Instructional Shift 1: Incorporate ongoing cumulative review into every day's lesson.

Chapter 2: Ready, Set, Review

What should we see in an effective mathematics classroom?

-A deliberate and carefully planned reliance on ongoing, cumulative review of key skills and concepts

  • Lead a discussion about common, critical concepts/skills that mathematics students struggle with throughout the course or grade levels in your school. Brainstorm and then help teachers build consensus around the identification of these topics. Narrow the list two about 5 or 6. Develop a collaborative plan for incorporating these concepts/skills in an ongoing and cumulative review fashion throughout the year.

-Using cumulative review to keep skills and understandings fresh, reinforce previously taught material, and give students a chance to clarify their understandings

  • Challenge your Algebra/Data Analysis, Geometry or Algebra II teachers to use the following Mini-Math review (Leinwand, 2009. pp. 13-14):
    1. What is the value of 3a - 6b when a = -4 and b = -3.
    2. A line is defined by the function g(x) = 2/3x - 2. What is the slope and what is the y-intercept of the line that represents this function?
    3. The cost of a substance is directly proportional to its weight. If 30 grams of the substance costs $45, what is the cost of 6 grams of the substance?
    4. A population P increases by 5% each year for 2 years. Write an expression for the population in terms of P after 2 years.
      How did students do? Lead a discussion about the results. Steve Leinwand, author of Accessible Mathematics believes that these are four straighforward items that all Algebra students should know and be able to do, but often cannot. What do these results mean for instruction?

-Classes that waste no time and begin with substantive mathematics at the very start of every class

  • Monitor the amount of instructional time spent doing warm-ups and homework checks each day over a period of one week. What is the range (Use a percentage) of class time spent over the course of the week? What is the average amount of time spent each day? Over the course of the school year? Brainstorm innovative methods for conducting these routines that will maximize their value and minimize any loss of instructional time.

-The use of a brief review and whole-class checking of "mini-math" questions as an opportunity to re-teach when necessary

  • In teaching pairs, design your own 5-6 item "Mini-Math" review that can be completed (administered and discussed within about 5-8 minutes). Be sure to emphasize items that cover previously taught topics that are weakest (e.g., measurement) and based on your own class/school formative/summative data. Also remember to include at least one item that requires students to estimate and justify their estimate.