Strategies in Teaching Math

Strategies in teaching math encompass various methods and instructional approaches aimed at fostering students' understanding and appreciation of mathematical concepts. The math curriculum typically includes five strands: numbers and operations, algebra, geometry, measurement, and data analysis and probability. Early exposure to mathematical ideas can ignite children's interest, as they often show a natural curiosity about numbers from a young age. Effective teaching strategies involve using diverse instructional methods to engage all learners, catering to different learning styles and preferences.

Incorporating problem-solving as a central element is crucial, as it helps students think critically and apply mathematical concepts in real-world scenarios. Teachers can enhance learning by utilizing manipulatives, cooperative learning groups, and structured learning sessions, which encourage collaboration and hands-on experiences. Formative assessments, such as journals and one-on-one conferences, can provide valuable insights into students' understanding and progress. Ultimately, the goal of math instruction is not only to impart knowledge but to make the learning process engaging and enjoyable for students, fostering a positive attitude toward mathematics.

Published in: 2021

By: Ludwig, Susan

Subject Terms

Strategies in Teaching Math

Abstract

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

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. Watching 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 & Operations. 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 do not 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 & Probability. 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 are not sure of or have forgotten the rule, students are often not able to solve the problem on their own. In many cases, problem solving in math has evolved into exercises in computation rather than real approaches to solving problems with numbers (Dolan & Williamson, 1983).

To help them be successful in mathematical problem solving, teachers must show students how to work with strategies. These strategies can ensure that students know what solution they are looking for, and the most direct routes they can take to reach this solution (Dolan & Williamson, 1983). Students who master problem solving strategies will generally learn higher-level math content with greater ease than students who struggle with learning these strategies (Lemlech, 2006).

Even preschool children can engage in some basic problem-solving experiences. Showing young students a pair of blocks and then hiding one is a good introduction to the concept of subtraction, and also invites the students to solve a problem. After one block is hidden, the teacher may ask the children how many blocks have been removed. The children can be encouraged to discuss how they were able to figure out that it was one block that was removed from the group. The teacher can also invite four students to stand in front of the classroom and then ask one child sit down. The children can call out how many of their classmates were originally standing in front of the class, how many are presently standing in front of the class, and how many were asked to sit down (Sarama & Clements, 2006).

Applications

Instructional Methods. With all ages and grade levels, teachers should vary instructional methods. Not only does variation help teachers reach all students, but eliminating stagnant classroom routines also helps motivate learners. Students have more fun when, walking into a classroom, they do not know if they will be participating in a hands-on activity, discussion, project work, or other learning scenario. (Ellis, 1988).

Formative assessment is the best way to begin a unit. By assessing students before learning begins, teachers can determine what students already know about a particular skill or strategy, and plan their instruction accordingly. The information gleaned from a formative assessment of students helps drive the classroom instruction (Minton, 2007).

As with teaching other subjects and strategies, planning a math lesson takes a purposeful approach. It is best to first set the stage by telling students the objective of the day's lesson so they will understand what they are building up to. Teachers should provide directives about how they plan to reach the day's goal and then provide a context for learning. They can illustrate the concept or particular skill through an assortment of activities, like discussions, or tools like manipulatives and visuals. Teachers should ask questions throughout the lesson to promote reflective thinking, and then clarify any extended expectations (Ellis, 1968).

Whenever possible, teachers should link mathematical concepts to other subject areas and realistic contexts with which students are familiar. Doing so will enhance students' understanding of and interest in math concepts (Lemlech, 2006).

Structured Learning. Many teachers use structured learning as a way to teach mathematical concepts. Structured learning is an instructional method in which the teacher works with the class as a whole to explain a concept or strategy, give instruction, provide demonstrations, and check for understanding. The teacher's goal, aside from helping students understand a particular concept or strategy in math, is to keep the students on task during the structured learning time. There is a strong correlation between the amount of time students are on task and the amount of material they are able to learn. This option, called the opportunity-to-learn variable, is especially important when teaching and learning math. Teachers should be aware of the importance of the opportunity-to-learn variable and take advantage of this research (Ellis, 1988).

Cooperative Learning Groups. Alternatively, teachers may choose to work with small groups or form cooperative learning groups. Students may be more apt to share their own problem-solving ideas and strategies when they are working within a small group of their peers rather than with the entire class. In small groups, students may also feel more comfortable explaining their ideas in their own words rather than attempting to use the "correct" vocabulary. In this way, small groups may foster more positive attitudes about learning and facilitate understanding among group members (Lemlech, 2006).

