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Why use math puzzles to teach?

Before reading, teachers can ask questions that they want students to consider as they approach a mathematics problem. Reinforcing the idea that a piece of mathematics text needs to make sense and that it can make sense is exceedingly important. Teachers need to provide explicit scaffolding experiences to help students connect the text to their prior knowledge and to build such knowledge.

How to make math class interesting?

In her book Yellow Brick Roads , Janet Allen suggests that teachers need to ask themselves the following critical questions about a text: What is the major concept? How can I help students connect this concept to their lives? Are there key concepts or specialized vocabulary that needs to be introduced because students could not get meaning from the context? How could we use the pictures, charts, and graphs to predict or anticipate content?

What supplemental materials do I need to provide to support reading? Consider the following three situations I encountered while working with two 6th grade mathematics teachers and an 8th grade mathematics teacher: In the first case, the 6th grade teacher was explicitly teaching students how to look for context clues. The teacher suggested that the students look for a word in the text of the question that might help them.

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It was interesting to see the different ways that students interpreted this simple exercise. Some seemingly did not look at the words at all; they simply executed the calculation. Some knew the word notation and knew that write meant to reformat the problem. Those who also knew the word exponent were able to answer the problem correctly, whereas some of those who didn't know what exponent meant used a different type of notation to rewrite the problem in words. It is clear that simple exercises such as these can help students to interpret mathematics text by looking at all the words, rather than assuming that a calculation is always sought.

In the second case, students in a 6th grade class were asked to find the percentage of cat owners who said their cats had bad breath. In a survey, 80 out of cat owners had said yes. The students used several different strategies to answer the question and discussed it as a class. They were then asked to read and answer some follow-up questions.

20 Math Puzzles to Engage Your Students

Explain your reasoning. They need to develop the simple strategy of taking the main question apart and listing the individual questions separately. As a teacher, I often had students come to me for help understanding a problem. I also think that, for some students, the attention of someone else listening may help them to focus.

As stated by Barton, Heidema, and Jordan , and as I've learned from my own experience in the classroom, just giving students vocabulary lists with definitions, or asking them to look up the definitions, isn't enough for them to develop the conceptual meaning behind the words or to read and use the vocabulary accurately. Teachers can also introduce various maps, webs, and other graphic organizers to help students further organize mathematics meanings and concepts. Two graphic organizers that can be particularly useful in mathematics classes are the Frayer Model Frayer, and the Semantic Feature Analysis Grid Baldwin, In the Frayer Model, a sheet of paper is divided into four quadrants.

In the first quadrant, the students define a given term in their own words; in the second quadrant, they list any facts that they know about the word; in the third quadrant, they list examples of the given term; and in the fourth quadrant, they list nonexamples. See Figure 2. Figure 2. Sample Frayer Model for Composite Numbers. The Semantic Feature Analysis Grid helps students compare features of mathematical objects that are in the same category by providing a visual prompt of their similarities and differences.

On the left side of the grid is a list of terms in the chosen category, and across the top is a list of properties that the objects might share. Read the problem quickly to get a general understanding of it. Ask what information the problem requires. Reread the problem to identify relevant information, facts, and details needed to solve it. Ask what operations must be performed, and in what order, to solve the problem. Do the computations, or construct the solution. Ask whether the solution process seems correct and the answer reasonable.

Strategies to help students

Teachers can model the steps for the students with a chosen problem and then have the students practice individually or in pairs. Students can then be asked to share their use of the strategy with a partner, within a group, or with the class. Most elementary teachers teach mathematics as one of several subjects; in many cases, they teach reading as well as mathematics, unlike teachers in middle school and high school.

They need to be aware of the particular difficulties involved in reading mathematical text. When encountering mathematical symbols, students face a multilevel decoding process: First they must recognize and separate out the confusing mathematical symbols e.

Graphs are also particularly hard for elementary students to read.

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I became aware of the need to help students learn to stop and analyze graph and table structures when working with what I thought were simple matrix puzzles, involving only two rows and two columns, with an operation sign in the upper left corner. The numbers at the top and to the left were to be combined using the operation sign, and the answers were to be written in the interstices of the rows and columns. The idea was for the student to fill in any missing cells in the matrix. Sample Matrix Puzzle. Several students had difficulty understanding what they were expected to do with the puzzle: What was to be added?

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Where did the answer go? This experience pointed out to me that specific strategies to decipher graphic representations need to be extensively modeled and repeatedly explored. It is important that students become aware that an underlying plan or pattern can usually be discovered by careful study. One strategy that may be familiar to elementary reading teachers, and which seems particularly useful in the context of mathematics, is that of guided reading sessions Allen, In such sessions, the teacher is still responsible for helping students connect what they are reading to prior knowledge.

