MATH INTERVENTIONS

Cover-Copy-Compare

Students who can work independently and need extra drill and practice with math computational problems may benefit from this intervention.

Materials

One index card
Math Fact Worksheet containing addition/subtraction/multiplication/division facts written vertically on the left hand side of the paper. The right side of the paper is blank and contains enough space for the student to write.
Math Fact Worksheet containing addition/subtraction/multiplication/division facts without the answers spaced evenly over both halves of the paper.
Stopwatch
Pencil

Directions

Place the first math fact worksheet with answers in front of the student. Instruct the student to do the following steps:

Look at the first problem on the worksheet.
Cover the problem and the answer with the index card.
Copy the problem in the white space next to it, while keeping original problem covered.
Remove the index card from the problem and compare to original problem.
If the problem is written correctly, move onto the next problem
If the problem is written incorrectly, provide the student with a separate sheet of paper and instruct them to copy the problem three times then continue to the next problem.

Once all problems on the worksheet have been copied, give the student the second math fact worksheet with no answers. Use the stopwatch to time how many problems he completes from the time you say begin until one minute has passed. Compute the number of correct digits per minute and graph the data.

Suggestions

You can boost a student’s motivation to complete the worksheets by creating a portfolio of all of the student’s Cover Copy and Compare (CCC) worksheets. Every so often, review the portfolio with the student commenting on how much improvement the student is making.

This procedure can be combined with folding in (see later entry).

Potential Problems & Solutions

Q: What do if the student just copies the answer without covering it up?

A: Have a peer tutor, adult in the classroom, parent, or classroom teacher to sit with the child to ensure the procedure is being followed correctly.

Q: What if the student keeps losing their index card?

A: Try folding the worksheet in half lengthwise so the student is forced to flip the paper over and write his/her answer on the blank side.

References:

Website:http://www.interventioncentral.org/htmdocs/interventions/ccc.shtml

Cover Copy and Compare worksheets can be made at:

Addition Worksheet Generator

http://www.lefthandlogic.com/htmdocs/tools/mathprobe/addsing.shtml

Subtraction Worksheet Generator

http://www.lefthandlogic.com/htmdocs/tools/mathprobe/subtsing.shtml

Multiplication Worksheet Generator

http://www.lefthandlogic.com/htmdocs/tools/mathprobe/multsing.shtml

Division Worksheet Generator

http://www.lefthandlogic.com/htmdocs/tools/mathprobe/divsing.shtml

Multi-Skill Worksheet Generator

http://www.lefthandlogic.com/htmdocs/tools/mathprobe/allmult.shtml

The Folding-In Intervention Technique

Preassessment Phase: To determine which number facts are know and unknown, the students are administered a quiz in which they are asked to answer computational problems. The number of problems not completed or incorrect provides an indication of the facts that have and have not been learned.

Instructional Structure: The students are the taught and participate in a 10-minute session in which they use peer tutoring to drill each other using the folding-in technique.

Each student selects seven cards frsom their pile of pre-assessed known facts.
Each student selects one card from his or her unknown pile of pre-assessed facts.
The teacher informs the two students that they have 20 minutes to begin tutoring.
After it is decided which student will begin the tutoring, the folding-in procedure begins. The teacher of the pair presents the first unknown fact to the learner. The learner is required to write the fact on a piece of paper, say it to him-/herself three times, and then turn the paper over.
The teacher than presents a known fact, followed by the unknown fact, the first known fact, and another known fact. The unknown fact is presented sequentially in this fashion until all seven known facts have been presented and fold-in among the unknown facts.
The groups of eight facts (one unknown and seven known) are shuffled. The second unknown fact is then presented and folded-in among the other eight facts. This is repeated again for the third unknown fact.
If the student hesitates or is incorrect on any fact, the teacher instructs him/her to complete a brief correction procedure. The teacher tells him/her the correct answer and has him/her write the incorrect fact three times. The incorrect fact is then presented again to the learner.
When all facts have been folded in, the entire group of 10 facts is presented three times. Each time, the packet of index card is shuffled to prevent the learner from simply remembering the sequence of responses.
The final step is a test of the 10 facts that the students have practiced.

On this test, a mark is placed on the unknown fact cards if a student is correct on this trial. When an unknown fact attains three consecutive marks, it is considered a learned fact.

The student graphs the number of new facts learned each week. In addition, the teacher administers weekly curriculum-based measurement math probes taken from across all fact families. These data are also graphed .

Reference:

Shapiro, E.S. (2004). Academic skills problems workbook (rev. ed.). New York: The Guilford Press.

Touch Math

Touch math is a way for students to learn addition by teaching them to touch specific points on a written digit.

Touch Math is a systematic, multisensory program used to introduce and improve basic computational skills. This program is effective for students who have difficulty memorizing math facts and the steps of the four basic operations. This supplemental program is used in conjunction with the existing math program in kindergarten through third grade or with students at any level who need help with basic math skills.

Each number is assigned the number of Touchpoints that are associated with its value. When the students no longer need them, the Touchpoints are gradually removed from the numbers (the student continues to “touch” them from memory), at which point the student can begin to use general classroom materials while continuing instruction in the Touch Math materials.

