My Angle, Pythagoras, By Julie Ellis

This paper will demonstrate the pre-service teachers’ understanding of mathematical practices as part of the Common Core State Standards in Mathematics. It will address two specific standards for Mathematical Practices, describing the essence of both and providing a description of how teachers facilitate these practices and how students are engaged in the practices.

Geometry in the early elementary grades can build on children's informal knowledge by giving them appropriate vocabulary and opportunities to practice identifying geometric shapes in the classroom and the real world.

In the essay “When Brights Girls Decide that Math is a Waste of Time” by Susan Jacoby, Jacoby claims that girls develop deficiencies during their adolescent years by not taking math or science in their high school years. It can be argued that Jacoby’s thoughts on high school girls and math are incorrect due to the sexism that takes place in her essay, the amount of inaccurate and outdated information, and her argument that math and science is highly important.

Algebra is a critical aspect of mathematics which provides the means to calculate unknown values. According to Bednarz, Kieran and Lee (as cited in Chick & Harris, 2007), there are three basic concepts of simple algebra: the generalisation of patterns, the understanding of numerical laws and functional situations. The understanding of these concepts by children will have an enormous bearing on their future mathematical capacity. However, conveying these algebraic concepts to children can be difficult due to the abstract symbolic nature of the math that will initially be foreign to the children. Furthermore, each child’s ability to recall learned numerical laws is vital to their proficiency in problem solving and mathematical confidence. It is obvious that teaching algebra is not a simple task. Therefore, the importance of quality early exposure to fundamental algebraic concepts is of significant importance to allow all

Van de Walle, J, Karp, K. S. & Bay-Williams, J. M. (2015). Elementary and Middle School Mathematics Teaching Developmentally. (9th ed.). England: Pearson Education Limited.

Part B. Describe two mathematical strengths for each student whose response indicates the need to reteach the math content.

As a student, I always enjoyed math. In high school I took all of the offered math classes, including Calculus. The first math class I took in college was a breeze, and I thought that this one would be no different. What could I learn about elementary school math that I did not already know? Contrary to my expectation, the first day of class, I learned things about math that had never been brought to my attention. This paper will discuss what I have learned about subtraction, about students, about the Common Core State Standards, and how my concept map has changed since my first draft.

The product EngageNY is an ELA and math curriculum created by the New York State Education Department (NYSED). Although it is not the adopted curriculum of this evaluator’s district, it is a resource that’s being used district wide as a key supplement in mathematics. The 4th grade math curriculum consists of 7 “module” (units) ranging from 20-40 days in length. The NYSED has converted all of the components into free, downloadable resources (including a pacing guide), which has made them a convenient and comprehensive resource.

Standard: A1.4. Linear functions, equations, and inequalities (Algebra) Students understand that linear functions can be used to model situations involving a constant rate of change. They build on the work done in middle school to solve sets of linear equations and inequalities in two variables, learning to interpret the intersection of the lines as the solution. While the focus is on solving equations, students also learn graphical and numerical methods for approximating solutions to equations. They use linear functions to analyze relationships, represent and model problems, and answer questions. These algebraic skills are applied in other Core Content areas across high school courses.

Geometry and Algebra are so crucial to the development of the world it is taught to every public high school in the United States, around 14.8 million teenagers each year (National Center for Education Statistics). Mathematics is the engine powering our world; our stocks, economy, technology, and science are all based off from math. Math is our universal and definite language “I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings.” (Rene Descartes, 1637).

After becoming dissatisfied with his life, a triangle makes a visit to a local shapeshifter to add another angle to his shape in hopes he will become more interesting. However, one more angle proves to not be enough for the triangle who becomes greedy and wants more and more angles. Readers will watch the triangle change into a quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, and finally a decagon before he finally realizes he was perfect as he was and wants to become a triangle again.

In my peer-tutoring class, I have noticed that gender differences play a significant role in the way students behave. The class is composed of more boys than girls and this has an effect on gender differences in the classroom. The article “Math Class is Tough”: The Role of Mindset in Middle School Girls’ and Boys’ Math Achievement” written by Erika Milligan, states that boys have a higher interest and enjoyment in math. Looking at my peer-tutoring class, I have seen that boys are more engaged to learn than girls. For instance, one of the male students in the class decided to stay after-school and ask more questions to the teacher, Ms. Punj, about the topic because it intrigued him. I feel like the greater population of boys in my peer-tutoring

To complete my mathematical requirement for the BS Healthcare Management Program, I am required to take Math 240 College Algebra. This course introduce students to major concepts of college level algebra. The course starts off with simple concepts such as sets and numbers, but quickly move on to intermediate algebra topics that emphasize concepts most often used in Computer Science. Students will also gain extensive knowledge in evaluating and manipulating expressions, equations, probabilities and logic. Mathematics many not be an easy subject to understand, but it can lead to better jobs and more money. While jobs and their specific skill-sets may change overtime, mathematics will not ( ).

Based on several studies, one of the best ways to understand mathematical ideas and apply these ideas is through the use of manipulatives. Students explore these manipulatives, however, it is important that they make their own observations. The teacher then should model and show how to use the materials and explain the link of these materials to the mathematical concept being taught. Schweyer (2000) stated that students learn best when they are active participants in the learning process where they are given the opportunity to explore, assimilate knowledge and discuss their discoveries.

Throughout the paper, we will compare a novice and expert responses to certain mathematical concepts in order to recognize the different techniques they practice. We will interpret the procedures they use to make connections and to check their level of comprehension on a specific mathematical concept. An expert typically has a broad interpretation and connects their ideas to more concepts, in this case introducing graphs, definitions, formulas and physics whereas the novice will have useful knowledge about the subject without making as many connections. The expert is Mr. Thilina Shihan, a doctoral student in Physics with a Masters and Bachelors in Math and Science whereas the novice, Guillermo Vasquez is a Computer Science and Physics Major. In the clinical interview, if mathematical concepts are introduced by gradually increasing the difficulty of the questions, then the comprehension level between a novice and an expert will be significantly visible when comparing their responses.