Mon 22 Mar 2010
Preparing Elementary Students for Success in Algebra
Posted by Tia under Blog
No Comments
Mathematics curriculum in elementary grades must include much more than teaching the four operations and isolated units on fractions, decimals, percentages, and geometry. The greatest challenge is that many teachers of K-5 do not themselves have a strong foundation in math because their teachers in turn did not. It is time to break that cycle and seek out new understandings in mathematics and learn how intricately connected are these isolated math subjects.
The Portland Public School District currently adopts Investigations in Number, Data, and Space for its K-5 graders and Connected Mathematics 2 for its 6-8 graders. While there is much controversy surrounding the benefits and detriments of various mathematics curricula, the focus of this article is how teachers, parents, board members, tutors and other educators of Portland’s children can best prepare elementary students for algebraic success in middle school and beyond. The National Council of Teachers of Mathematics’ (NCTM) reported recently that overall, high school students are not achieving adequate levels of success in algebra. As a result there is a push for improving algebraic instruction at the middle school level. I further assert that algebraic concepts can and should be addressed at the elementary school level. NCTM lists four Pre-K-12 algebraic understandings, that students:
- Understand patterns, relations, and functions
- Represent and analyze mathematical situations and structures using algebraic symbols
- Use mathematical models to represent and understand quantitative relationships
- Analyze change in various contexts
The Connected Mathematics 2 website from Pearson Publications states about algebra that “variables are not letters that stand for unknown numbers. Rather they are quantitative attributes of objects, patterns, or situations that change in response to change in other quantities.” Algebraic skills addressed and emphasized in the Connected Math 2 curriculum include the following skills and understandings gleaned from their website, that students:
- Represent and interpret graphs
- Understand and use the commutative, distributive and inverse properties
- Understand and use exponential relationships
- Develop rules, procedures and formulas
- Estimate and judge accuracy of answers, provide proof of reasonable solutions
- Find missing factors and addends
- Understand relationships among variables
One important concept to focus on in the elementary classrooms to develop algebraic reasoning, is the mathematics of change. Teachers can use growth and change in plants, pattern blocks, or similar tools to help students learn about constants and variables, observe how the variables change, discover the pattern of change, represent and analyze those patterns. Growth problems can also teach exponential relationships. Teachers should often use missing addends that are not at the end of the equal sign in teaching the four operations. For example, ⬶ x 8 = 32. This will help students understand inverse properties, how division and multiplication are related as well as addition and subtraction. Constructing and deconstructing two and three digit numbers helps students understand commutative and distributive properties. Mental math problems in 2-5 minute increments are a great use of stagnant time in school and encourage children to be quick thinkers and adroit problem solvers. Using a scale for weighing objects will help younger students better understand equalities. Teachers should be sure to use weights and other forms of measurements, then have students write out the equalities in an equation (2 blue Legos=5 yellow Legos, 1g + 1g + 1g = 3g) Using multiple numbers on each side of an equation will help children understand the concept of equalities. For example 17-5=6+6 (True or False?). Also use missing addends such as 3x⬶=14+7. When teaching fractions, decimals and percentages, teachers can use ratios and equivalent fractions to further aid students in understanding relationships among variables. An important concept is to understand that a number can be equal to another number that does not look the same. For example: 3/9=1/3. Students should understand this on a conceptual level with the help visual aids such as pattern blocks, Cuisinart rods, or similar tools, rather than memorizing the rules on how to find the greatest common factor.