By Sergei Abramovich

This booklet addresses middle concepts through the convention Board of the Mathematical Sciences - an umbrella employer such as 16 expert societies within the usa - in regards to the mathematical training of the academics. based on the Board, the concept that of a capstone direction in a arithmetic schooling application comprises lecturers' studying to exploit normally on hand academic software program with the aim to arrive a undeniable intensity of the maths curriculum via safely designed computational experiments. In flip, the idea of scan within the instructing of arithmetic units up a course towards improving the 'E' section of the academics' literacy within the STEM disciplines. This ebook discusses reviews in instructing a computer-enhanced capstone path 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**

This parabola can be used as a tool for answering many questions about the roots of quadratic equation (1) without having a formula that solves this equation. In fact, the very formula can be derived from the inquiry into the properties of the locus. Following are examples of eight explorations that can be carried out in the context of equation (1) using the locus approach enhanced by the GC. Exploration 1. 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.

Then lim v(n) 0 n Proof. According to formulas (13) and (15), v ( n) (n 1)(4n 2 8n 3) 4n 2 8n 3 . 3(n 1)3 (3n 1) 3(n 1) 2 (3n 1) Therefore, 8 3 ) 4n 8n 3 1 n n2 0 . lim v(n) lim lim n n 3( n 1) 2 (3n 1) 3 n n3 (1 1 )2 (3 1 ) n n 2 Let n 2 (4 The Multiplication Table from an Advanced Standpoint 35 Proposition 20. On an odd size checkerboard, the sequence v(n)satisfies the inequalities 2 5 v ( n) 9n 8n (26) for all n = 1, 2, 3, … . Proof.

In turn, 1 3 2 3 2 where n – 1 and n + 1 are, respectively, the reciprocals of the reciprocal of the average of two numbers is called the harmonic mean of these numbers. This property of the reciprocals of counting numbers explains the term harmonic series. In n general, the fraction is the harmonic mean of the numbers 1 1 1 ... , n . Proposition 10. The harmonic series 1 n diverges. In other words, the infinite sum of n 1 (monotonically decreasing) reciprocals of counting numbers is infinite.