Class Discussion. Whole class discussions can foster students' understanding of certain concepts by enabling them to listen to others' ideas about how they problem-solve. Students who may not have originally understood the concepts, may find their peers' explanations helpful. By asking students how they solved or approached a particular problem and came to their solutions, students learn to verbalize the problem-solving phase. Since students will approach problems in different ways, students can discuss and learn the most efficient strategies to solving problem types (Lemlech, 2006).

Communication and discussion are vital factors to students' mathematical understanding. It is important for teachers to help the students engage in rich and relevant discussions as they review and discuss strategies. Even those students who do not participate in class discussions will benefit from the reinforcement they provide (Lemlech, 2006).

Teaching Vocabulary & Symbols. Math vocabulary can be confusing to learners of any age. Words that have one meaning in everyday English (e.g., squared, root, product) can have a different mathematical definition. It may also be difficult to define words within their mathematical context. Some mathematical words may even have different definitions within different mathematical contexts (Kenney, 2005).

Similarly, symbols may also pose a problem for students since they often look alike, or just similar enough to cause confusion (e.g., the square root and division symbol). Different symbols may sometimes have the same meaning. For example a dot, parentheses around sets of numbers, and the "x" symbol may all denote multiplication. Reading data on a graph can also be confusing for many students (Kenney, 2005). Teachers need to be aware of these potential problems and attempt to trouble shoot.

Word walls are a common sight in many classrooms, but usually as a part of the language arts curriculum. Math teachers who use walls to highlight math words, symbols, and concepts provide an additional reinforcement for students (Lucas, 2004). Since no one method of learning and reinforcement works for all students, teachers should implement as many helpful components as possible. All teachers should strive to find approaches that are suitable to the concept being discussed and the students' learning styles (Rudnick & Krulik, 1982).

Manipulatives. Manipulatives can be used in a variety of ways. Students should have them available, for example, to practice ordering objects from large to small or small to large. As students work with geometrical concepts, too, they might first focus on shapes and their similarities and differences to understand how geometry relates to real life. As much as possible, students should be encouraged to work with hands-on activities that enable them to create their own geometric figures and objects and make reasonable assumptions. Students who are able to think logically will usually have an easier time learning mathematics. At about the time they reach the age of 11, children are usually able to think at the formal operational level. By then, they are usually ready to learn formal, abstract-level mathematics. Still, most children of this age can improve upon their understandings of math concepts by working with manipulatives (Lemlech, 2006).

Assessment & Evaluation. Students' progress can be evaluated in a number of ways. Teachers can observe students to ascertain understanding, make use of performance assessments, administer tests that they create, use standardized assessments, and conference with individual students. Conferencing can be especially useful since, as students talk about their reasoning processes, teachers can assess the strengths and weaknesses of their understandings. However, students should not have to follow one method of solving a problem. Rather, teachers should discuss alternate problem-solving methods with students as they attempt to assess student understanding (Lucas, 2004).

Math journals can also be helpful and powerful instructional tools. Journal writing can help math teachers assess the effectiveness of their instruction and monitor student learning as students reflect on what they have learned. As students think about what they will write, they must first mentally refine their understanding—a very useful way to help students make connections and reflect on what they have been doing in the classroom. Just as in a language-arts journal, open-ended questions can act as writing prompts and often work to help students crystallize their thinking. These questions may include: What did you notice?, What surprised you?, Did you find any patterns?, Why do you think it worked the way it did?, Can you make any connections? (Minton, 2007).

Assessing student understanding and evaluating what they have learned are important ways to monitor what is taking place with each student in the classroom. Evaluating students' progress helps the teacher see weaknesses and errors in student thinking, and sometimes in the way the lesson or concept was presented. This knowledge can help the teacher re-teach or review certain lessons or concepts before moving on (Underhill, 1988).

Conclusions. Eighth grade students in almost fifty countries were questioned about their math and science confidence as part of an international math achievement assessment. The results of the assessment showed that students in countries with the highest achievement scores tended to admit that they did not enjoy math and felt that they did not do well in math either. Students from countries with lower scores, however, felt that they did fine in math and enjoyed the subject ("Happy Math," 2007).

In Singapore, the country with the highest achievement scores in math, less than 20% of the students believed that they usually do well in mathematics. Almost 40% of eighth grade students in the United States responded positively to the same statement despite the fact that these most confident American students scored lower than the less-confident students from Singapore. Some researchers believe this may mean that the American educational culture focuses more on helping students feel confident about their math skills, rather than helping them develop strong skills ("Happy Math," 2007).

