Using Touch Math to Improve Computations The purpose of this paper is to share the results of a 1-week intervention that focused on the effects of simply teaching basic touch math to third grade students in an effort to increase their speed and accuracy in computation. For the purposes of this study, it focused on computations of single digit addition and subtraction and up to three or four digits in addition and subtraction with and without regrouping.
Introduction and Intention I am a third grade teacher in a suburban elementary school that is part of a city school system in the Piedmont of North Carolina. The school s families range from upper-middle class to poverty level incomes, with about 64% of the school s student population receiving free and reduced lunches. The school population is 56% White/other, 23% Black, 20% Hispanic and 1% each of Asian and Native American. The school receives federal support through both Title I and Reading First grants, and is in danger of becoming a Title I School of Improvement in math during the next year. The school employs 23 teachers, and has an average enrollment of about 358 students, giving it a student-teacher ratio of 16:1. The school is brand new, having just opened in December of 2006. The classroom in which the research was conducted has 17 students. It consists of 59% White students, 18% Black students, and 24% Hispanic students; with 53% males and 47% females. The academic make-up of the classroom is 5% Academically/Intellectually Gifted (AIG), 35% Exceptional Children (EC), 6 students diagnosed with Attention Deficit Hyperactivity Disorder (ADHD), 2 with Oppositional- Defiance Disorder, 1 receiving speech services, and an additional 25% being served by Title I services. Approximately 50% of the class is still working below grade level in math. Our classroom is equipped with the latest technologies and many math manipulatives and reading support materials. We have a part-time teacher s assistant available to work with students in whole group and small group settings during both our reading and math blocks. The principal and senior staff members of my school have
informed me that last year s second-grade team had a lot of unrest, and that a member of the team left mid-year. With this in mind, I have been told that it is possible that through the transition, some key math concepts may not have been presented to the students as well as intended. For the purposes of this study, as well as student achievement, I would like to implement strategies, such as touch math, to improve my lower-achieving math students performance on basic addition and subtraction facts and concepts, and ideally bring them back up to grade level in math. A grasp of basic math facts and concepts is essential for students to master in order to move on to higher-level math concepts in the upper elementary grades. When students in the third grade still do not know basic addition and subtraction facts and are still using their fingers to count out the sums and differences of these basic facts, it becomes obvious that customary ways of teaching math have failed them in some way over the years. When it comes to multi-digit addition and subtraction with or without regrouping, these students at many times still seem to have no concept of what to do with the numbers. Without these basic math concepts, these students also have extreme difficulty in learning and truly comprehending higher-level math concepts such as multiplication and division, which they are, according to North Carolina state standards, expected to have a handle on by the end of third grade, and in time for the End of Grade tests. Literature Review Several theorists and researchers have hypothesized and proven through the years that children learn better through hands-on application of many concepts,
including math. This can be held true in the use of manipulatives and other multisensory approaches to teaching math facts and problem-solving. One such approach to teaching math facts is the Touch Math (Bullock, 1996) approach, which utilizes the corresponding number of dots on numerals 1-9 to help students remember the numeral s value when computing basic math concepts. This approach can be used in solving addition, subtraction, multiplication, or division (Scott, 1993; Wisniewski & Smith, 2002). Touch Math is beneficial for many struggling students because other traditional math strategies have failed them and because of its use of auditory, visual, and tactile strategies to reinforce the counting technique. In both studies, all students involved improved their math computation time and accuracy considerably. Scott (1993) also cited that Touch Math is useful because of its use of a variety of learning styles and modalities in teaching math. Interventions After researching various math teaching strategies and approaches to improving students' basic math fact recollection and computation, I chose to implement the Touch Math system (Bullock, 1996) with my students. This was a change from other more traditional math teaching approaches such as flash cards, games, timed tests, and repeated drill and kill activities that have been implemented in small group instruction. Unfortunately, it had become obvious that these traditional methods were not meeting many of my struggling learners, resulting in the need for a new teaching approach. As both Scott (1993) and Wisniewski and Smith (2002) demonstrated in their studies, I conducted small group instruction in Touch Math following a timed preassessment (that I created on my own) of the whole class in basic addition and
subtraction computations with and without regrouping. I initially planned to focus my instruction of Touch Math only on my low-performing students, but after discussing it with a colleague, decided to try introducing it to my whole class. I provided interventions for at least 30 minutes a day everyday for a week on Touch Math strategies. Following the 1-week intervention, I assessed my students with an identical post assessment and compared their scores to measure for improvement in the accuracy and speed of their computations. My basic small and whole group lessons were laid out as follows: I spent one day teaching the touch math touch points on the numerals followed by one day of review of the points for mastery. The next day of instruction focused on addition strategies such as counting on with the touch points to solve addition problems. The following two days focused on counting backwards in subtraction starting with the large number and counting back using the touch points. Review of these concepts was done through the use of manipulatives, dry erase board practice and worksheets for the remainder of the week. At the end of the intervention, the post assessment was administered. RESEARCH QUESTIONS Students' attitudes: How will the use of touch math strategies affect my students' attitudes/confidence as they attempt math computations? Students' achievement: How will the use of touch math strategies affect my students' success with math computations? Teacher's attitudes and skills: How will the organization and management of touch math in small group instruction affect the teacher's attitude in planning and implementing small group math instruction?
