Showing posts with label RTI. Show all posts
Showing posts with label RTI. Show all posts
Monday, November 3, 2014
Response to Intervention in Math
The following posts below are for an assignment of my current college course
CBSE 7402T. They are summaries of chapter 8 and 9 of "Response to
Intervention in Math". They outline the main ideas of three specific
math intervention programs targeted towards elementary and middle school
students with special needs. The final post outlines particular
interventions for building vocabulary in young students deficient in
mathematical language.
RTI - The Importance of Mathematical Vocabulary
Chapter 9 of Response Intervention in Mathematics is focused on the importance of teaching mathematical vocabulary. This is what I feel to be an unnecessarily long chapter. Therefore, I will try to briefly summarize this chapter and some include good takeaways.
The authors make a sound argument that the lower a students understand of mathematical language, the less proficient they will be in mathematics. Students with a low level of mathematical vocabulary (that is, they have mathematical terminology, understand the terminology and the contexts in which it is applied, and are proficient in using/applying it) have difficulties learning whatever it is being taught. I learned this last year, where most of my students were very deficient in mathematical language. It made it hard to teach new concepts and it was difficult for them to understand new things. This chapter includes seven recommendations for teaching vocabulary in math class. The following four resonated with me the most:
A) Establish a list of essential vocabulary words for each chapter or grade level
B) Evaluate student comprehension of mathematical vocabulary on a periodic basis
C) Develop an environment where mathematical vocabulary is a normal part of mathematics class.
D) Probe students' previous knowledge and usage of important terms before they are introduced during instruction.
Incorporating even a few of these recommendations will allow students to view mathematical vocabulary as important and not just a sidekick to what is being taught. Instead, they go hand in hand.
The book argues that teachers should devote instructional time to developing students' mathematical vocabulary. I certainly agree, but there is such little time to begin with. As such, one of the wonderful ideas that I found in this chapter included creating a list of mathematical words for students and sending it home (kind of like what is done for language arts). Here is an example of a vocabulary sheet taken from the book:
Let's face it: There's simply not enough time in a 45 minute period to teach concepts, procedures and vocabulary, all heavily dependent on the students in your classroom and the range of their abilities. However this is a great tool that can be used for students to study on their own time, and you can evaluate how useful it has been.
Another great tool that was presented in this chapter is an online math dictionary for kids. It can be found here: Children's Math Dictionary
It is an online interactive dictionary that students can use to learn new mathematical terms, along with a visual representation or interactive way to learn its meaning.
Another idea that resonated with me in this chapter is the use of graphic organizers. Graphic organizers are a great way for all students to organize information and help them see the connections between concepts and their application.
Another interesting one that I found (and is inspiring me to make one for my students as I type this):
Lastly, to evaluate students knowledge (and the usefulness of explicit vocabulary instruction), teachers can put vocabulary questions on quizzes/tests, or timed assessments in which teachers pick a few random words from their created list of words students should know (by the end of the year). The idea is that as the year progresses, students vocabulary will also progress, therefore, students should score higher on these types of progress-monitored assessments over time. Using the book again as a resource, the following photo is an example of the "progress-monitoring probe" discussed in the textbook:
To summarize, many students do not learn fundamental mathematical vocabulary, and therefore, have difficulties become strong students in math. Strong students in math have excellent mathematical vocabulary and understand the meaning of many different math terms and know when they are applied. This chapter went over many different ways to help students gain the vocabulary fluency in math.
Edit: Here is a prime example of why mathematical vocabulary is important. I went over some home work with a student. While he was able to get the correct answer, his articulation of his reasoning is low (due to a low level of mathematical vocabulary).
The authors make a sound argument that the lower a students understand of mathematical language, the less proficient they will be in mathematics. Students with a low level of mathematical vocabulary (that is, they have mathematical terminology, understand the terminology and the contexts in which it is applied, and are proficient in using/applying it) have difficulties learning whatever it is being taught. I learned this last year, where most of my students were very deficient in mathematical language. It made it hard to teach new concepts and it was difficult for them to understand new things. This chapter includes seven recommendations for teaching vocabulary in math class. The following four resonated with me the most:
A) Establish a list of essential vocabulary words for each chapter or grade level
B) Evaluate student comprehension of mathematical vocabulary on a periodic basis
C) Develop an environment where mathematical vocabulary is a normal part of mathematics class.