Terms & Concepts

Data Analysis: "Preparation of factual information items for dissemination or further treatment (includes compiling, verifying, ordering, classifying, and interpreting)" (ERIC Thesaurus).

Formative Assessment: Diagnostic assessment used to shape lesson content.

Journal Writing: "Writing done regularly in logs or notebooks to gather thoughts or ideas, sometimes for later use in more formal writing" (ERIC Thesaurus).

Manipulatives: Concrete objects students can use to practice math concepts.

Probability: The likelihood that a certain result will occur.

Structured Learning: An organized and systematic approach to learning.

Word Wall: A wall or board on which words, and often their definitions, are displayed for students to see.

Bibliography

Dolan, D., & Williamson, J. (1983). Teaching problem-solving strategies. Menlo Park, CA: Addison-Wesley.

Ellis, A. (1988). Planning for mathematics instruction. In T. R. Post (Ed.) Teaching mathematics in grades K-8: Researched-based methods. Newton, MA: Allyn & Bacon.

ERIC Thesaurus. (1988). Retrieved November 19, 2007, from Education Resources Information Center http://www.eric.ed.gov/ERICWebPortal/Home.portal?_nfpb=true&_pageLabel=Thesaurus&_nfls=false

Faulkner, V. N. (2013). Why the Common Core changes math instruction. Phi Delta Kappan, 95, 59–63. Retrieved December 15, 2013, from EBSCO Online Database Education Research Complete. http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=90612594&site=ehost-live

Fisher, P. J., & Blachowicz, C. Z. (2013). A Few words about math and science. Educational Leadership, 71, 46–51. Retrieved December 15, 2013, from EBSCO Online Database Education Research Complete. http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=91736077&site=ehost-live

Freedman, L., & Johnson, H. (2004). Inquiry, literacy, and learning in the middle grades. Norwood, MA: Christopher-Gordon Publishers.

Hachey, A. C. (2013). Early childhood mathematics education: The critical issue is change. Early Education & Development, 24, 443–445. Retrieved November 3, 2014 from EBSCO online database Education Research Complete. http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=87398825

Happy Math. (2007). Wilson Quarterly, 31 , 16. Retrieved October 28, 2007 from EBSCO Online Database Education Research Complete. http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=23653789&site=ehost-live

Kenney, J. (2005). Literacy strategies for improving mathematics instruction. Alexandria, VA: Association for Supervision and Curriculum Development.

Lemlech, J. (2006). Curriculum and instructional methods for the elementary and middle school. Columbus, OH: Pearson.

Minton, L. (2007). What if your ABCs were your 123s?. Thousand Oaks, CA: Corwin Press.

Rudnick, J., & Krulik, S. (1982). A guidebook for teaching general mathematics. Boston: Allyn & Bacon.

Sarama, J., & Clements, D. (2006). Teaching Math: A Place to Start. Early Childhood Today 4. 15. Retrieved October 28, 2007 from EBSCO online database, Education Research Complete, http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=19436977&site=ehost-live

Seeley, C. (2017). Turning teaching upside down: Students learn more when we let them wrestle with a math problem before we teach them how to solve it. Educational Leadership, 75(2), 32–36. Retrieved March 1, 2018 from EBSCO Online Database Education Source. http://search.ebscohost.com/login.aspx?direct=true&db=eue&AN=125627094&site=ehost-live&scope=site

engül, S., & Dereli, M. (2013). The Effect of learning integers using cartoons on 7th grade students' attitude to mathematics. Educational Sciences: Theory & Practice, 13, 2526–2534. Retrieved November 3, 2014 from EBSCO online database Education Research Complete. http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=91880632

Underhill, R. (1988). Mathematical evaluation and remediation. In T. R. Post (Ed.) Teaching mathematics in grades K-8: Research-based methods. Newton, MA: Allyn & Bacon.

Zhang, L., & Jiao, J. (2013). A study on effective hybrid math teaching strategies. International Journal of Innovation & Learning, 13, 451–466. Retrieved December 15, 2013, from EBSCO Online Database Education Research Complete. http://search.ebscohost.com/login.aspx?direct=true&db=ehh&AN=87951298&site=ehost-live

Strategies in Teaching Math

On this Page

Subject Terms

Strategies in Teaching Math

Abstract

Overview

Applications

Terms & Concepts

Bibliography

Suggested Reading