Teaching Student Centered Mathematics Book Study: Chapter 10

Chapter 10


Chapter 10 was all about helping students to master basic addition and subtraction facts meaning facts where both addends are below 10. The philosophy behind this chapter speaks a lot to my personal philosophy on math intervention in general. Learning basic facts is not meant to be a rote activity. If a student doesn't know, for example, 4 + 5 you could teach them that it equals 9 but, at the end of the day, all they would know is that 4 + 5 = 9. There would still be 99 other facts for numbers 0-9 that the student does not know. That is a LOT of facts to learn and memorize! If, instead, you take a more systematic and strategy based approach based on number relationships, your students will have the skills to efficiently reason through the facts that they don't know until they are known from memory.

Three Phases of Basic Facts

  1. Students will intially use counting strategies in order to solve addition and subtraction facts. This will include counting all and then counting on. When counting all, a student has an object to represent each and every item. These may be manipulatives or fingers. A student will then move towards counting on. This may originally look like stating the first amount and counting on the second amount but students will then move to the more efficient strategy of counting on from the larger number. 
  2. Students move next to reasoning strategies which cover a lot of ground. Reasoning strategies include the properties of addition and subtraction (adding and subtracting 0 and 1) along with the commutative property. This also includes using related facts. This includes doubles +/- 1, make a ten, finding five, finding a double, etc.) When teaching reasoning strategies, you can provide a story context that lends itself to a particular reasoning strategy or you can explicitly teach a strategy and then ask students to apply this strategy to a variety of other problems. In order to use reasoning strategies, students need to have a strong concept of how to decompose the numbers to 10. For example, if adding 9 + 3 using the make a ten strategy, a student would need to know that nine and one more makes ten. They also need to know that 3 is made of 1 and 2. Without a strong foundation and understanding of how to decompose numbers to 10, the reasoning strategies will be little more than a rote application of counting activities. 
  3. As students become proficient with reasoning strategies, students will move from reasoning strategies to knowing their facts from memory. To know a fact from memory is defined as a students knowing a fact within 3 seconds without using any overt inefficient strategies. 
A last note, the chapter stressed that timed tests are NOT a strategy for teaching facts! There is no reason why students should publicly display the facts that they currently know. This encourages quick rote memorization with flash cards and a move to quick recall too quickly so that students are not focused on the relationships between numbers. Instead, encourage a student to compete only against themselves and their ability to be more efficient than they were the last time they tested their fact mastery. 

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