At each stage, visual cues and simple rule statements reinforce the student’s learning of the sequence of steps. For example;

Step 1 addition, the student begins by touching and counting all of the Touchpoints.

In step 2, the student names the larger number and touches points of the smaller number, point by point, while counting on.

The student also verbalizes the procedure: “I touch the larger number, say its name and continue counting.”

When the student advances to two-digit addition, an arrow is drawn over the units, column, and the student learns, “I start on the side with the arrow. The arrow is on the right side.” A square over the tens column serves as a reminder to “carry over” a number.

An example of a worksheet for second grade Touchmath is provided on the following page.

References:

Scott, K.S. (1993). Multisensory mathematics for children with mild disabilities. Exceptionality, 4(2), 97-111.

Simon, R. & Hanrahan, J. (2004). An evaluation of the touch math method for teaching addition to students with learning disabilities in mathematics. European Journal of Special Needs Education, 19(2), 191-209.

Website:

http://www.touchmath.com

Reciprocal Peer Tutoring to Improve Math

Brief Description:

The purpose of this intervention is to improve math performance and behavior during math instruction by means of peer tutoring, group rewards, and self-management procedures.

Students monitor their academic progress in a group context, acting as instructional partners for each other, setting team goals, and managing their own group reward contingencies. Reciprocal peer tutoring has been demonstrated to improve not only math performance but also students’ perceptions of their own academic competence and self-control, and earns high satisfaction ratings from both teachers and students. The intervention takes approximately 30 minutes – 20 minutes for peer tutoring and 10 minutes for individual class drills and checking.

Materials Needed

Reinforcement Menus with activity rewards, one per student pair.
“Team Score Cards,” consisting of 3” by 5” index cards or sheets of paper, one per student pair per week.
Stickers for team score cards.
Flash cards with math problems printed on the front and the problem plus computational steps and answers printed on the back, one problem per card, one set of cards per student pair.
Sheets of paper divided into four sections: “try 1,” “try 2,” “help,” “try 3.”
Instructional prompt cards or sheets with specific instructions related to common mistakes in solving math problems, one per student pair
Problem drill sheets with 10 or more problems, one per student per session.
Answer sheets for problem drill sheets, one per student per session (optional).

Procedure:

Assess students’ current level of math performance by calculating percent-correct scores on daily math drill sheets or weekly quizzes, administering Curriculum-Based Math Probes, and/or observing students’ behavior during math work periods.
Tell the students that they will be learning to work in teams to help each other do well in math.
Divide the class into pairs. Provide each pair with a reinforcement menu listing activity rewards. Help each pair select a reward for the day.
Meet weekly with each team to help the students select their team goal.
After each pair has chosen a team goal, have the pairs record their expected individual contribution to the team (individual goals), the sum of the individual goals (team goal), and their choice of a reward on the team scorecard.
Give a set of flash cards to each pair, and tell the students to choose who will act as “teacher” first.
Have the “teachers” hold up the flash cards for the students, and tell the students to work the problem on their worksheets in the section marked “try 1” while their teachers observe their work.
If the problem is solved correctly, the teachers praise the students and present the next problem. If the solution is incorrect, the teachers give students instructional prompts read from a prompt card and tell them to try again in the worksheet section marked “try 2.”
If the students do not solve the problem correctly on the second try, teachers help them by computing the problem in the “help” section of the worksheet. As teachers work the problem, they explain what they are doing at each step and answer students’ questions. Then the teachers tell the students to work the problem again in the “try 3” section. If teachers have trouble answering students’ questions, they can ask the classroom teacher for help.
After 10 minutes, signal the pairs to switch roles for a second 10 minute tutoring session.
During tutoring sessions, walk around the room supervising and identifying strategies “teachers” can use to help their students.
After the second tutoring session, give each student a problem drill sheet and have students work on their own for a fixed period of time, such as 7 to 10 minutes.
Have students switch papers with their team partner. Have them use an answer sheet to correct their partner’s work or provide the correct answers yourself as students check papers.
Have the pairs first determine their team’s total score by counting the number correct, and then have them compare their team score with their team goal to see if they have “won” (met their goal).
If a team wins, give the students a sticker to put on their scorecard for that day. After five wins, schedule a time when the team can engage in the previously selected reward activity.
Evaluate the intervention by repeating the first step and comparing results.

Tips:

Rewards can also be provided on a weekly class wide basis rather than on a daily team basis when a pre-determined percentage of teams meet their goals 4 out of 5 days during the week. Deliver the rewards to the entire class on Friday.

References:

Fantuzzo, J.W., King, J.A., & Heller, L.R. (1992). Effects of reciprocal peer tutoring on mathematics and school adjustment: A component analysis. Journal of Educational Psychology, 84, 331-339.

Fantuzzo, J.W., & Rohrbeck, C.A. (1992). Self-managed groups: Fitting self-management approaches into classroom systems. School Psychology Review, 21, 255-263.

Rathovan, Natalie (1999). Effective School Interventions. Guilford Press: New York, NY

Procedure for Self-Instruction in Math

This is an intervention for early elementary school years, when children are learning addition problems.