D) Probe students' previous knowledge and usage of important terms before they are introduced during instruction.
Incorporating even a few of these recommendations will allow students to view mathematical vocabulary as important and not just a sidekick to what is being taught. Instead, they go hand in hand.
The book argues that teachers should devote instructional time to developing students' mathematical vocabulary. I certainly agree, but there is such little time to begin with. As such, one of the wonderful ideas that I found in this chapter included creating a list of mathematical words for students and sending it home (kind of like what is done for language arts). Here is an example of a vocabulary sheet taken from the book:
Another great tool that was presented in this chapter is an online math dictionary for kids. It can be found here: Children's Math Dictionary
It is an online interactive dictionary that students can use to learn new mathematical terms, along with a visual representation or interactive way to learn its meaning.
Another idea that resonated with me in this chapter is the use of graphic organizers. Graphic organizers are a great way for all students to organize information and help them see the connections between concepts and their application.
Edit: Here is a prime example of why mathematical vocabulary is important. I went over some home work with a student. While he was able to get the correct answer, his articulation of his reasoning is low (due to a low level of mathematical vocabulary).
RTI In Mathematics - Solving Math Word Problems
The third and last intervention program outlined in chapter 8 is called the "Solving Math Word Problems" program. It is targeted towards students with disabilities in elementary and middle school. The program is comprised of eight units, five of which are addition & subtraction problems, and the remaining are multiplication and division problems). Lessons are 30-60 minutes long. There are four major components to this program.
First -To start, like the other programs, there is a big emphasis on teaching students to recognize different types of word problems. In this program, they are called "change", "group" and "compare" (these correspond to addition & subtraction word problems), "multiplicative compare" and "vary" for division & multiplication word problems.
Secondly - There is a diagram that accompanies each problem type, and students are to extract information from each problem and translate this information into the diagram. Each of the problem types has a corresponding diagram, showcasing the biggest aspects of those particular types of word problems. Teachers model how to use the diagrams, and students are given opportunities to practice transferring information from story situations and word problems onto the corresponding diagram.
Third - Students are to use a series of rules they learn to determine the correct operation necessary in solving the problem. Lastly, students must actually solve the problem. These four steps have been broken down into a Mnemonic called "FOPS". That is:
Find the problem type
Organize the information in the problem (using the diagram)
Plan to solve the problem
Solve the problem
Lastly - Compute/Solve the problem!
A key component of the program is that it starts out by giving students story situations instead of questions, making it easier for students to blend and understand the mathematical concepts behind the situations presented in future problems.
Example of a story situation (from the textbook): "Tyler has 37 Star Wars cards on Tuesday. He gives his sister 5 cards on Wednesday. Tyler now has 32 Star Wards cards". This is to get students to focus solely on the math behind the problem. No question is asked.
When students are able to accurately categorize story situations and the correct operation, story situations end and the lessons move on to actual questions.
Example of a question (based off of example from the textbook): "Ku has some cookies; he gives 5 to his sister. Now, he has 32 cookies. How many cookies did he have before he gave his sister cookies?
Likewise, when students progress further through the lessons, the use of the diagrams also stops. This gives students the chance to solve problems independently without any scaffolds.
First -To start, like the other programs, there is a big emphasis on teaching students to recognize different types of word problems. In this program, they are called "change", "group" and "compare" (these correspond to addition & subtraction word problems), "multiplicative compare" and "vary" for division & multiplication word problems.
Secondly - There is a diagram that accompanies each problem type, and students are to extract information from each problem and translate this information into the diagram. Each of the problem types has a corresponding diagram, showcasing the biggest aspects of those particular types of word problems. Teachers model how to use the diagrams, and students are given opportunities to practice transferring information from story situations and word problems onto the corresponding diagram.
Third - Students are to use a series of rules they learn to determine the correct operation necessary in solving the problem. Lastly, students must actually solve the problem. These four steps have been broken down into a Mnemonic called "FOPS". That is:
Find the problem type
Organize the information in the problem (using the diagram)
Plan to solve the problem
Solve the problem
Lastly - Compute/Solve the problem!
