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.

Working Together to Achieve the Vision

Policymakers in Local, State, and National Governments

The decision to implement mathematical text books, standardized tests, and the money for resources is decided by government officials who do not consult the teachers who implement the program. Students need to be given the opportunity to use current technology, software, and manipulatives materials learning mathematics. Government officials need to consult with teaching professionals about the needs to instructing mathematics by providing the funds necessary for all children to have the tools and the chance for higher achievement (NCTM, 2007).

Business and Industry Leaders

What is taught in the classroom and how the text book is written makes the foundation of how our children learn mathematics. We need to look at publishing companies and reform the content of the literature published. This can be done by allowing students to learn mathematics through solving problems in multiple representations including verbally and in written formats. Educators not only need to look at the textbook publications and standardized test but how they can provide classrooms with the needed resources to teach. Students need to use current technology as it applies to business and real-world application to benefit training of today’s youth. Businesses can mold how students perceive the teaching of mathematics by coming into the classroom and informing students on how their profession relates to mathematics. This participation not only helps the students today but informs tomorrow’s workforce of the importance education (NTCM, 2007).

Schools Districts

Administrators and Superintendents need to understand the national commission on teaching mathematics standards in order to implement programs, and the funding that will improve the mathematical achievement of students in the classroom. School districts need to provide teachers the time to adequately plan, reflect and collaborate to accomplish the changes suggested in the NTCM standards. It is the school officials who are responsible for encouraging the necessary change. By creating an environment where the professional development where there is a program that provides a reward system and salary increases in which encourage personal improvements in education (NTCM, 2007).


Change

To create this environment of change we need to look at the profession itself. Teachers do not receive the necessary support from the community that they deserve. Teachers are not the decision makers and are only one tool in where the programs that are implemented into the classroom. Through professional development and colleges educating future teachers the necessary change needed in mathematics education will indeed take place. It is when we share learning and help implement these changes that our students will be successful (NTCM, 2007).

Reference List:

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.

Standards for the Education & Continued Professional Growth of Teachers of Mathematics

Teachers’ Mathematical Learning Experiences

Teachers spend many hours studying how to teach mathematics in education classes, workshops, and observation of teaching techniques used in the classroom. This education experience needs to expand its focus to train teachers how to create ma thematic activities for students to work in group settings. Service workshops must refocused to teach teachers how to learn and apply mathematics rather than how to teach (NCTM, 2007).

Knowledge of Mathematical Content

Teachers need to create a positive environment of interaction in their classrooms to teach mathematics by helping students to learn math by experimenting, visualizing, theorizing and by building on concepts already learned. Teaching mathematics includes incorporating the use of current technology into the lesson plans. This can be done through the use of computer programs or the use of calculators. We need to help students make the connection between math and the application of math in other subject areas in order to succeed in establishing student interest and improved performance in math. In order to accomplish this task teachers need to be provided with the tools to help students succeed by continuing their own education and improving upon the strategies needed to help students (NCTM, 2007).

Knowledge of the Student as Learners of Mathematics

Learning is a process that continues throughout a person’s life. As teachers we need to teach in our classrooms in ways which engage our student’s natural curiosity to learn mathematics. We need to take into account each student’s ability to learn, their age, and their interest to learn mathematical concepts when creating lesson plans. The current practice of ability grouping has shown to have little effect on the improvement of math skills in students and therefore the need to use alternative strategies to teach students is necessary (NCTM, 2007). By looking at differentiated learning we can create mathematical lessons to motivate students with a variety of skill levels to learn mathematical concepts.

Knowledge of Mathematical Pedagogy

Teachers need to have a knowledge of basic math principles, their application to real-world problems and the capability to effectively express this information in their teaching. Today teaching requires the use of variety of resources for instructional purposes, such as the text books, online resources, computer programs, calculators, and material that is shared from other teachers. We need to teach math concepts in ways that promote student to communication visually and orally and enable student understanding and application of mathematical principles to real-world problem solutions (NTCM, 2007).


Reference List:

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.

Standards for Observation, Supervision, and Improvement of Mathematics Teaching

The Continuous Improvement Cycle

The observation, supervision, and improvement of teaching of mathematics should include a periodic collection and analysis of a lesson plan, evaluation of professional growth based on analysis of teaching and students performance, and the improvements made in students performance resulting from professional growth (Martin, 2009). Educators should strive to look at ways to improve instructional techniques within their classrooms. This will improve student mastering of mathematical concepts. As teachers we need to look at a ways we can improve professionally by attending workshops, college classes, and observations the techniques of peer teachers (NCTM, 2007). We need to look at strategies to improve students understanding of mathematical concepts and one way to accomplish this task is to understand how to implement differentiated instruction techniques to lesson plans.

