Selected Strategies
These strategies could be beneficial to all mathematics students, but they will be especially helpful to students in the Pre-Algebra class. Pre-Algebra is not offered at all high schools. Most students start their freshman year in Algebra 1 or higher. The high school Pre-Algebra curriculum reviews many of the basic concepts- such as fractions, decimals and percentages, exponents, and one step equations- that students will need to be successful in Algebra. Why not take the time now to help them solve word problems? That is a skill that most students struggle with, even in a higher level math class. Also, many students in the Pre-Algebra class scored in the low or below average categories on their reading and math MAP tests. MAP tests are used to measure a student’s performance level at different times during the school year. As students take the test on the computer it adapts based on their responses. The score is used to help the teacher determine where the student is at and how to best help them grow. The combination of low reading and math scores could indicate that some of their struggles with word problems could come from a misunderstanding of the vocabulary and structure of a word problem. Annotating word problems and using schematic diagrams will help these students organize their math.
It is so important to help students improve their problem solving skills. Word problems are one of the ways in which teachers can be culturally responsive based on their students. Word problems can be made more engaging by making them about topics that are interesting to the students. For example, when teaching area, one might choose to talk about the area of a basketball court. It would be simple to bring a student’s favorite team into the problem. When solving problems about percentages one could discuss a sale at student’s favorite clothing store. There is no need to talk about something uninteresting like the amount of apples a person has when there are unlimited possibilities for the context of a word problem.
It is so important to help students improve their problem solving skills. Word problems are one of the ways in which teachers can be culturally responsive based on their students. Word problems can be made more engaging by making them about topics that are interesting to the students. For example, when teaching area, one might choose to talk about the area of a basketball court. It would be simple to bring a student’s favorite team into the problem. When solving problems about percentages one could discuss a sale at student’s favorite clothing store. There is no need to talk about something uninteresting like the amount of apples a person has when there are unlimited possibilities for the context of a word problem.
#1 Mathematics Vocabulary
The students and teacher discussed common mathematical words and their meanings then recorded them in the students notes. For example, when dealing with inequalities the words "at most" would indicate that the less than or equal to sign should be used. If students were unfamiliar with certain vocabulary they were encouraged to ask what the meaning of the word was.
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These strategies address different styles of learning. Some students struggle with word problems because they are overwhelmed by the words and their meanings. Organizing vocabulary by its mathematical meaning helps students to determine what they are being asked to do.
#2 Understanding the Structure
The teacher and students also focused on understanding the structure of a given word problem. Students were instructed to cross out information that is not meaningful. They circled numerical information and underline the words or clues about what operation to perform. A box was drawn around the label. Label refers to the number included in the final answer. Numbers written in word form were translated into digits. These rules were posted in the classroom and given to students as a handout. They were able to keep this handout in their Pre-Algebra folders. Breaking down the structure of a word problem with specific steps allows students to organize important information. |
#3 Schematic Diagrams
Diagrams are visual examples that include relevant numbers and pictures from the given word problem. To show students the difference, the teacher will practice drawing diagrams with the class during notes. During independent word time the teacher will check students’ diagrams.
Drawing schematic diagrams is a a good strategy for the visual learner. The pictures students include in their diagrams give meaning to the problem. For example, students who get area and perimeter mixed up might find it helpful to draw a picture. |
Materials were accessible to all students via Canvas. The school recently went 1:1 so all students have a device on which they can access materials. Paper copies were also handed out during class and could be kept in the student’s Pre-Algebra folder.
Timeline
The research process began February 6 and concluded April 3.
Beginning with the square roots unit in February, students were introduced to the strategies. This was done during the class notes. Notes refers to the time students are learning new material under direct instruction of the classroom teacher. The students use Cornell notes. The main portion of these notes is guided. It has fill in the blank sections and examples for the students to follow along. After learning a skill the students practiced computation problems before trying word problems.
Students were already taking district assessments at the end of each unit. A unit test was taken over exponents on February 6, the square roots test was taken on March 5, and the equations test was taken April 3. Once the research was completed two-sample t tests were done between the first and second unit tests, the second and third unit tests, and the first and third unit tests. Only the word problems were looked at for these tests.
Likert scale surveys were administered to the students on three occasions. Students completed the survey the class periods following each of the unit tests. The survey was intended to measure changes in students' confidence levels regarding word problems.
Anecdotal notes were taken weekly during the research process. These notes included comments made by students about word problems and the strategies used. The students homework assignments and quizzes were also examined.
Beginning with the square roots unit in February, students were introduced to the strategies. This was done during the class notes. Notes refers to the time students are learning new material under direct instruction of the classroom teacher. The students use Cornell notes. The main portion of these notes is guided. It has fill in the blank sections and examples for the students to follow along. After learning a skill the students practiced computation problems before trying word problems.
Students were already taking district assessments at the end of each unit. A unit test was taken over exponents on February 6, the square roots test was taken on March 5, and the equations test was taken April 3. Once the research was completed two-sample t tests were done between the first and second unit tests, the second and third unit tests, and the first and third unit tests. Only the word problems were looked at for these tests.
Likert scale surveys were administered to the students on three occasions. Students completed the survey the class periods following each of the unit tests. The survey was intended to measure changes in students' confidence levels regarding word problems.
Anecdotal notes were taken weekly during the research process. These notes included comments made by students about word problems and the strategies used. The students homework assignments and quizzes were also examined.