Word Problems
Seminal Article Review: A Reading Strategy Approach to Mathematical Problem Solving
by Linda Limonds
by Linda Limonds
This article discusses a reading strategy approach to word problems. Limonds chose reading strategies because the students are already familiar with the vocabulary and strategies that are being used. Limonds encourages students to use a graphic organizer shaped like a diamond to help them to determine what the problem is asking them to do. The diamond graphic organizer includes finding the main idea, brainstorming, finding connections, solving the problem, and writing a summary on how the problem was solved. In this strategy, one section of the diamond is not more important than the others. Students can fill in the information as they come across it. It is not a step by step process. To use this strategy, students first take a blank sheet of paper and fold it in quarters so that there is a cross in the center of the page. Students then take the corners and fold them into the center so that they are all touching. When the paper is unfolded, there should be a diamond with a cross in the center of it. The main idea goes in the diamond and the other four categories (brainstorming, connections, solving, and writing) go in the corners outside of the diamond.
In the main idea section, student rewrite the word problem as a statement. In the brainstorming section, students write operations or strategies they may use to solve the problem. In the connections section, students write out the important information from the word problem and make connections to life and other problems they have done before. In the solving section, students solve the problem and label each step. In the write section, students summarize how they got their answer and what steps were used.
The use of reading strategies and/or graphic organizers helps students to understand word problems and formulate their thoughts. The diamond method organizes students thoughts for them and provides them with a resource to check back with when they are solving the problem. The students in this study struggled with word problems at the beginning. They would miss important information when reading the problems and solving them. After working with the reading strategy approach and the diamond graphic organizer, the students improved their comprehension of word problems and increased their scores when completing word problems.
Article Reference:
Morrison, J. (2012). A Reading Strategy Approach to Mathematical Problem Solving. Illinois Reading Council Journal, 40(2), 31-42.
In the main idea section, student rewrite the word problem as a statement. In the brainstorming section, students write operations or strategies they may use to solve the problem. In the connections section, students write out the important information from the word problem and make connections to life and other problems they have done before. In the solving section, students solve the problem and label each step. In the write section, students summarize how they got their answer and what steps were used.
The use of reading strategies and/or graphic organizers helps students to understand word problems and formulate their thoughts. The diamond method organizes students thoughts for them and provides them with a resource to check back with when they are solving the problem. The students in this study struggled with word problems at the beginning. They would miss important information when reading the problems and solving them. After working with the reading strategy approach and the diamond graphic organizer, the students improved their comprehension of word problems and increased their scores when completing word problems.
Article Reference:
Morrison, J. (2012). A Reading Strategy Approach to Mathematical Problem Solving. Illinois Reading Council Journal, 40(2), 31-42.
Seminal Article Review: The Effects of Using Drawings in Developing Young Children's Mathematical Word Problem Solving: A Design Experiment with Third-grade Hungarian Students
By Csaba Csíkos, Judit Szitányi, and Rita Kelemen
By Csaba Csíkos, Judit Szitányi, and Rita Kelemen
This article discusses the importance of visual imagery and spacial representation when working with word problems. The study was working to stop students from using "superficial coping strategies". Some examples of these are: searching for numbers in the text, using key words to determine what operation to use, and simply looking at the numbers to determine what operation to use. None of these strategies help students to develop logical and abstract thinking. 216 Hungarian students were used in this study. The study was done to determine if representing a word problem visually helps students to do better when solving it.
At the end of the study, a greater number of students stated that using visual representations will help them to find the solution easier. The results of the study show that the students in the experiment group did better on their post-test than students in the control group. This tells us that the intervention worked. Using visual representations for word problems is effective with students. This is important because it shows that students should be taught how to draw pictures of a word problems, or how to use objects to represent a word problem. This is a technique that teachers can easily implement into their classrooms to increase student's comprehension of word problems and their abilities to solve them correctly.
Article Reference:
Csíkos, C., Szitányi, J., & Kelemen, R. (2012). The effects of using drawings in developing young children's mathematical word problem
solving: A design experiment with third-grade Hungarian students. Educational Studies In Mathematics, 81(1), 47-65.
doi:10.1007/s10649-011-9360-z
At the end of the study, a greater number of students stated that using visual representations will help them to find the solution easier. The results of the study show that the students in the experiment group did better on their post-test than students in the control group. This tells us that the intervention worked. Using visual representations for word problems is effective with students. This is important because it shows that students should be taught how to draw pictures of a word problems, or how to use objects to represent a word problem. This is a technique that teachers can easily implement into their classrooms to increase student's comprehension of word problems and their abilities to solve them correctly.
Article Reference:
Csíkos, C., Szitányi, J., & Kelemen, R. (2012). The effects of using drawings in developing young children's mathematical word problem
solving: A design experiment with third-grade Hungarian students. Educational Studies In Mathematics, 81(1), 47-65.
doi:10.1007/s10649-011-9360-z
Tips and Strategies for Teaching Word Problems!
Dear Parents,
Word problems can be a challenge for students, and I know many of you are looking for some tips on how to help your child with his/her math word problems. First of all, I would like to say that word problems are used to help students develop logical and abstract thinking and mental discipline. We want students to be able to solve problems in real life situations. To be able to do that, they need to understand what the problem is and have strategies to solve it. This is precisely why we do word problems in math. Here a some tips on how to teach and review word problems with your child.
The steps to solving a word problem are:
Another way to increase your child's word problem skills is to give him/her short word problems and ask him.her to find what operation(s) are needed to get the answer, but not to solve them. This keeps the student from guessing what the problem is asking and instead causes them to read the problem for comprehension.
