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.
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.