DATA COLLECTION METHODS AND TRIANGULATION OF DATA Question Focus Method 1 Method 2 Method 3 Attitude of Students How will the use of touch math strategies affect my students attitudes/ confidence towards math? Attitude of Teacher How will the implementation of touch math in small group instruction affect the teacher s attitude in teaching math? Achievement of Students Students will take a math pre/post attitude survey. (see appendix) Anecdotal notes will be made after each lesson on how it went and how students performed. Students in the intervention groups will be verbally interviewed throughout the intervention process. Observing my students using the strategies outside of touch math instruction. Students in the intervention groups will be given a response question at the end of each week of intervention to respond to in writing. The question will be: Do you feel that using touch math is improving your ability to solve math problems? Students will be given the opportunity at the end of the intervention to suggest ways that the presentation of strategies or lessons could have been improved. How will the use of touch math strategies affect my students math achievement? Pre/Post Test (see appendix) Mini-assessment scores Performance rubric (see appendix) I used three data collection methods to assess how the use of touch math affected my students attitudes and confidence towards math. The first method to assess this was to administer an identical pre and post attitude survey, which I created, (see appendix) to my students. It consisted of five questions about student s attitude toward math, their perceived ability of math, and how important they think it is to learn math. This assessment was given prior to the intervention, and following the
intervention for this research. The scores of the pre and post surveys were compared for each student to measure their change in attitudes towards math. The second method I used to assess this question was verbal interviews with the students throughout the intervention. I took notes of their responses as to how well they thought they were doing in math, and in learning and using the new math strategies. The third method that I used to assess the student attitude question was in a response question given to the students at the end of each week of intervention. The question was, do you feel that using touch math is improving your ability to solve math problems? They responded to this question in a short paragraph. I used a separate set of data collection methods to assess how the implementation of touch math in small group instruction affected my attitude in teaching math. This question was very important to evaluate whether teaching touch math to my students is something I feel would continue to help my students in the future, as well as how effective the teaching of it in small group instruction was. The first method to assess this question was anecdotal notes made by the teacher following each lesson on how well the lesson went and how the students performed. The second method of assessment for this question was done by simply observing my students using the strategies outside of touch math instruction. In the third method of assessment for this question, students were given the opportunity at the end of the intervention to suggest ways that the presentation of strategies or lessons could have been improved. A third set of data collection methods was used for my third research question, how will the use of touch math strategies affect her students math achievement? The first method was a timed identical pre and post test given to the whole class in basic
addition and subtraction computations with and without regrouping. It consisted of twenty questions including single digit addition and subtraction and up to four digit addition and subtraction with and without regrouping. The test was given with a ten minute time frame, and assessed based on the number of correct digits, not only correct complete answers. The scores of the pre and post tests were compared for each student to measure their growth. The second method of data collection for this question was the informal mini-assessments given in each small group session. Students had the opportunity to work with the teacher then were given short mini-assessments consisting of two to four problems to demonstrate their understanding of that day s lesson. Instruction was constantly adjusted based on student achievement. The third method of data collection was the performance rubric which assessed if and how well the students used their new touch math strategies to solve math problems. It was constantly considered informally throughout the intervention. All of the above data collection methods were chosen to best serve my students needs. The students needs thus far had proven the need for new methods of math instruction to improve their basic math computations in addition and subtraction that will later lead to better multiplication and division. By continually assessing student performance and needs, as well as my reactions to teaching the touch math strategies to her students, I used this data to guide my future math instruction. Data Analysis and Interpretation Following a one week intervention using touch math instruction with my third grade class of seventeen students, I found that it appeared to positively affect most of
my students addition and subtraction computations. I documented this progress through a variety of methods which are outlined below. The first method was used to measure student achievement. It addressed a research question which asked how the use of touch math strategies would affect my students math achievement. An identical pre- and post-test was given one week apart following daily small and/or whole group instruction of touch math strategies. For both tests, every student was given exactly ten minutes to complete as many addition and subtraction problems, with and without regrouping, as possible. The number of digits that each student calculated correctly was counted. The total number of possible digits correct was 54. The findings are graphed and shown in a table below. Pre-Test and Post-Test Scores