The teacher should first present the text or graphic to students in small, coherent segments, being sure to process each segment before going on to the next one. As the reading progresses, the teacher should ask process questions that she wants the students to ask themselves in the future. They may be asked to predict what the reading will be about simply by reading the title of the piece if there is one, such as a graph or story problem. At this point, the teacher should ask students questions such as the following: What would you be doing in that situation?

Does this make sense? How does the title connect to what we're reading? Why are these words in capital letters? Why is there extra white space here? What does that word mean in this context? The text would be unveiled one paragraph or equation at a time rather than given to the students as one continuous passage. There were twice as many girls as boys, so the decision was made to give the girls twice as much money. How much did each group receive? We number the equations in the system for reference. Did you come up with two equations in answer to question 2 above?

Are the equations here the same as yours? If not, how are they different?

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  • Why use math puzzles to teach?.
  • 1. Make it meaningful.

Can you see a way to substitute? Will the boys get twice as much as the girls? Yes, it is as close as possible. McConnell et al. Guided reading is best done in small groups, with the teacher encouraging students to think of their own questions as they read. A predetermined set of questions isn't necessary. The purpose of guided reading is to help students realize that they can engage with and make sense of the text, whether it be in language arts or mathematics.

Mathematics teachers don't need to become reading specialists in order to help students read mathematics texts, but they do need to recognize that students need their help reading in mathematical contexts. Teachers should make the strategic processes necessary for understanding mathematics explicit to students. Teachers must help students use strategies for acquiring vocabulary and reading word problems for meaning. Students are helped not by having their reading and interpreting done for them, but rather by being asked questions when they don't understand the text. The goal is for students to internalize these questions and use them on their own.

Mathematics teachers are ultimately striving to help their students understand mathematics and to use it in all aspects of their lives. Being aware that students' prior knowledge and background affects their comprehension is vastly important, as is explicitly analyzing the organization of mathematics texts.

When we share strategies for understanding text, question our students about their conceptual processes, and model strategies and questioning techniques, we are helping students to develop metacognitive processes for approaching mathematics tasks. Mathematics teachers should recognize that part of their job in helping their students become autonomous, self-directed learners is first to help them become strategic, facile readers of mathematics text. All rights reserved. No part of this publication—including the drawings, graphs, illustrations, or chapters, except for brief quotations in critical reviews or articles—may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission from ASCD.

Subscribe to ASCD Express , our free e-mail newsletter, to have practical, actionable strategies and information delivered to your e-mail inbox twice a month. ASCD respects intellectual property rights and adheres to the laws governing them. Learn more about our permissions policy and submit your request online. Sale Book Oct Tuttle Table of Contents Chapter 2. Reading in the Mathematics Classroom by Diana Metsisto The students know how to do the math, they just don't understand what the question is asking.

Reading Requirements for Mathematics Text Let's look at some ways in which mathematics text differs from text in other subjects. Same Words, Different Languages Adding to the confusion of this dense language of symbols is the fact that many mathematical terms have different meanings in everyday use. Small Words, Big Differences In English there are many small words, such as pronouns, prepositions, and conjunctions, that make a big difference in student understanding of mathematics problems.

Strategic Reading Literacy researchers have developed some basic strategies for reading to learn. Sample Frayer Model for Composite Numbers The Semantic Feature Analysis Grid helps students compare features of mathematical objects that are in the same category by providing a visual prompt of their similarities and differences. What you learn can guide your instruction and determine next steps, says Fennell.

Testing is not something separate from your instruction. It should be integrated into your planning. A capable digital resource designed to monitor your students in real time can also be an invaluable tool, providing actionable data to inform your instruction along the way. Walk through your classroom as students work on problems and observe the dynamics. In response, make decisions to go faster or slower or put students in groups.

When students are given the opportunity to choose how they learn and demonstrate their understanding of a concept, their buy-in and motivation increase. It gives them the chance to understand how they learn best, agency over their own learning, and the space to practice different approaches to solving math problems.

Engage students during conversations about their work and have them describe why they solved a problem in a certain way. Instead of seeking a specific answer, Andrews wants to have deeper discussions to figure out what a student knows and understands. Meaningful math education goes beyond memorizing formulas and procedures.

Set high goals, create space for exploration, and work with the students to develop a strong foundation. Present a broad topic, review various strategies for solving a problem, and then elicit a formula or idea from the kids rather than starting with the formula. This creates a stronger conceptual understanding and mental connections with the material for the student. Kids get excited about math when they have to solve real-life problems. For instance, when teaching sixth graders how to determine area, present tasks related to a house redesign, suggests Fennell.

Provide them with the dimensions of the walls and the size of the windows and have them determine how much space is left for the wallpaper. Or ask them to consider how much tile is needed to fill a deck. When giving students an authentic problem, ask a big question and let them struggle to figure out several ways to solve it, suggests Andrews.

Provide as little information as possible but enough so students can be productive.