Why are ‘Word Problems’ or ‘Number Stories’ such an issue? Because the Common Core State Standards from:
- Kindergarten OA “2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.”
To grade 1 with the following Standard:
- “Operations and Algebraic Thinking: 1.OA Represent and solve problems involving addition and subtraction. 1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2 2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.”
To Grade 4 – Measurement and Data 4.MD
- Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.
And finally in grade 7
- Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.
More than that the CCSS requres students learn to solve word problems, students need to develop their skills to decipher and solve word problems or number stories because they more accurately reflect real world experiences. It is not very often that you will be presented with simple mathematical equations where you have to add, subtract or multiply or divide numbers. The real world experience is:
I have $10.00. How many apples can I get at $0.35 a pound?
With this type of real world math challenge, there is estimation and rounding and division, and more. Students need to learn the proper sequence to perform mathematical tasks in order to determine the correct answers to real life situations.
Word problems are challenging enough to the typical student. What of our students with learning differences? How do we make this demanding mathematical process accessible?
Part of making math accessible is helping students acquire the vocabulary. Bill Atwood of Collins Education Associates has developed a fun and engaging, full body method of teaching the vocabulary of Mathematics as can be seen here in this video: https://www.youtube.com/watch?v=AOAJpcye7BI
Learning the vocabulary of Mathematic helps demystify Mathematics and give students more confidence when approaching math word problems as they will have a better understanding of what they are reading. They will understand what a ‘Face’ is in math as they have the picture of it with their body.
This method of teaching the vocabulary hits various points of the UDL Concept, among them:
- Multiple Means of Representation – he use voice and gross motor movement – even the inflects of his voice changes.
- Multiple examples and Means of Expression – a ‘game’ he plays is to see how many the students can ‘teach’ others in the class, giving the students the opportunity to demonstrate their knowledge.
So now that they know what the words sound like and their meanings, how do the students recognize them when they see the words in the word problems?
Word Walls have been shown to have a positive impact on learning. It exposes the students to the words consistently, and provides a reminder when needed. Michèle S. Weiner, Regional Center II Instructional Supervisor created a marvelous Mathematic Word Wall available at: http://www.sas.com/content/dam/SAS/en_us/doc/event/math-summit/2014/112M.pdf
Some examples of the vocabulary words are:
The Virginia Family Special Education Connection has included a link to the Mathematic Word Wall as they recognize that it touches on several modes of learning for our students with difficulties.
These are two strategies to learn the vocabulary of math in order to help our students learn how to manage Word Problems. They meet UDL criteria of helping students develop the networks needed to recognize the information and concepts, to apply the information and, as Lev Vygotsky recommends, are engaging.
Resources
http://www.collinsed.com/resources.htm
http://www.onesassyteacher.com/2014/06/using-cubes-problem-solving-strategy-in.html
http://www.attainmentcompany.com/sites/default/files/pdf/sample/SSS-Sample_0.pdf
http://www.ncpublicschools.org/docs/ccsa/conference/2013/presentations/48.pdf
https://udlstrategies.wikispaces.com/Math
http://www.ldonline.org/article/62401/
https://www.youtube.com/watch?v=AOAJpcye7BI
https://goalbookapp.com/toolkit/strategy/math-flashcards
https://goalbookapp.com/pathways/#!/strategies/d5d5297a-69f9-434f-9293-c75f6493c41c
https://itunes.apple.com/us/app/flashcards/id408490162?mt=8
https://vafamilysped.org/Resource/JWHaEa5BS74tjB2sBVD-Mg/Resource-mathematics-word-wall
http://www.corestandards.org/Math/
Examples
- Board games– There are many board games available, such as Equate, Math Bingo and Allowance. These games can be incorporated into math lessons and address mathematical objectives. For example, having students practice creating and solving mathematical expressions while playing Equate would correlate with 6th grade Math Common Core Standard Expressions and Equations
- Playing Cards– Students can play a version of the card game War (addition, subtraction, multiplication, division). For addition, each student flips two cards over and adds the two cards together. The student with the pair that adds to the largest number wins. For more ideas, see math with playing cards.
- Math Jeopardy– There are multiple ways that Math Jeopardy can be played in the classroom. Some teachers prefer to use colored index cards with the points on one side and the Jeopardy question on the other side. The index cards can be easily taped to a classroom whiteboard under chosen math categories. Some teachers use a Powerpoint presentation or math Jeopardy games available online and a projector for whole-group instruction. When playing as an entire class, students typically break into two teams. Each team member has a mini-whiteboard on which to work out the mathematical problem. However, the teams must collaborate and agree on the correct answer (e.g., there cannot be more than one answer per team). The team that chooses the mathematical question has the opportunity to answer the question first. If the first team answers incorrectly, the next team has a chance to answer. Each team takes turns choosing the questions, and the teacher (or a student scorekeeper) keeps track of the score.
Implementation Tips
- Teach the rules to the students prior to playing. If you have a set of 3-4 basic math games, you do not have to re-teach the rules every time the students play the game, but you can change the parameters around playing (e.g. addition one day, subtraction the next).
- Math games are a great way to incorporate peer buddies or peer tutors for students. The peer buddies can help support students with learning the rules of the game, practicing math facts, and participating in class. You can differentiate the instruction of math games by thinking about how students are grouped together while playing the games.
- Always consider the mathematical objective that is being practiced. Make sure that the game matches the mathematical objective or educational outcome. Math games can enhance student learning and practice of mathematical skills. In addition, math games can become a part of the overall classroom structure. For example, some teachers have math learning centers once a week and have games available.