Thinking, Fractions And Decimals

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

Mathematics has become a very large part of society today. From the moment children learn the basic principles of math to the day those children become working members of society, everyone has used mathematics at one point in their life. The crucial time for learning mathematics is during the childhood years when the concepts and principles of mathematics can be processed more easily. However, this time in life is also when the point in a person’s life where information has to be broken down to the very basics, as children don’t have an advanced capacity to understand as adults do. Mathematics, an essential subject, must be taught in such a way that children can understand and remember.

Another idea to improve mathematics performance in elementary level is to encourage the student to link the existing knowledge and the new knowledge effectively while working math problems/examples. A worked example is “a step-by-step demonstration of how to perform a problem” (Clark, Nguyen, & Sweller, 2006, p. 190). This will prepare the students for similar problems in the future as they bridge the connection between the problems and the examples. In many cases, students are encouraged to link the informal ideas with the formal mathematics ideas that are presented by the teacher to be able to solve problems. When students examine their own ideas, they are encouraged to build functional understanding through interaction in the classroom. When students share among themselves on differences and similarities in arithmetic procedures, they construct the relationship between themselves hence making it the foundation for achieving better grades in mathematics. Teachers can also encourage students to learn concepts and skills by solving problems (Mitchell et al 2000). Students do perform successfully after they acquire good conceptual understanding because they develop skills and procedures, which are necessary for their better performance. However, slow learning students should engage in more practice

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

Objective: Student will inform audience on how to add and subtract decimals with and without regrouping.

In the article, “Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities,” the authors believe that number sense is as foundational to learning mathematical concepts as phonemic awareness is to reading. Gersten and Chard’s theory is based on “conceptualization of constructivism as a joint approach” where students learn conceptually with a focus on terminology and explore operations using a variety of methodologies. Furthermore, the authors support the merging of number sense activities with fact families’ automaticity activities.

In the fifth grade, students move on to greater decimal places such as the thousandths place. This can get confusing for some students because we are mainly only teaching them to use this place value when being very specific. To represent this in the classroom it is beneficial to use a thousandths grid. Each grid is made up 100 sets of 10 rectangles. Another way to teach thousandths place is by using base ten blocks. It is important though when using

Mini-Lesson that focuses multiplying a fraction by a whole number using an area model. To start the lesson will make a connection between whole number multiplication and repeat addition, multiplication

In math we are supposed to learn or memorized plenty of formulas and compute them. In the video Why is Math Different Now by Dr. Raj Shah he talks about “how in math we give children standard algorithms, but we don’t understand where these numbers are coming from” (Shah). He provides an example by using two digit numbers multiple by two digit numbers. In this example he is saying how children do not understand the place values and where the extra zero is coming from, but in this new way of doing multiplication it shows the place values and where the zeros are coming from. This helps children understand the problem and not just getting the right answer like we have been doing in the past. The old method does not let students think freely or creatively. This approach helps children understand the number and just not worry about getting the right

Through step by step lesson plans, Alan Walkers’ Multiplication in a Flash uses specific tricks and mnemonic techniques to teach the two, five, and nine times tables to students. It also has quick lessons to teach the zeros and ones. This program uses pictures, stories, and activities to teach the remaining multiplication

Teachers are encouraged to teach their students using the “Big Ideas” . Typically in the past, when a teacher taught measurement he or she would think of teaching how to use a ruler. In today's classroom, teachers need to encourage their students though the use of standards and non-standard forms of measurement. Teaching them to focus on zero points, partitioning, and counting units. The presenter even said, “If you don't teach them to contrast the big ideas then they will never take certain things into consideration.” For example, in the podcast, the teacher had the students use their feet to measure a four square. The children had to make the connection that not everybody's feet are the same size and therefore a standard unit of measure was needed. And so then at this point, the ruler was introduced to the students, as a standard form of measurement. Deborah Junk, and the others contributing to this podcast said teachers must consider teaching students to transition from counting to measuring, translate these ideas into construction of rulers, translate the understanding behind their rulers to standard measure. Teachers get students to pose questions based off their learning. A teacher develops a deep understanding of the big ideas. In the fourth and fifth grade classroom this translates to being able to solve problems involving

The article, “Representations in Teaching and Learning Fractions,” explains the concept of teaching and learning fractions using representations. One of the Common Core Concepts that is supported in this article is CCSS.Math.Content.3.NF.A.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram (Grade 3). Watanabe talks about using linear model to represent fractions. The article discuss about how number lines do not help children comprehend fraction as numbers but only makes sense to those who already know fractions. Watanabe says that some teachers think that number lines are “useful tools to teach children relationships between whole numbers and fractions.”

In light of the recent changes to the mathematics curriculum, reflect on the key issues surrounding mathematical subject knowledge for teaching.

During the sixty-minute lesson, the students will determine one, ten, or one hundred more or less than a given number. This lesson teaches students how to determine one, ten, or one hundred more or less using the DWS (draw it, write it, solve it) strategy, a place vale chart, and expanded form (391, expanded form = 300+90+1). This lesson builds on the student’s prior knowledge of place value disks, and helps them to make connections between a representational drawing and expanded number form. The place value chart and place value disks are used to help students visualize one, ten, or one hundred more or less than a number in connection to place value understanding (ones, tens, hundreds place). The goal of this lesson is for students to apply their knowledge of place value understanding in order to determine one, ten, or one hundred more or less of a given number, using the lesson strategies to help them explain their

“Algorithms are elegant strategies for computing that have been developed over time” (Van de Walle, Karp, & Bay-Williams, 2013). All these clever methods permit students to perform the different operations in a successful manner. However, to use these algorithms, students must possess a deep understanding of how the steps relate to other operations and patterns. In the case of division, students can implement the unknown side method, unknown group size method, standard algorithm, and the scaffold algorithm to solve division problems. Provided in the diagrams below are examples of each method or algorithm.