For many word problems it is helpful to draw the problem on paper or use some other object(s) as a representation of the problem so that your child can visualize what it is asking.
Many times it is helpful to solve a problem in front of your child. As you do this, model the strategies you want them to use when they come across a word problem. Let them hear you think out loud as you work, and be sure to share your process with them so they can see how you solve the problem.
Word problems can be a challenge for students, and I know many of you are looking for some tips on how to help your child with his/her math word problems. First of all, I would like to say that word problems are used to help students develop logical and abstract thinking and mental discipline. We want students to be able to solve problems in real life situations. To be able to do that, they need to understand what the problem is and have strategies to solve it. This is precisely why we do word problems in math. Here a some tips on how to teach and review word problems with your child.
The steps to solving a word problem are:
- Understand the problem.
- Devise a plan.
- Carry out the plan.
- Look back.
Another way to increase your child's word problem skills is to give him/her short word problems and ask him.her to find what operation(s) are needed to get the answer, but not to solve them. This keeps the student from guessing what the problem is asking and instead causes them to read the problem for comprehension.
For many word problems it is helpful to draw the problem on paper or use some other object(s) as a representation of the problem so that your child can visualize what it is asking.
Many times it is helpful to solve a problem in front of your child. As you do this, model the strategies you want them to use when they come across a word problem. Let them hear you think out loud as you work, and be sure to share your process with them so they can see how you solve the problem.
Vocabulary Signposts
It can also be helpful for children to learn to recognize key words or signposts in word problems that correlate to certain operations (addition, subtraction, multiplication, and division). Here are lists of the signpost words that go with each operation.
All of the signpost words were retrieved from:
Moreno, M. S. (2004). Key words for solving word problems. Retrieved Oct. 12, 2013, from http://www.gateways2learning.com/Algebra/KeyWords4WordProbs.pdf
All of the signpost words were retrieved from:
Moreno, M. S. (2004). Key words for solving word problems. Retrieved Oct. 12, 2013, from http://www.gateways2learning.com/Algebra/KeyWords4WordProbs.pdf
Addition
Multiplication
|
Subtraction
Division
|
Example Word Problems
![Picture](/uploads/2/3/9/1/23914081/3471261.jpg?328)
1. Examine the letters below. Which are symmetric? Draw all lines of symmetry on the letters that are symmetric.
E N S X
Answer: E and X are symmetrical.
E N S X
Answer: E and X are symmetrical.
![Picture](/uploads/2/3/9/1/23914081/2471994.jpg?356)
2. Jen got 24 bricks and built a wall along one side of her garden. The wall was 4 bricks high and 6 bricks across. Jen painted the wall. She painted all the exposed faces of the bricks. How many faces of bricks did Jen have to paint?
Answer: 62 sides
Answer: 62 sides
![Picture](/uploads/2/3/9/1/23914081/167271739.jpg?193)
3. All my sides are equal. All of my angles are equal. I have three sides. What am I?
Answer: Equilateral Triangle
Answer: Equilateral Triangle
Pennsylvania Standards
M3.C.1.1.1: Name/identify/describe geometric shapes in two dimensions (circle, square, rectangle, triangle, pentagon, hexagon, octagon).
M3.C.1.1.2: Name/identify geometric shapes in three dimensions (sphere, cube, cylinder, cone, pyramid, rectangular prism).
M3.C.2.1.1: Identify/draw one line of symmetry in a two-dimensional figure.
M3.C.2.1.2: Identify symmetrical two-dimensional shapes.
1.5.3.F: Use grade appropriate conventions of language when writing and editing. Spell common, frequently used words correctly. Use capital letters correctly. Punctuate correctly. Use correct grammar and sentence formation.
1.4.3.B: Write informational pieces using illustrations when relevant (e.g., descriptions, letters, reports, instructions).
1.5.3.A: Write with a focus, with an understanding of topic, task, and audience.
Common Core Standard
CC.2.3.3.A.1: Identify, compare, and classify shapes and their attributes.
CC.1.4.3.M: Write narratives to develop real or imagined experiences or events.
CC.1.4.3.Q: Choose words and phrases for effect.
CC.1.4.3.A: Write informative/explanatory texts to examine a topic an convey ideas and information clearly.
CC.1.4.3.D: Create and organizational structure that includes information grouped and connected logically with a concluding statement or section.
M3.C.1.1.1: Name/identify/describe geometric shapes in two dimensions (circle, square, rectangle, triangle, pentagon, hexagon, octagon).
M3.C.1.1.2: Name/identify geometric shapes in three dimensions (sphere, cube, cylinder, cone, pyramid, rectangular prism).
M3.C.2.1.1: Identify/draw one line of symmetry in a two-dimensional figure.
M3.C.2.1.2: Identify symmetrical two-dimensional shapes.
1.5.3.F: Use grade appropriate conventions of language when writing and editing. Spell common, frequently used words correctly. Use capital letters correctly. Punctuate correctly. Use correct grammar and sentence formation.
1.4.3.B: Write informational pieces using illustrations when relevant (e.g., descriptions, letters, reports, instructions).
1.5.3.A: Write with a focus, with an understanding of topic, task, and audience.
Common Core Standard
CC.2.3.3.A.1: Identify, compare, and classify shapes and their attributes.
CC.1.4.3.M: Write narratives to develop real or imagined experiences or events.
CC.1.4.3.Q: Choose words and phrases for effect.
CC.1.4.3.A: Write informative/explanatory texts to examine a topic an convey ideas and information clearly.
CC.1.4.3.D: Create and organizational structure that includes information grouped and connected logically with a concluding statement or section.