By Daniel J. Brahier
Teaching Secondary and heart college Mathematics is designed for pre-service or in-service teachers. It combines up to date expertise and study with a colourful writing kind to aid lecturers snatch curriculum, educating, and evaluation matters as they relate to secondary and heart university mathematics. The fourth version deals a stability of conception and perform, together with a wealth of examples and outlines of pupil paintings, school room occasions, and know-how utilization to help any instructor in visualizing fine quality arithmetic guide within the center and secondary lecture room.
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Extra resources for Teaching Secondary and Middle School Mathematics
His students were asked to select a real-life problem and find a function that modeled it. We can analyze the class project and student responses through the lens of the five mathematical processes described in this chapter. Students selected a function and were faced with the problem of expressing it in a variety of ways and determining how the function behaved so that they could explain it to others. As they explored the ways to write the function in a sentence, in a table, with an equation, and as a graph, they were faced with the task of representing their functions in a variety of ways and determining the strengths and weaknesses of each method of representation.
Some of these strategies include writing an equation, making a physical model, working backward, drawing a graph, making a table, and using guess and check. Reasoning: Reasoning is the mathematical process by which students seek to explain “why” something happens the way it does or “what would happen if . ” something were different in a problem. Mathematical reasoning deals with constructing proof (either formally or informally) that conjectures are true or false. Representation: Representation is the mathematical process by which students take a given problem situation and attempt to model it in a useful way that will enable them to solve the problem.
Similarly, the following three equations describe the same function: (a) y = x2 + 2x - 15 (b) y = (x - 3)(x + 5) (c) y + 16 = (x + 1)2 Although the first version is in Standard Form and communicates a y-intercept at (0, Ϫ15), equation (b) is factored to make it much easier to determine that the parabola intersects the x-axis at the points (3, 0) and (Ϫ5, 0). And although equation (b) is useful for finding the roots of the function, equation (c) may be much more helpful if one needs to know that the vertex is at the point (Ϫ1, Ϫ16) and that the minimum y-value is at Ϫ16.
Teaching Secondary and Middle School Mathematics by Daniel J. Brahier