## Strategies in Teaching Math

(Research Starters)Math instruction is generally broken down into five math strands: numbers and operations; algebra; geometry; measurement; and data analysis and probability. Though concepts are more advanced than others, even the youngest children can learn basic math strategies that will prepare them for future learning. Students also learn problem solving as a way to think critically about and integrate math strategies. Teachers should use a variety of instructional methods to keep lesson interesting and fun for all students, and to ensure that their lessons are reaching students of all learning styles. Assessment and evaluation can be done through tests and quizzes as well as one-on-one conferences and journal writing

Keywords Algebra; Curriculum; Data Analysis; Formative Assessment; Geometry; Journal Writing; Learning; Lesson Planning; Manipulatives; Math; Measurement; Numbers; Probability; Problem Solving; Structured Learning; Word wall

### Overview

Teaching math is an important job for instructors who work with learners of any age. The goal of the math teacher shouldn't just be for the student to understand the concept or strategy being taught, but also for the students to be interested in the learning process. Ideally, students should find mathematics both intriguing and enjoyable.

Even the youngest children seem to be hard-wired to do math and be interested in numbers. From their earliest days, babies seem to have a basic understanding of mathematical concepts like adding and subtracting. Watch two objects move on a screen in front of him or her, a baby's face will often register surprise when another object is introduced, indicating a simple understanding of addition. Children may be ready to learn math at a very early age, and, when they are given opportunities, will usually be interested in learning (Sarama & Clements, 2006). Teachers are challenged to maintain that interest throughout the strands of the math curriculum.

### Math Strands

The basic math curriculum is usually thought of in five strands. These components include: numbers and operations; algebra; geometry; measurement; and data analysis and probability (Lemlech, 2006).

### Numbers

The numbers and operations strand includes the number systems and how they are used. Strategies and techniques for computing with numbers are taught at this stage of learning, beginning with basic counting and advancing to activities that involve comparing numbers and sets. Fundamental addition and subtraction facts are also part of numbers and operations, and methods of computing are introduced and refined as well.

Children need to understand that, just as the letters of the alphabet represent parts of words, numbers represent ideas. When they have grasped this concept, they will be able to work with the counting process more readily (Lemlech, 2006). To work with young learners at this stage, teachers can instruct children to sort objects by shape and size, classify objects by their different characteristics, and fit objects inside of other objects. Children can also be taught to perform basic balancing activities (Lemlech, 2006). In their discussions with preschool children, teachers should also incorporate the use of small numbers. Instead of saying, for example, that there are chairs available, teachers can be more instructive by saying that four chairs are available. Inserting numbers across the curriculum will help children learn to attach meaning to them (Sarama & Clements, 2006).

As numbers become more a part of the curriculum, so should counting. Teachers can make counting part of the school day by inviting students to count small numbers that are part of their daily routine, like the number of doors they pass as they go out to the playground, or steps it takes to get to the front of the classroom. Later, they can instruct children to compare numbers. They can ask students to look at a pile of pencils and determine if there are enough for each child in the classroom. Children can also do a one-to-one match with items from two piles (e.g., plates and cups, pencils and paper) to figure out if there are enough of each group to form pairs (Sarama & Clements, 2006).

When students are under the age of six and still at a preoperational level of thinking, they often don't realize, for example, that despite the unfamiliar ordering of a specific set of numbers (e.g., {3.1.2}, {2,1,3}), the numbers themselves are still the same. Students will often have to count the numbers ordered in the original, left-to-right way and the new right-to-left way to discover that the numbers are the same even when listed both ways. As students develop, the concept of reversibility will begin to seem logical and automatic (Lemlech, 2006).

### Algebra

The study of algebra entails working with the language of variables. Important skills typically taught in the algebra strand are: performing operations within equations containing variables; working with functions; and manipulating symbols within equations. Even the youngest students can understand basic algebra. Number patterns and sentences using objects and manipulatives, for example, can help preschool students begin to think algebraically. Arranging blocks and objects in a simple pattern and inviting students to say which block would logically be placed next helps students begin to think algebraically (Lemlech, 2006).

### Geometry

In the geometry strand, students work with space and form to learn how these concepts are linked to numbers and math. Students are taught about figures, lines, points, lanes, polygons, geometric solids, and three-dimensional space. In geometry especially, manipulatives help students explore and discover; young students will likely grasp geometric concepts more clearly when links to real-life experiences are stressed (Lemlech, 2006).

Basic geometry concepts can also be introduced to young learners. Matching shapes is interesting and fun for preschool children, and putting shapes together within a puzzle is one way for children to learn how certain shapes can work together. Teachers can cut colorful basic shapes from construction paper and encourage the children to create pictures and then talk about what they have made (Sarama & Clements, 2006).

### Measurement

Since measurement is part of everyday life, it is a key strand in teaching mathematics. Within the measurement strand, students learn to gauge capacity, distance, and time as they are taught about units of measure, estimation, and the nature of measurement. Students should be encouraged to use an assortment of units of measure to understand the importance of using common and accepted units of measure. Estimation and approximation are also a part of this strand of math (Lemlech, 2006).

### Data Analysis

The data analysis and probability strand involves teaching the students how to plan and collect data, organize and infer conclusions from what they have collected, and share what they have learned. As with other mathematics strands, even very young children can gather and organize data. They can collect information about the color of leaves, how many birds are seen outdoors at certain times of the year, or how many hours of television people they know watch each day. Students can attempt to solve science, health, and social studies problems with the data they glean from themselves and their family members. In the process, they will reinforce counting techniques as they organize and interpret data (Lemlech, 2006).

### Problem Solving

Problem solving is an integral part of every strand of mathematics. When teaching math, instructors must be wary of introducing problem solving as simply another basic skill which can be solved in a step-by-step fashion. Many students work through problems without much thought, or by using a rule they believe the problem follows. If they aren't sure...

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