Math Strategies
- Manipulatives - Use number lines, number cubes, pattern blocks, etc. to model concepts. Ensure that students understand why what they are doing is correct. Do not simply teach steps in a process.
a. Example: in simple addition, the teacher could use a floor number line. The students would be the adders by standing on the first number and walking steps on numbers representing the second number in the problem. I they were asked to add 5+4, the student would start on the 5 and walk four numbers up to the answer of 9.
b. If the teacher is teaching 10’s and 1’s, he could use tens blocks and ones block to demonstrate that 10 one blocks are equal to a 10’s block. If the school does not have 10’s blocks, use sticks to represent bundles of tens and individual ones.
- Chunking and Modeling - Skill development requires breaking the task into parts and modeling. Well-structured practice should progress from the simple to the complex. We need to teach students to chunk the Math problem just as we tell them to chunk unfamiliar words.
a. Break the concept down into parts or steps.
b. Have the students chart these steps and use the chart until they are comfortable completing the problems without the chart. One example of this would be
1. PLEASE-Parenthesis
2. EXCUSE-Exponents
3. MY-Multiply
4. DEAR-Divide
5. AUNT- Add
6. SALLY-Subtract
3(4+6/2) =
The first step is to complete what is in the parenthesis.
That would include first dividing 2 into 6 and getting 3
Then add 4+3 which equals 7
Next multiply 3x7 which equals 21
- Algorithms - Explore several algorithms for calculations, including student-invented strategies. While most students will adopt the conventional approaches, exploring alternatives aides in understanding and memory.
- Estimate - Have students use estimation in the simplest problems to the most complex questions. It helps them understand the relationships between numbers and pulls them into the learning experience.
- Compare Processes - As you move to multiplication from addition, show how they are similar in concept. Do the same with division and subtraction.
- Math Families - Teach math families just like you would teach word families. It helps the students to see relationships.
- DRAW - Strategy Instruction – DRAW (Mercer, C.D., & Miller, P.S., 1992)
a. Discover the sign.
b. Read the problem.
c. Answer or DRAW a conceptual representation of the problem using lines and tallies, and check.
d. Write the answer and check.
First three steps address problem representation and the last problem is the solution.
- STAR - for older students (Maccini, P. & Hughes, C.A., 2000)
a. Search the word problem:
i. Read the problem carefully.
ii. Ask yourself questions “What facts do I know”? “What do I need to find?”
b. Translate the words into an equation in picture form:
i. Choose a variable.
ii. Identify the operation(s).
iii. Represent the problem with the Algebra Lab Gear (concrete application).
iv. Draw a picture of the representation (semi-concrete application.
v. Write an algebraic equation (abstract application).
c. Answer the problem.
d. Review the solution.
i. Reread the problem.
ii. Ask question “Does the answer make sense? Why?
e. Check answer.
- STAR Modified - from Strategic Math Series by Mercer and Miller, 1991.
Six elements used in each lesson:
a. Provide an advance organizer – identify the new skill and provide a rationale for learning.
b. Describe and model.
c. Conduct guided practice.
d. Conduct independent practice.
e. Give post test.
f. Provide feedback (positive and corrective)
- 5 Evidence Based Recommendations for Teaching Fractions - The US Department of Education's What Works Clearinghouse published specific recommendations for teaching fractions. Each recommendation is thoroughly detailed in the practice guide.
1. Build on students’ informal understanding of sharing proportionality to develop initial fraction concepts
2. Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward
3. Help students understand why procedures for computations with fractions make sense
4. Develop students’ conceptual understating of strategies for solving ratio, rate, and proportion problems before exposing them to cross-multiplication as a procedure to use to solve such problems
5. Professional development programs should place a high priority on improving teachers’ understanding of fractions and of how to teach them
