Posted by: Gary Ernest Davis on: June 8, 2012

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Educators of pre-service elementary teachers face a constant challenge: their students’ limited understanding of what constitutes mathematics and a mathematical approach to problems. Pre-service elementary teachers’ attitudes to mathematics are generally instrumental, viagra focussed on formulas and correct answers. Here are some illustrative remarks from our students:

- “… I was under the impression that finding a formula to solve a problem was, doctor in reality, treatment the answer to the problem.”
- “I was used to having a formula and all I cared about was getting the right answer.”
- “… we all came in with our preconceived notions of mathematics as simply finding a formula and getting the right answer …”
- “All throughout school, we have been taught that mathematics is simply just plugging numbers into a learned equation. The teacher would just show us the equation dealing with what we were studying and we would complete the equation given different numbers because we were shown how to do it.”
- “As long as I could remember I have seen math as getting the right answer, and that being the only answer.”

What is the alternative to training (we refrain from writing “educate”) elementary teachers who fail to see algebra as having meaning, but who know how to push syntax around? We suggest these experiences described in this paper are repeatable and can be taken as the basis for a set of teaching experiences that help place pre- service elementary teachers in the right ball-park for teaching early algebra. In summary, pre-service elementary teachers can become more effective teachers of early algebra by:

1. Facing their unspoken attitudes to mathematics being all about using formulas to get correct answers.

2. Seeing children solve problems that they themselves struggled with.

3. Seeing and hearing other pre-service teacher’s insights into mathematical solution processes and thoughts.

4. Being asked to continually and actively seek out connections.

5. Practising interpretation of syntactical forms in more concrete terms.

6. Reading and discussing mathematics education literature that speaks to their learning styles and content knowledge.

7. Constantly adding to their content knowledge and relating it to previous mathematical knowledge,

8. Relating their learning to that of their prospective students.

A tall order? We think it is achievable:

- “This process of teaching gives the student a true understanding of mathematics. Not only did we get the answers, we made connections with other ideas. That is a true way of learning mathematics and what it means. All the learning I accomplished was taught relationally. Math isn’t just about getting an answer.”
- “From the beginning of the semester on, problem solving was the main source of working though class material. From problem solving came the goal of building connections. Connections to powers of two and subsets came through the use of the concrete manipulatives to assemble towers.”
- “Without a solid understanding of the concept behind the algorithm, a students hasn’t really learned anything, just memorized an equation.”
- “I have learned that mathematics is indeed a series of interrelated ideas. I was challenged to extract these connections from our daily work while acquiring new skills in mathematics.”
- “If I had been asked to make these connections back in high school, I probably could not have done it. I succeeded at these exercises because of our group discussions and Jim’s recognition of the 1, 4, 6, 4, 1 pattern of Pascal’s triangle.”

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