student number pre-test score post-test score gain/loss 1 21 25 +4 2 51 52 +1 3 35 3-32 4 6 15 +9 5 19 26 +7 6 51 52 +1 7 51 54 +3 8 8 17 +9 9 3 10 +7 10 24 49 +25 11 0 25 +25 12 23 48 +25 13 27 32 +5 14 n/a 15 30 36 +6 16 25 33 +8 17 22 31 +9 18 8 17 +9 The table and graph show that every student except for student number 3 showed growth in the number of digits they completed correctly. Student number 3 broke out with a rash and reported not feeling well that day, which probably affected his score along with the fact that he has a history of Oppositional Defiant Disorder (ODD) and was refusing to work that morning. It should also be noted that students 2 (in AIG) and 6 completed the post test in six minutes rather than ten, so though they made only one digit growth, they completed the problems much more quickly. Student number 17 also completed the assessment early, within six minutes. Though he missed several problems, he still made significant growth for also working much more quickly. I noted with him and many other students that they still do not seem to understand how to regroup with subtraction, causing many computation errors. Students 10, 11, and 12 all made a large amount of growth over the course of a week. None of them have received
any additional services over the rest of the class other than the touch point instruction. With EOG s quickly approaching, however, all students have had a lot of support in their math skills with small group and individualized instruction and extra time on our skill builiding computer program, Successmaker, recently, but these three students only received what the rest of the class also did. My interpretation of their growth is simply that they found using touchpoints very helpful. Student number 14 moved shortly before the study began which is why his scores are blank. To address the research question, how will the implementation of touch math in small group instruction affect the teacher s attitude in teaching math, I reflected upon my anecdotal notes and observations. When I first began this intervention technique, I was going to just show it to my lower math students, but after a talk about touch math with our AIG (Academically Intellectually Gifted) teacher, decided to introduce it to my entire class. It is interesting to note that in math centers and on Successmaker I have seen many students (both higher and lower achieving) using the touch math strategies either by drawing the points or tapping out their value. Additionally, on the assessments I witnessed students counting out the answers using their fingers very few times, which before the intervention would have been commonplace. I believe that while many students do not visually use the touch points, that after our extensive practice with them in class, they have better internalized the value of the numbers as they count them out. The above observations, in addition to a reflection of anecdotal notes made after each touch points math lesson, help to support the overall good feeling I have about using and teaching my students touch points. It has pleasantly surprised me that after at least four years of working on number sense, touch points seem to have definitely made
an impact on their performance in basic math computations. With a reflection of my attitudes on teaching touchpoints to third graders, I would have to say that it is very positive. I also used multiple data collection methods to gather information of how my students felt about touch math, addressing the research question, how will the use of touch math strategies affect my students attitudes and confidence towards math? One of the methods was an identical pre- and post- attitude survey that I created asking five questions about my students attitudes towards math. The pre-survey was given prior to any introduction of touch math on a Tuesday morning at the beginning of my math block. I gave the post survey at the end of my math block on a Friday following a math assessment. As I have heard before though, hind sight is 20/20 and I believe that I made a poor choice in when I gave the post-survey. As you will see on the graphs below which show the responses to the pre and post surveys, there were no truly significant changes in student attitude. There was however, a slight negative skew to some of the answers. I believe that after the post assessment some students were frustrated with themselves for not finishing more problems or for knowing that they struggled on the assessment, and these feelings may have skewed the attitude survey results. It should also be noted that the survey only surveyed students attitudes towards math in general, not specifically touch math. (see graph on next page)
Attitude Survey Pre-Intervention Attitude Survey Post-Intervention
On the other hand, following the touch math post assessment I asked each student to also write a brief journal-type entry regarding their feelings toward touch math. I asked them to consider whether or not they liked touch math and whether or not they thought touch math helped them. The results are graphed below and show that a majority of students (ten) liked touch math or felt that it was helpful to them. One student did not know whether or not she found touch math helpful, and six students did not find it helpful. Compared to the general math attitude survey, these journal entries showed more significant and positive attitudes toward touch math. Touch Math Journal Entry Results CONCLUSION AND FUTURE PLANS After reviewing and analyzing all of my data, I feel that my students improved their computation ability as a result of learning touch math strategies. For the purposes of this class and the mini-research project, this intervention only lasted one week but still had a positive effect on my students. I look forward to continuing to implement Touch Math practices and seeing my students succeed with its use.
