-starter problem that students begin immediately upon entering the classroom. In, they present at least one problem for each Common Core math standard for grades 6-12. Each is designed to be completed in 5-10 minutes, which includes reviewing the answer and any follow-up discussion. This strategy is also good for classroom management, as during this time the teacher can take attendance, pass back papers, interact individually with students, and observe students as they work (p. 3).

### Positive attitudes and perceptions about learning

The IRIS Center at Vanderbilt University provides details on three evidence-based strategies for teaching mathematics:. John Malouff (n.d.) grouped and explained, many of which can be applied to mathematics problem solving. Strategies can help understand the problem, simplify the task, determine the cause of a problem, involve external aids to help identify problem solutions, use logic to help identify possible solutions. Strategies can also identify a possible solution to serve as a starting point to solve a problem, or determine which possible solution is best. Strategies can employ geometric thinking, help you to function optimally while problem solving, and help solve multiple problems. George contain details of his four principles that have become a classic for math problem-solving: understand the problem, devise a plan, carry out the plan, and look back.

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The concept of differentiated instruction is not new. Historically it has been discussed in other terms related to addressing individual differences in instruction.

## What do teachers say about using video in instruction?

Read the ASCD Express (1953). ASCD devoted its to the theme "The Challenge of Individual Difference," which is available online. In the lead article, , Carleton Washburne presented a short history of reform efforts aimed at making education more individualized. What a find.