Materials needed: Marked number line, pencil, & sheet of addition problems

Ask, “What is my problem?”
Circle the “+” sign.
Match “+” sign to sign on number line
Copy arrow over problem
Find top/largest number on number line
Hold place with finger or pencil
Find bottom/smallest number and move in direction of arrow that many spacers on the line.
Read answer from the number line.
Copy answer below the equals sign.
Ask, “How did I do?”

Reference:

Shapiro, E. S., & Cole, C. L. (1994). Behavior change in the classroom: Self-management interventions. New York: Guildford Press.

Learning Strategies for Math

Please see information on Learning Strategies in the last section of Reading Comprehension Interventions.

Model when to use the strategy (its purpose).
Model what each letter in the mnemonic stands for and how it relates to solving the math problem.
Model how to apply it to what students have already learned about solving problems.
Provide students with cue cards to place on their desks or to place in their math folders.
Put up posters of a mnemonic on the walls of the classroom.
Use rapid-fire-verbal-rehearsal to help students remember the learning strategy.

Following are several examples of learning strategies to when solving math problems.

Sir Right

Give a problem solving strategy the student can follow for word problems, checking off each step as they goes. For example, the letters SIR RIGHT stand for:

S = S tart by reading the problem

I = I dentify all numbers (digits and words)

R = R eread problem and draw a picture of diagram

R = R eread problem again to find the question

I = I nquire, "What do I have to do to answer the question?"

G = ‘ Guesstimate,’ or estimate, an answer (use smaller numbers if puzzled by large numbers)

H = H ave a go at computing an answer

T = T ake a check back to see if the answer makes sense

DRAW

strategy for teaching students to solve multiplication facts that are not yet committed to memory.

D = Discover the sign. (The student looks at the sign to figure out what operation to use.)

R = Read the problem. (The student says the problem aloud).

A = Answer or draw and check. (The student thinks of the answer or draws lines to figure out the answer).

W = Write the answer.

You can help students make the transition from pictures to abstract numbers by teaching the FAST DRAW Strategy.

F = Find what your solving for. (The student looks for the question in the problem).

A = Ask yourself “What are the parts of the problem?” (The student identifies the number of groups and the number of objects in each group).

S = Set up the numbers. (The student writes the two numbers in the problem in a vertical format).

T = Tie down the sign. (The student adds the multiplication sign to the problem).

LAMPS - strategy used as an aid to remember the steps in regrouping in addition.

L = Line up the numbers according to their decimal points

A = Add the right column of numbers and ask…

M = “More than 9?” If so, continue to next step.

P = Put the 1s below the column.

S = Send the tens to the top of the next column.

References:

Friend, M., & Bursick, W.D. 2001). Including students with special needs: A practical guide for classroom teachers (3 rd ed.) Boston, MA: Allyn & Bacon/Pearson Education, Inc

All Kinds Of Minds: Understanding Differences in Learning Website: ( http://www.allkindsofminds.org/CaseStudy.aspx?casestudyid=6 )

Strategy for Solving Math Problems

Read the problem aloud. Have a teacher help you identify any unknown words.

Paraphrase the problem . Reread the problem, identify the question that is asked, and summarize the information that will be important for solving the problem.

Visualize . Draw a picture of the problem or visualize the situation and tell what it is about.

State the problem . Underline the most important information in the problem and then complete the sentence: “What I know is…” and “What I want to find out is…”

Hypothesize . Complete the sentence: “If…then..”

Estimate . Estimate an answer that would make sense. Write it down.

Calculate . Calculate the answer and label it.

Self -check. Review the problem, check computation, and ask if your answer makes sense.

Reference:

Montague, M., & Bos, C. S. (1986). The effect of cognitive strategy training on verbal math problem solving performance of learning disabled adolescents. Journal of Learning Disabilities, 19, 26-33.

Tips for Math Interventions

Teach key math terms separately. Provide students with a dictionary of math term. Include drawings and examples to illustrate the various steps of the problem.

When teaching abstract concepts, use drawings, diagrams, and visual demonstrations to help the student establish a visual and concrete relationship.

Use colored chalk or pens when demonstrating assignments to focus student’s attention on the important points. An example would be to color code the groups of ones, tens, and hundreds.

Highlight similar math operations on each page to help focus on the specific operation.

Cluster math problems in groups. Direct the student to complete all the math problems with the same operation before proceeding to the next set of problems.

It is best to use real money when teaching the concept of money.

When teaching strategies for using the number line. Draw a large number line on the floor so the student can actually ‘walk’ the problem solution out.

If using timed tests, reduce the number of problems on the page or lengthen the time limit. Provide ample workspace.

Place arrows on the student’s worksheet to assist with directionality.

10. Box in the ‘ones’ column so the student knows where to begin the math calculation.

11. Turn lined paper vertically so the student has ready made columns.

12. If consumable texts are unavailable, enlarge the text so the student may write on the photocopied page.

References:

Hammekan, P. (1997). 450 strategies for success: A practical guide for all educators who teach students with disabilities. Minnetonka, MN: Peytral Publications.