“Supporting Diverse Learners: Teacher Collaboration in an Inclusive Classroom,” by Wendy S. Bray, copyrighted in 2005 by The National Council of Teachers of Mathematics, focuses on the need of collaboration between general education teachers and special education teachers to facilitate fair and successful learning for each individual student. This article speaks mainly to general education teachers about reform based mathematics and how general classroom teachers can implement this new style of learning in a way that will benefit all students, even special education students. Furthermore, the article searches for ways to help special needs students learn in their own special way, in order to keep up with the other students in their regular classroom.
The article begins by discussing the challenges learning disabled students face when integrated in a classroom that uses the reform-based, constructivist mathematical approach, which focuses on whole group discussions, small group discussions, and problem solving. Some of these problems include: LD students not participating and/or “focusing on nonmathematical aspects of tasks (Bray).” Next, the article discusses how a group of teachers manage this type of classroom. One tactic they implemented is “small, teacher-led groups (Bray)” where the teachers played games and did other activities, encouraging the students to talk about their mathematical thinking.
Another tactic the teachers used is breaking students up into groups according to their ability and what they needed to work on. In these groups teachers did not just tell the students what to do to solve a problem, but instead they asked the students questions to help them figure out on their own what they needed to do. These teachers also gave their students “opportunities for choice (Bray),” which allowed students to choose what they wanted to work on, individually, with a group, or with the teacher. This gave the teachers the opportunities to work with students individually. The end of the article discussed how the three teachers collaborated to discuss the progress of individual students, and what should be done to help them continue to grow.
This article was written by Wendy S. Bray, “a doctoral candidate at the University of North Carolina at Chapel Hill (Bray).” She is a “former elementary classroom teacher,” and “her research interests include mathematics education and teaching strategies that facilitate learning for students with special needs (Bray).” Her information came from her research, and her information was supported by excerpts from various books and journals of education professionals including: “Effects of Reform-Based Mathematics Instruction on Low Achievers in Five Third-Grade Classrooms” by Baster, Woodward, and Olson; “Mathematical Problem-Solving Process of Primary-Grade Students Identified as LD” by Behrend; “Four Variables for Success” by Coleman; “How Effective Is Inquiry Learning for Students with Mild Disabilities?” by Mastropieri; and “Mathematical Instruction for Elementary Students with Learning Disabilities” by Thornton. She also ascerts that her information supports the Equity Principle, which she also cites from the “National Council of Teachers of Mathematics.”
We have students achieve success in reading and writing through individualized instruction, where they learn at their own pace, so why don’t we do this in math? I feel that the idea that this article circles is a great one. To learn math students need to participate in discovery learning. They need to understand the “why” of mathematics before they are really going to begin to understand and learn the concepts. Students also need to learn at their own pace. Everything is connected in mathematics and if students do not understand one concept before the class moves on to the next, pretty soon that student is going to fall way behind.
This is unfortunately what happens to most learning disabled students that are integrated into the regular classroom. So, in my own classroom I will try to implement the constructivist approach for learning mathematics and simultaneously create an atmosphere where every student can succeed, no matter what pace they learn at. I will do this by creating learning centers around my classroom. The subject of these learning centers will be based on the mini-lesson that is taught the first day. Students will pair up and move around the learning centers at their own pace. The beginning stations will focus on the “why” of the concept, helping students deepen their understanding, so that when they work their way around to the other stations they will be ready to try a variety of ways to solve the problem, with the collaborative help from their partner.
Before each pair moves to the next station I will check their answers to make sure they are progressing in their understanding correctly. We will do this the entire week, giving those students with learning disabilities plenty of time with their partners to understand the concept. Some pairs will finish before the end of the week. These pairs will continue to work on the concept, but at a higher level. At the end of the week the class will discuss what problem-solving techniques they tried and what they have learned.
This article was very useful. I had never thought of grouping students according to ability in math. I have heard the effects of this grouping in other subjects as a valuable way to individualize teaching, and I was surprised that I have yet to see this technique implemented in mathematics. I wholly agreed with all the approaches these teachers took in this article, except for the approach took in the “Opportunities for Choice” section. It seems that the students would just pick something that they were good at if given a choice to work on anything.
I know I wouldn’t choose something that I had trouble with. I am skeptical that this approach would help students very much. Otherwise, this article gave me much insight as how to help students with learning disabilities grow in the classroom with regular classroom students. This approach allowed more opportunities for students to discuss their ideas and deepen their understanding, while providing them with the help they needed to understand concepts that would be integral for their understanding in future lessons.
By: Jamie Burchfield
Posts Tagged ‘Special Education’
Support Diverse Learners in Mathematics
February 22nd, 2010Opening Mental Doors
February 18th, 2010
When I first met Jose as a junior in high school, he had spent his first two years in resource (special education) classes where the teachers are specialized in addressing different types of learning disabilities (LD). LD is a very inclusive term that characterizes thousands of challenged students whose main difficulty lies in reading comprehension and/or math calculations. Jose was a very slow reader who had trouble understanding the concepts described in his textbooks. Needless to say, his self-esteem was very low and he often experienced severe mood swings from elation to total despair. He was sure that he could never graduate.