A key component of the program is that it starts out by giving students story situations instead of questions, making it easier for students to blend and understand the mathematical concepts behind the situations presented in future problems.
Example of a story situation (from the textbook): "Tyler has 37 Star Wars cards on Tuesday. He gives his sister 5 cards on Wednesday. Tyler now has 32 Star Wards cards". This is to get students to focus solely on the math behind the problem. No question is asked.
When students are able to accurately categorize story situations and the correct operation, story situations end and the lessons move on to actual questions.
Example of a question (based off of example from the textbook): "Ku has some cookies; he gives 5 to his sister. Now, he has 32 cookies. How many cookies did he have before he gave his sister cookies?
Likewise, when students progress further through the lessons, the use of the diagrams also stops. This gives students the chance to solve problems independently without any scaffolds.
RTI In Mathematics - Pirate Math
The second of the intervention programs outlined in chapter 8 is called "Pirate Math". This program is a 16 week tutoring program targeted towards second and third grade students. Lessons are organized into five activities and the central theme is one of "pirates".
For the first activity, students are given a set of addition and subtraction flash cards and are taught to "count up". For addition, students start from the larger number and count up to reach the sum. For subtraction, students start from the number being subtracted, and count up to find the difference. Then, students play with a tutor to try to beat their previous score (of flash cards answered correctly). As this program continues, students are taught how to recognize three different problem types. They are:
A) Total - Combining two numbers to find a sum
B) Difference - Finding the difference between a bigger number and a smaller number
C) Change - A problem in which there is a starting amount, and something in the problem increases or decreases this amount (students must find the ending amount).
The second activity is called "Word Problem Warm-Up". Students are asked to explain the correct way to solve a word problem from a previous lesson. It allows students to display their thinking, as well as re-teach/review things that have been taught previously.
To classify the problem type, students are asked to follow an acronym called "RUN" which stands for:
Read the problem
Underline the question
Name the problem type
After students figure out the problem type, they work their way through three questions that guide them to set up the correct number sentence to solve the problem.
Lastly, there are "Sorting Cards" which students use to continue practice in classifying problem types. The flash cards contain word problems that are read by the tutor and the student is to identify the problem type, and places the flash card on a sorting mat. Cards that are sorted incorrectly are reviewed at the end of the lesson. Teachers circulate and give feedback to student pairs.
There is an incorporated behavior management system in which students rewarded with "treasure coins" for exhibiting student-like behaviors such as: listening, following directions, completing assigned work, and improving their skills. Students color in a treasure map at the end of a lesson (based on the number of coins earned). When the map is fully colored, students earn a prize.
For the first activity, students are given a set of addition and subtraction flash cards and are taught to "count up". For addition, students start from the larger number and count up to reach the sum. For subtraction, students start from the number being subtracted, and count up to find the difference. Then, students play with a tutor to try to beat their previous score (of flash cards answered correctly). As this program continues, students are taught how to recognize three different problem types. They are:
A) Total - Combining two numbers to find a sum
B) Difference - Finding the difference between a bigger number and a smaller number
C) Change - A problem in which there is a starting amount, and something in the problem increases or decreases this amount (students must find the ending amount).
The second activity is called "Word Problem Warm-Up". Students are asked to explain the correct way to solve a word problem from a previous lesson. It allows students to display their thinking, as well as re-teach/review things that have been taught previously.
To classify the problem type, students are asked to follow an acronym called "RUN" which stands for:
Read the problem
Underline the question
Name the problem type
After students figure out the problem type, they work their way through three questions that guide them to set up the correct number sentence to solve the problem.
Lastly, there are "Sorting Cards" which students use to continue practice in classifying problem types. The flash cards contain word problems that are read by the tutor and the student is to identify the problem type, and places the flash card on a sorting mat. Cards that are sorted incorrectly are reviewed at the end of the lesson. Teachers circulate and give feedback to student pairs.
There is an incorporated behavior management system in which students rewarded with "treasure coins" for exhibiting student-like behaviors such as: listening, following directions, completing assigned work, and improving their skills. Students color in a treasure map at the end of a lesson (based on the number of coins earned). When the map is fully colored, students earn a prize.
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