Teachers as Participants in the Observation, Supervision, and Improvement

Teachers need to take the time to analyze their own teaching methodology, have time to collaborate with colleagues, and be interaction with administration to establish standardized tools and approaches for improving mathematical teaching. We play an important role when improving the delivery of mathematical instruction (NCTM, 2007).

Data Sources for Observation, Supervision, and Improvement of Mathematics Teaching

When looking at ways to improve the mathematical teaching of our students it is key to providing educators with techniques that support improvement. Observation and guidance from administration alone is not enough. We needing this process of observation to include the feedback from our peer professionals to create news ideas and opportunities to improve teaching. Using this information to form a plan to which our students are engaged in the learning process. This includes the careful attention of the ongoing instructional improvement sharing of materials, strategies and encourage when we collaborative plan activities (NCTM, 2007).

Teacher Knowledge and Implementation of Important Mathematics

To assess the improvement of the teaching we must acknowledge that the teaching of mathematics include; sound knowledge of the skill, connection to daily living. When developing student math activities the teacher need to explore problems that can be applied to real world situations taking advantage of the interest and experiences of a student to help them understand the application of mathematical concepts. No longer asking student only to simply calculate problems from their text books. We need to have them apply that understanding to real world situations (NCTM, 2007).

Teacher Knowledge and Implementation of Effective Learning Environment and Mathematical Discourse

By implementing discourse in the classroom we are looking at teachers to effectively communicate mathematical concepts in a positive learning environment. This effective discourse includes the promotes the understanding of mathematical concepts through procedures that make connections. Engaging the student in ways that extends the students understanding of concepts taught. To align with mathematical concepts where the students can relate understanding and apply that understanding to real world examples and to be able to communicate that mathematical to both the teacher and to fellow classmates (NCTM, 2007).

Reference List:

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.

Standards for Teaching and Learning Mathematics: Differentiated Instruction

Knowledge of Mathematics and General Pedagogy

As educators we need to implement learning techniques that motivate students having a variety of skill levels to learn and apply mathematical principles. To Develop this motivation we need to allow our students to explore mathematical concepts using technology, manipulatives and projects which make the connections between real-life applications and solving math problems. Through differentiated instruction we find that our lesson plans can engage our students in problem-solving on a variety of skill levels without having multiple plans on hand (NTCM, 2007).

Knowledge of Student Mathematical Learning

In order to differentiate mathematical instruction we need to assess what each student already knows about mathematics. Teachers need to work with their students to build an understanding of each students capability in math by applying evaluation tools and analyzing their mathematical writings. The evaluation must include assessment of the ability to apply mathematics to the solution of real-world problems (NCTM 2007).

Worthwhile Mathematical Tasks

Creating assignments for students can no longer be strictly memorization of facts to solve the problem at hand. We need to create lessons to teach students mathematical concepts which require high levels of logical thinking and mathematical understanding. By using differentiated instructional approaches we can teach our students mathematical concepts on the level that they will be able to grasp, and then to communicate (NCTM, 2007).

Learning Environment

The classroom set-up is important for the students to learn. It is not just the physical appearance of the class that we need to focus on, but also the students comfort level within the classroom environment. Students need to be able to communicate what they have learned and supply answers to mathematical questions whether the answer is right or wrong. They need to discuss how they obtained their answers as each question may have many solution pathways. When we differentiate instruction we are taking a lesson and having students complete tasks on their level. Our students need the skills to discuss their conclusions with the class resulting in a complete understanding of mathematical concepts. Students need to feel secure that when they share information with classmates in small groups or the whole class. Every piece of information learned is a building block for the next step to understanding (NCTM, 2007).

Discourse

We know as educators that a problem can be mathematically solved with multiple activities tailored to a groups level of capability. By allowing students engaged in multiple activities we are encouraging them to explain why they solved a mathematical problem in a particular way. This encourages our students to find this answer themselves and share that with their peers. We are modeling respect that their solution is justified mathematically (NCTM, 2007).

Reflection on Student Learning and on the Teaching Practice

We always need to reflect our students’ progress on understanding the mathematical concepts presented within the classroom in adaptation of our teaching methodology. No longer can we assess purely by means of paper-and-pencil tests. Differentiated instruction allows for multiple forms of assessment to check mathematical comprehension. We should encourage students to journal their learning activities and share how problems are solved. This is one way in teaching approach which we may assess understanding. As educators we also need to reflect on our lessons, noting and sharing with peers which parts were successful and which provide opportunities where to improve (NCTM, 2007)

Reference List:

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.