By Sergei Abramovich

ISBN-10: 1611227844

ISBN-13: 9781611227840

ISBN-10: 1612090311

ISBN-13: 9781612090313

This publication addresses middle innovations via the convention Board of the Mathematical Sciences - an umbrella company together with 16 expert societies within the usa - concerning the mathematical education of the academics. based on the Board, the concept that of a capstone direction in a arithmetic schooling software contains academics' studying to exploit usually to be had academic software program with the objective to arrive a definite intensity of the maths curriculum via competently designed computational experiments. In flip, the suggestion of test within the educating of arithmetic units up a course towards bettering the 'E' section of the lecturers' literacy within the STEM disciplines. This publication discusses studies in instructing a computer-enhanced capstone direction for potential lecturers of highschool arithmetic.

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**Extra info for Computer-Enabled Mathematics: Integrating Experiment and Theory in Teacher Education (Education in a Competitive and Globalizing World)**

**Example text**

9(n 1) 9n 8(n 1) 8n Therefore, inequalities (27) can be replaced by inequalities (26). This completes the proof. Proposition 21. The series v(n) diverges. n 1 2 2 1 . 9 n 1 n n 1 9n Proof. It follows from Proposition 17 that v(n) n 1 7 In the words of Langtangen and Tveito (2001): ―Much of the current focus on algebraically challenging, lengthy, error-prone paper and pencil work can be significantly reduced. The reason for such an evolution is that the computer is simply much better than humans on any theoretically phrased well-defined repetitive operation‖ (pp.

78... , demonstrating an extremely slow divergence which can even be taken for n 1 convergence if approached from a computational perspective alone. More information on the divergence of the harmonic series can be found in Chapter 6. Proposition 15. The series q ( n) converges to the number 2. n 1 Proof. Due to (21), q(n) n 1 n 1 1 q ( n ) 2 n 2 2 n2 and, thereby, due to Proposition 14, we have . However, noting that q(n) 1 2 1 1 2( ) tn n(n 1) n n 1 1 2 . 14.

For what values of parameter c does equation (1) have two real roots? Reflections. 25. However, the last inequality can be directly derived from Figure 1 if one interprets the roots of equation (1) as the x-intercepts of the locus and the horizontal line c = constant. 25. 5. Exploration 2. For what values of parameter c does equation (1) have two positive roots? Reflections. Note that in order to answer this question through the locus approach, one does not need to construct a series of graphs y = x2 + x + c for different values of parameter c (using graphing technology) or to carry out transformation of inequalities involving radicals Algebraic Equations with Parameters 39 that result from the use of the quadratic formula.

### Computer-Enabled Mathematics: Integrating Experiment and Theory in Teacher Education (Education in a Competitive and Globalizing World) by Sergei Abramovich

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