Recommendation 2: Instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8. These materials should be selected by committee.
What are the connections between Recommendation #2, the Common Core Standards (CCS), and what it might look like instructionally (for this recommendation, what are some materials that can be used)?
This is the fifth in a series of six postings that connect the Institute of Education Sciences (IES) practice guide recommendations, Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle School Students with corresponding CCS indicators, and an instructional look alike for that RtI recommendation. The sixth posting will look at the part of Recommendation #2 that addresses rational numbers G4 – 8.
The IES guide identifies eight recommendations that are designed to help teachers, principals, and administrators use Response to Intervention for early detection, prevention, and support of students struggling with mathematics. This guide is a synthesis of research that provides instructional recommendations in support of engaging those struggling mathematics students.
RtI Recommendation 2: Instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8. These materials should be selected by committee.
CCS indicators that correspond to the RtI recommendation of focusing intensely on in-depth treatment of whole numbers in kindergarten through grade 5 are listed below. For the CCS, the focus on whole numbers provides an opportunity for in-depth experiences with whole numbers which in turn provides skill fluency for problem solving entry points. The words used in the recommendation to consider are – “fewer topics in more depth, and with coherence.”
Additionally, the actual language of the CCS indicator provides ample examples of the required conceptual understandings that should be considered in selecting materials.
Only a few of the CCS topics for whole numbers are listed; note how easily the wording of each should be used in choosing materials to support those students needing assistance. Also, there is a direct correlation between whole numbers and how they are used within the realm in algebraic thinking.
- Discuss, and use efficient, accurate, and generalizable methods for operating with numbers.
- Explain why addition and subtraction, multiplication and division strategies work, using place value and the properties of operations.
- Generalize place value understanding for multi-digit whole numbers.
- Use place value understanding and properties of operations to perform multi-digit arithmetic.
- Use the four operations with whole numbers to solve problems.
- Gain familiarity with factors and multiples.
- Generate and analyze patterns.
What are recommended criteria for choosing materials and some possible instructional materials for K – G5 students receiving interventions for an in-depth treatment of whole numbers?
- NCTM, FOCAL POINTS K-8 that define in-depth and coherence of number development for K – G5; Math in Focus (Singapore materials); Jump Math for a few.
- The National Research Councils’ publications: HOW STUDENTS LEARN (2004) and ADDING IT UP, Helping Children Learn Mathematics (2001) provide strategies based on research, examples, and student work devoted exclusively to developing proficiency with whole numbers.
– For HOW STUDENTS LEARN, Chapter 6 is “Developing Proficiency with Whole Numbers.” Concepts covered are: single/multi digit addition, subtraction, multiplication, and division; estimation, mental arithmetic, and word problems.
– For ADDING IT UP, Helping Children Learn Mathematics, Chapter 6 is “Fostering the Development of Whole-Number Sense: Teaching Mathematics in the Primary Grades.” Within that Chapter, research and suggestions are provided that look at building on children’s current understandings and problem solving strategies; how to teach to the knowledge already acquired; developing conceptual/procedural knowledge, number sense, and positive attitude about mathematics.
- Use of relationships defined/illustrated in previous posts (RtI#3, RtI#4).
- Attention to the other six RtI recommendations that provide “look fors” in material selection.
– Using problem solving as a way to reinforce computation with whole numbers.
– Developing algorithmic proficiency
– Making sense of mathematics by reasoning through the underpinnings that justify the algorithms.
– Using frequent reviews that make connections for conceptual understanding.
– Using a number line for understanding ordinal position and relationships between addition/subtraction and multiplication/division.
– Having students verbalize their rule and/or way of thinking so that clarifications/extensions can be immediately provided.
– Distinguishing amongst Factual Knowledge (knowing that); Procedural Knowledge (knowing how); and Conceptual Knowledge (knowing what it all means).
- Numerous websites that engage students in the above. Especially (May 8, 2011), see the most recent analysis of counting and Cardinality and Operations and Algebraic Thinking (K–2) and the progression from K-2:
Additionally, view the blog from Bill McCallum that provides tools in support of implementing the CCS: http://commoncoretools.wordpress.com/
- Research reports to not do what has always been done to get students to the point of needing intervention (meaning – drill, drill, drill and expect students to repeat after you; no opportunities to communicate their thinking.)
What materials/research are you using….is it possible to share not only the materials but the results of your intervention?