Acquiring Concepts
Teens usually acquire second degree conceptualization during puberty, building on the first degree concepts obtained at a very early age that we can call conceptualization of concrete objects. Piaget, the famous Swiss biologist whose research on the development of intelligence established a cornerstone upon which the whole cognitive theory is built, named the ability to remember objects the “Internal Representation System” which occurs according to the scientist between the ages of 18 and 24 months. In other words, a child that age begins to remember the toy even when it has been hidden under the rug for example. The baby doesn’t need to see the object to “know” that it exists. What seems to be so obvious for adults is actually a tremendous feat that will eventually culminate in our higher order of thinking or second degree conceptualization. As an example, if we ask the question ‘What is life?’, a child 8 or 9 years-old will usually respond in very concrete terms, such as ‘The opposite of death’ or he may actually be stumped for a answer. Now ask a teen between 15 and 18 and you will get a much more sophisticated answer.
Closed Door
Unfortunately, for some teens, that second degree of conceptualization never opens. For some reason, and that it the case for Jose, some adolescents remain at the childhood level of concrete concepts or ‘Internal Representation System’. Some argue that low levels of intelligence prevent some people from passing to the higher level; others claim that these youngsters were never exposed to adequate stimuli as children and that too much television did not allow for the practice of concept forming offered by the written text. Thus, whatever the reason, the door to higher order of thinking remained closed. Schools struggle to tailor instruction to such students, even though the curriculum is the same. Resource classes are smaller, usually between 6 and 10 students, and the teaching strategies must take into account the learning disabilities. There is however a trend to eliminate special education classes and mainstream challenged students into regular classrooms. This would eliminate the stigma of being separated from regular students, an emotional problem that led Jose to an ‘I don’t care’ attitude.
Opening Other Doors
As I started working with Jose in his junior year (he had been promoted to a regular class), I noticed that the transition was extremely difficult for him. My role as an inclusion teacher consists mainly in working with special education teens as a support for the regular teacher. This requires a close cooperation between the two instructors so as to make sure that students like Jose are not left behind. Both teachers must employ special strategies acquired in training courses throughout the year. But in order to motivate students like Jose who feel totally inadequate, teachers have to open some emotional doors that have been closed as defense mechanisms: “If I say I can’t do it, maybe the teacher will leave me alone.”
We have to find the key that will open these doors and that requires the establishment of trust with the youngster. One tactic that has worked well for me is humor, the kind type. Once I had managed to make him laugh, often at my own expense, I had broken through his resistance. Another one is sharing a passion, for example a sports team, a famous athlete or some kind of non-academic activity. In Jose’s case, we both discovered that we loved soccer: He favored Chivas (a Mexican team) and I favored America (a classic rival). We spent hours outside of class (of course) discussing the merits of each team and thus a bond was formed that transcended the considerable difference in age and culture.
Graduation At Last
Even though Jose will not go to college, he is quite capable of taking a 2-year technical course which will offer him a chance to be productive and successful. He finally graduated this year and had trouble believing that he was walking on the dais to receive his diploma. This success will do more to boost his self-esteem than any word of encouragement I may have provided over the last 2 years. He knows that he can achieve his goals because he has learned to plan according to his skills and potential. There are many Jose’s out there who need special attention and that is the main role of special education teachers.
By: Jacques Sprenger
How Parents Can Find Answers to a Child’s Mathematics Problems
February 11th, 2010
According to some research reports, few students are referred to special education testing for mathematical disabilities. In fact, mathematical disabilities do not exist as a structured whole in testing situations but rather as a group of abilities, usually distilled into the arithmetic or computational disability. Children and even adults who cannot remember multiplication tables or add a set of numbers are often thought of as disabled or un-abled while those who are said to have spatial talents are often viewed as talented. Many separate mathematical abilities and disabilities may exist side-by-side and either may be neglected based on the teacher’s or the school’s approach to teaching math.
What is viewed as mathematical ability cannot just depend on the computational, but should also take into account the spatial reasoning, symbolic reasoning, logic and broad problem-solving ability.
Many have heard of the child known as the autistic savant who can tell someone the day of the week on which they were born within seconds when given only the date of birth. There are many people who are blessed with a high degree of intelligence and ability in a very narrow area, such as calculations of calendar dates, but who lack broader abilities in more conventionally accepted areas.
While many students have difficulties remembering multiplication tables and formulas, these same students may have talent in problem-solving or in computer programming. Mathematical reasoning is not monolithic and it is not a simple quality to define.
If a parent feels one’s child is experiencing difficulty in math class, this may not mean the child needs remediation in all areas of mathematical reasoning. Various techniques, such as drill or mnemonic devices, may help to alleviate specific difficulties with a trained and sensitive teacher or tutor.
If a parent’s child is failing in math, it is important to ask some questions: What specific skills is my child deficient is? Computation? Reasoning? Logic? Verbal problems? Spatial relationships?
If the teacher cannot specify areas which need improvement, ask for a review of the child’s anecdotals to pinpoint areas of weakness. Is the math syllabus geared to specific areas of competency? If so, what are those areas?
Does the child seem to have specific problems with language in math? If so, has the teacher given the students an extensive and detailed list of definitions of terms used in the course? Are mimeographed sheets being used instead of modeled lessons with reinforcement by homework? Is the child given time and opportunity to use manipulatives in the classroom if it appears the difficulty is related to understanding word problems?
It’s important to remember that no one is born mathematically challenged and that many are born with great capacities in a very narrow area. To expand a child’s math abilities, work with the teacher to determine whether the child’s difficulties lie in the area of language or perception of quantity or space.
If, after talking to the teacher, a parent still has questions about pronounced deficiencies, the questions should be further pursued to the department chair or to the principal.
Parents are often a child’s best advocate for ensuring optimum education.
By: Ann R Knapp