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The New Zealand Ministry of Education has introduced a Numeracy Project for students aged 5-14 years in selected schools. The project encourages the adoption of flexible strategies for solving numerical problems, and discourages reliance on standard computational algorithms. One potential benefit of the project is that the methods students acquire in the project may provide a foundation for algebraic thinking through the use of quasi-variables in numerical operations. In order to evaluate this possibility, we constructed a 21-item test of numerical manipulation that required an underlying awareness of the presence of quasi-variables. The test was administered to 431 12-year-old students who participated in the project and to 468 students who did not. The test consisted of six sections, each of which examined the application of a different aspect of reasoning to numerical problems. The results showed that students who participated in the Numeracy Project solved numerical problems that required manipulation with more success than did students who had not participated in the project. This proved to be the case for three different levels of analysis: for the test as a whole, for each of the six sections of the test, and for every individual item of the test. The results were interpreted as showing that the project fostered students' awareness of numbers as quasi-variables and thus provided an early indicator of algebraic thinking.

An Algebraic Thinking Test was given to 116 students aged 12-14, at the end of each of three years. This age span crosses two levels of school in New Zealand. This test assessed their ability to represent compensation in the four arithmetic operations both numerically and with letters for variables. The analyses of these results, together with the results from separate interviews designed to report individual progress of students in the New Zealand Numeracy Project, showed that students who had developed advanced mental strategies for dealing with additive, multiplicative and proportional operations, were the students who were capable of making full use of the alphanumeric symbols of algebra. These results, taken together with earlier studies by the authors, led to a proposal for a ''pathway for algebraic thinking'' accessible to all students.

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