Making Sense Book Report

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.

The purpose of the study is to identify how varying ways of knowing mathematics manifests in the use of the core practice of facilitating classroom discourse. I am interested in better understanding how teachers use their mathematical knowledge for teaching to facilitate meaningful discourse. Gaining greater understanding it this area will aid in assisting teachers in developing the skill of facilitating meaningful discourse. The ability to engage students in mathematical discussions that enhance student learning has continued to be a topic in mathematics education and is viewed as a major component of mathematics education reform. It is vital that teachers, novice and experienced, develop the skills necessary to create a learning environment

It also requires the student to understand approaches to problem solutions utilized by other students and being able to provide peer feedback. Students should be introduced to the use of mathematics to: organize data, solve problems applicable to their life, and understand the world around them. This approach makes the subject both interesting and enjoyable. The use of these strategies is addressed in the next standard “#4 Model with mathematics” (Academics), which helps the student to make connections, surpass procedural knowledge and gain a conceptual understanding of a

How are your lessons designed for student learning of mathematical concepts, procedures/algorithms, and mental math strategies through problem solving?

The Case of Randy Harris describes the lesson of a middle school mathematics teacher, and how he uses diagrams, questions, and other methods to guide his students to a better understanding. Throughout his case study, Harris’ methods could be easily compared to that of the Effective Mathematics Teaching Practices. There are eight mathematical teaching practices that support student learning, most of which are performed throughout Randy Harris’ lesson. Harris didn’t perform each teaching practice perfectly, despite doing the majority of them throughout his lessons. The following are examples of how Randy Harris implemented the eight mathematical teaching practices into his lesson, and how the ones that were neglected should have been

The primary goal of the lesson sequence was to actively engage students through fostering problem solving skills and develop conceptual understanding about mathematics. Consequently a range of authentic learning experiences that aimed to actively engage learners through the use of real life contexts, concrete materials and peer collaboration was incorporated in the lessons. The purpose of designing authentic learning experiences was to enthral students in true mathematical problem solving. Fisher, (2005) supports this theory by stating ‘The true use of maths is seen in its application to real-life problems. The activities throughout the lesson plan were intended to support students in actively constructing knowledge by completely immersing students in relevant and authentic learning experiences to become an expert on the content.

There are several parallel thoughts concerning the mathematical learning process. NCTM Standard 1: Mathematics as Problem Solving outlines the expectations for students to refine their method of problem-solving by investigation and integration of

Students will be encourage on using multiple ways to solve the math problems. Each student will have different preferred method so after trying solving them in different ways, each student will find out the most appropriate method for them, the one that they like most, take shorter time and more accuracy than other methods.

As a result of implementing any of the ten lesson plans, the students will learn about quantities and their relationships. Moreover, the students will use their curiosity to explore and learn about the world around them. For example, they can learn about how and why leaves change colors. As a result of developing and implementing this artifact, I learned that educators need to ask and respond questions to help foster students’ inquisitiveness and scientific thinking. I also learned that teaching mathematics can be done through interactive activities, and not through hand outs. To improve these lesson

Their 2000 publication, the Principles and Standards for School Mathematics, is still prevalent. This document, setting forth ten guidelines for improving math education, refined, extended, and replaced NCTM’s earlier recommendations. Not only does the Principles and Standards for School Mathematics address five important content areas, it also establishes five important mathematical processes deemed necessary in quality education, like problem solving, reasoning and proof, communication, representation, and connections. When it comes to making connections, NCTM further asserts that instructional programs from prekindergarten through grade 12 should enable all students

Aharoni states that it is difficult to understand an individual’s lack of understanding if they themselves understand the topic. Another difficulty of teaching relates to the idea that children think differently. It is concluded that good teachers must find ways to connect with how their student thinks—more specifically, connect with their inner child. Another topic discussed in this section relates to the idea of the being the mediator of information to their students and examples of how to mediate young students are presented. The final topic presented examines the use of calculators and other aids in the field of math, and their subsequent impact on knowledge retention and complacency in mathematics. Reliance on calculators grows as children move forward in math and elementary concepts learned in the beginning of their journey in math are forgotten. The negative impact of student reliance on calculators makes it difficult for children to move forward in advanced math since they may not understand basic calculations—steps cannot simply be bypassed in

What does “best practice” look like in the mathematics classroom? As the focus of math changes students are asked to develop their mathematical thinking rather than their calculating skills. “While math traditionalist are correct that it is beneficial to memorize formulas, facts, and algorithms, the math reformists emphasize the need for students to have avenues such as journals, portfolios, or projects to demonstrate their understanding” (Kostos, Shin, 2010). As a result, students are asked to become critical thinkers and problem solvers.

When teaching mathematical concepts it is important to look at the big ideas that will follow in order to prevent misconceptions and slower transformation

In today’s society mathematics is a vital part of day-to-day life. No matter what a person is doing at home or at the workplace, he/she is constantly using different mathematics skills to simply function. Then what does this mean for mathematics education? When someone needs to utilize a skill every day then he/she needs a strong background in the skill. Therefore, today’s students need more than a just a working knowledge of mathematics or enough knowledge to pass a test. Today’s students need to understand how mathematics works and how to utilize mathematics skills in the best way possible.

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.