# Mathematical Musings | Nick Wasserman

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## Understanding of the reals: 0.9999…. = 1

Many people, including mathematics teachers, wrestle with the claim that 0.9999... is the same as 1. Some think of it as incorrect - the former is something just slightly less than but never "reaching" 1. Others perhaps follow the proof but think of it as mathematical "hocus-pocus" - the same as those "proofs" demonstrating that …

Posted 50 months ago by

I am definitely biased. As a professor of mathematics education, I have fairly strong opinions about the mathematical education of children. Two of perhaps the most current, publicized, political, and divisive issues around math education in the United States are the Common Core Mathematics Standards (CCSS-M) and Khan Academy. Both have certainly entered my …

Posted 51 months ago by

## Assumptions in Geometric Probability  ☆

Geometric probability makes use of measurement to determine probabilities. For example, the probability of hitting a bullseye could be found by computing the ratio of the area of the bullseye (4π in^2) and the area of the entire dart board (64π in^2), which is 4/64 = 0.0625; or the probability of breaking a stick randomly …

Posted 58 months ago by

## Inappropriate Trimming  ☆

One of the things that makes mathematics as a discipline relatively unique is the constant progression of ideas - that is, mathematics from elementary school onward continues to build on previous developments. As a teacher, this means that one of the aspects that mathematics teachers in particular need to attend to relates to the future …

Posted 61 months ago by

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## Functions, Bijections, and Combinatorics  ☆

At times, studying general definitions of functions and particular classifications of functions (e.g., bijective, surjective) can seem tedious. As a secondary teacher, the functions we consider nearly always map real numbers to real numbers, which can make it difficult to be motivated to push past this into the abstract. While bijections have implications for infinite …

Posted 66 months ago by

## Pyramid Volume in SketchUp  ☆

Frequently, students' first instinct about the volume of a pyramid is that is must be 1/2 the volume of a prism. While there are many ways of helping students understand the correct relationship, including conducting an experiment to see how many times "filling" a pyramid, say with rice, is needed to fill a prism (with …

Posted 69 months ago by

## Unrolling Circles in GSP  ☆

From my own experiences, students often struggle to understand what circumference means as a measurement. (Such difficulties are also reiterated on student's performance on standardized test questions.) In order to help their conceptualization, I created a GSP document that allows students to roll and unroll a circle, keeping visual track of its length. The aim …

Posted 70 months ago by

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## A Mathematical Group  ☆

While many future mathematics teachers may never step foot in an abstract algebra course, those that do are often initially presented with the axiomatic definition of a group (closure, associativity, identity element, inverse elements) and then presented with some common examples of group tables - frequently small finite sets - to illustrate the impact of …

Posted 70 months ago by