Implementing Differentiated Instruction into the Classroom as it Applies to the NTCM Standards

Why Differentiate Instruction:

When we use differentiated instruction as it is implemented in the classroom and how do we use this technique to improve the teaching if math skills. The instruction of students are at different skill levels and the lesson taught is the same for all but the assignment is geared to their individual skill level (Bender, 2009). Students today perform on multiple skill levels in reading and math which can vary from the gifted to the struggling student. Educators are challenged to design lesson plans that will work with each individual in mind. When we focus on the National Council of Teachers of Mathematics standards we can begin to understand how to improve the teaching of students in math (Bender, 2009).

In order to use differentiate instruction we need to understand how to implement this process into the already overwhelmed classroom. This process will provide students with a better understanding of mathematics and reach all students of all ability levels in the classroom. Exploring the NTCM recommended guidelines we as teachers can improve how we teach in the classroom when applying differentiated instruction.

Knowledge of Mathematics and General Pedagogy

Teachers need to have an excellent understanding of the material in order to be an excellent educators of mathematics. Colleges and Universities have a great amount of influence on how well teachers enter the profession and understanding how students learn about the concepts needed to teach mathematics (Wilburne, 2006). In order to teach students the necessary problem solving skills teachers need to be confident in these skills in or they will transfer that fear to their students (Wilburn, 2006). As a result teachers need to be trained and believe in a better way to implement mathematical instruction using a differentiated instructional approach. In order to meet the strengths and weaknesses of our students instructors need to keep up with professional developments and prepare for these challenges within the classroom. In order to be fair to all students our instructional approach and assessment needs to meet the needs of every individual (Cooper, 2009).

Knowledge of Student Learning

Students who work together in groups can be beneficial to each student when learning math. Interacting with their peers helps to increase student achievement and assists in the learning of mathematical theories to justify and reorganize their work (Papanastasiou, 2002). Studies prove that when students worked in groups that they discover multiple arguments and have justification to computing the same math problem (Papanastasiou, 2002).

Worthwhile Mathematical Tasks

To engage students learning math we need to develop activities to promote the students understanding of the concepts. Teachers can differentiate their instructional approach by including graphic organizers, journals, and discussion (O’Connell, 2005). Teachers have difficulty incorporating group work into the regular routine of math lessons.

When teacher implement journals into the math curriculum students learn to incorporate writing and communicate math theories with each other. Teachers can differentiate the journals by modifying individual expectation to their ability level. Using journals as a tool to establish a deep understanding of the problem solving process covers individual levels and can assist in other areas of study (O’Connell, 2005).

Another way to help students is the use the graphic organizer where they explore what they already know about the problem and brainstorm with others on how to solve the equation. As the students are analyzing the equation they can explore multiple ways that can solve the problem (Zollman 2009). During the brainstorm section the students work in groups to discuss different possible ways to solve the equation. Students formulate ways to communicate about math and justify their work when using the organizer. NCTM clearly states that the teaching process should involve a creative learning environment to help students make sense of their ideas (Herrera 2007). The graphic organizer is a way to help teach math skills to students on multiple levels. Encouraging students to solve problems effectively while using writing in math which has shown to be positive for students to retain and understand the math concepts (Zollman 2009).

Learning Environment

One way to implement differentiated instruction into the classroom as it applies to problem solving skills. Includes students in elementary grades this is illustrated by applying the five steps to problem solving to their differentiated instruction plan. The five steps are in applying their understanding of the problem, strategies used to solve the problem, solving the problem, reflection, and extension activity (Wilburne, 2006). These five steps can be tailored for each individual student, depending on their ability.

When elementary classroom is created in the 1-2-3 model students are exposed to small group assigned tasks that reinforce the mathematical lesson. The class is divided into three groups based on math center activities while students are grouped according to their ability in a flexible setting to work on the math lesson for the period. The three centers in this class are; technology activities, creative math writing, and small group direct instruction. The 1-2-3 model allows time to teach by incorporating technology, games, literature, and writing into the math lesson (Edwards, 2010).

Discourse

Discussion of the material collected through problem solving steps helps students of all ability levels to communicate about math problems and learn new ways to achieve the correct answer. In creating a classroom environment where solving problems with journals that allow the students of all ability levels to be more confident in their problem solving skills and incorporates language arts and writing (Wilburne, 2006).

There needs to be a move beyond finding the answer to questions and to involve critical thinking and reasoning as students start to understand math skills. This is accomplished by examining instructional practices where the focus is in place on asking questions and helping the students develop a better understanding of math theories. When teachers use a model to promote the use of discourse as a way to promote students to make sense of mathematic skills it seems to be productive. Teachers must model these practices by guiding students to clarify and provide feedback that will promote them and to find the solution. Students should be given time to complete this task to find support for their solution.

When applying discourse to the classroom teachers need to look at how the question is asked in order to see how the students explore their understanding of math concepts. These questions need to vary in order to consider each student’s ability to respond thus differentiating instruction. It is beneficial to promote the inquiry method into the classroom. Educators need to encourage students to extend their understanding and to develop their ability to communicate mathematically (Kilic, 2010).

Continued Professional Growth of Teaching of Mathematics

When looking to the future and how to improve upon our teaching techniques we need to focus on the communicating in multiple ways to our students and responding with multiple solution patterns. This might be through groups or in journals but in both cases the mathematical concepts is understood and reinforced as the students justifies their answer. We in the education field must strive to continue to learn to improve techniques by seeking professional development and to improve techniques that can be used in the classroom to teach.

References:

Bender, W. (2009). Differentiating Math Instruction: Strategies that work for K-8 Classrooms. Corwin A Sage Company.

Cooper, C.. (2009). Myth 18: It Is Fair to Teach All Children the Same Way. The Gifted Child
Quarterly, 53(4), 283-285. Retrieved January 25, 2010, from Research Library. (Document ID: 1940617191).

Edwards, S., Maloy, R., and Anderson, G. (2010) Classroom Characters Coach Student to
Success: Learning mathematical problems solving is as easy as 1, 2, 3 when teachers use flexible instructional strategies. Teaching Children Mathematics, 16(6) 342-349.

Herrera, T., Kanold, T. D., Koss, R. K., Ryan, P., & Speer, W. R. (2007). Mathematics Teaching
Today: Improving Practice, Improving Student Learning. Reston: The National Council of Teachers of Mathematics, Inc.

Kilic, H., Cross, D., Ersoz, F., Mewborn, D., Swanagan, D., and Kim, J. (2010)
Techniques for small-group Discourse. Teaching Children Mathematics, 16 (6) 351-356.

O’Connell, S., Beamon, C., Beyea, J., Denvir, ., Dowdall, L., Friedland, N., and Ward, J. (2005)
Aiming for Understanding: Lesson Learned about Writing in Mathematics: Reflect and Discuss. Teaching Children Mathematics, 12(2) 192-199.

Papanastasiou, E. (2002). Factors that Differentiate Mathematics Students in Cyprus, Hong
Kong, and the USA. Educational Research & Evaluation, 8(1), 129-146. Retrieved from Academic Search Complete database.

Wilburne, J. (2006) Preparing Preservice Elementary Teachers to Teach Problem Solving. Teaching Children Mathematics, 12(9) 454-463.

Zollman, A. (2009) Mathematical Graphic Organizers. Teaching Children Mathematics, 16(4)
222-230.