On a reflection of my student achievement question which asked whether touch math would help to improve my students computations, I would have to say it had a very positive effect. All but one of my seventeen students increased their score on the post test and three of my students made a significant improvement of 25 digits on the post test. The touch math strategies seem to help all students regardless of their math ability. In helping all of my students, it covered every ability level from students in EC (Exceptional Children), those receiving Title I services, as well as those in AIG (Academically-Intellectually Gifted). Two of my higher level students completed the test in 33% less time and still improved their score on the post test. My second research question inquired as to how my students would respond to the use of touch math strategies. After a post-attitude survey as well as a reflection of their journal entries, it seems that a majority of the class liked touch math or found it helpful. Not one student claimed not to like touch math, but some said they did not need it or did not find it helpful. Considering their score improvements, however, I feel that even if students did not consciously use touch math, the intervention still helped them to better internalize the value of the numbers and therefore make fewer computation errors, as was proven in their post test scores. My third research question addressed my attitude toward teaching touch math which I must say is very good. The simplicity of the program makes it easy to teach, and its versatility in use in all areas of math makes it very useful. My students caught on quickly, and were observed using it in a variety of math situations independently even outside of explicit touch math lessons.
It would have been interesting to have continued my intervention this year for a month rather than a week and seen how much more improvement my students would have made. In the future I plan to introduce touch math to all of my students at the beginning of each school year and infuse its use in all areas of math throughout the year, as Scott (1993) and Bullock (1996) stated it could be used. Scott, as well as Wisniewski and Smith (2002), also stated that touch math not only improves computation accuracy, but also improves students computation time which was also proven in my research. I hope that in introducing touch math to all of my students at the beginning of the year I will see higher overall math achievement for all of my students throughout the year. In summary, though my research had a small sample size and was done over a short amount of time, it aligned with what other similar research (Scott, 1993; Wisniewski & Smith, 2002) has found. It provided students with auditory, visual, and tactile strategies to reinforce the counting technique that can be used across the math curriculum as well as in real life. I am pleased and encouraged by the results it has shown with my students and plan to continue to use it now, and to use it with my classes in the future. Bibliography Bullock, J. K. (1996). Touch Math Instruction manual, Colorado Springs: Innovative Learning Concepts, Inc. Scott, K. S. (1993). Multisensory mathematics for children with mild disabilities. Exceptionality, 4(2), 97-111. Wisniewski, Z. G. & Smith D. (2002). How effective is touch math for improving students with special needs academic achievement on math addition mad minute timed tests? Retrieved January 30, 2008, from ERICdigest.org.
Appendix Name Pre-Student Attitude Survey towards Math Disagree I don t know Agree Name Post-Student Attitude Survey towards Math Disagree I don t know Agree
Touch Math : Performance Rubric Student Name: CATEGORY 3 2 1 0 Strategy/Procedures Typically, uses an efficient and effective strategy to solve the problem(s). Typically, uses an effective strategy to solve the problem(s). Sometimes uses an effective strategy to solve problems, but does not do it consistently. Rarely uses an effective strategy to solve problems. Mathematical Errors 90-100% of the steps and solutions have no mathematical errors. Almost all (80-89%) of the steps and solutions have no mathematical errors. Most (70-79%) of the steps and solutions have no mathematical errors. More than 69% of the steps and solutions have mathematical errors. Completion Almost all problems are completed. (90-100%) Most of the problems are completed. (70-89%) Some of the problems are completed. (50-69%) Few or none of the problems are completed. (0-49%) Touch Math : Performance Rubric Student Name: CATEGORY 3 2 1 0 Strategy/Procedures Typically, uses an efficient and effective strategy to solve the problem(s). Typically, uses an effective strategy to solve the problem(s). Sometimes uses an effective strategy to solve problems, but does not do it consistently. Rarely uses an effective strategy to solve problems. Mathematical Errors 90-100% of the steps and solutions have no mathematical errors. Almost all (80-89%) of the steps and solutions have no mathematical errors. Most (70-79%) of the steps and solutions have no mathematical errors. More than 69% of the steps and solutions have mathematical errors. Completion Almost all problems are completed. (90-100%) Most of the problems are completed. (70-89%) Some of the problems are completed. (50-69%) Few or none of the problems are completed. (0-49%)
Pre and Post Assessment