Mathematics is a unique language. Teaching mathematics is like teaching young children the alphabet. Quality instruction gives students the key to access this language that is understood universally. Just as we teach a child the sounds that correspond with each letter in the alphabet, we must explicitly teach our students what the symbols in mathematical language represent. When teaching a child how to read, we build upon their knowledge of the alphabet to create words, and eventually guide them to form coherent sentences with these words. Only after our students have a firm grasp on what the symbols used in mathematics mean can we begin to teach them the formulas and equations that these symbols are an integral part of. Just like learning to read, mathematical precision requires constant repetition and opportunities to practice.
Mathematics is also a discipline of discovery. It is not simply about memorization of unconnected, isolated facts that demonstrates mastery when correctly regurgitated back to the teacher. Everything we know about mathematics stems from something else; it is all connected. Direct instruction lessons are highly useful in helping students learn algorithmic skills and basic math facts. However, inquiry and problem-based learning is where the real magic happens. Inquiry lessons allow students to engage in a deeper level of thinking, where they can construct concepts, discover relationships between topics, and learn to apply their knowledge in various situations. In such activities, teachers are given the power to give the mathematics taught in their classrooms real world relevance, and allow students to see where and how it fits into their lives. In creating these lessons, teachers can foster motivation by incorporating students’ interests, and allowing them to have a choice in the ways in which they can display their learning, such as through a poster presentation or a physical model.
Cooperative learning activities are imperative in teaching mathematics. Working alongside peers of varying ability can afford students the opportunity to gain new understanding and appreciation by considering different viewpoints. Students in the group that need more assistance acquiring skills or content knowledge can benefit by having it explained in a different way from a peer. Additionally, attempting to break down information in alternate ways so that others may understand it can be a valuable learning experience for those in the group that are already proficient in the content.
Students need to be shown that mathematics is not only about the final product, but about the problem solving process. Problem solving is a skill that children and adults take with them and utilize everywhere they go. Mathematics is meant to teach us that when we are faced with a problem, we must first make sure we understand what is being asked of us, which may actually be the most difficult part of the process. We need to determine what is the most useful out of the information given to us, and what information is missing or irrelevant. Then, we can decide on a path to take to solve the problem, and what tools we posses to tackle it. Finally, we execute, and assess if our plan was successful. In mathematics, as in life, sometimes we fail, but the true test of success is getting back up when we have fallen down, adjusting our plan, and trying again.
Mathematics is also a discipline of discovery. It is not simply about memorization of unconnected, isolated facts that demonstrates mastery when correctly regurgitated back to the teacher. Everything we know about mathematics stems from something else; it is all connected. Direct instruction lessons are highly useful in helping students learn algorithmic skills and basic math facts. However, inquiry and problem-based learning is where the real magic happens. Inquiry lessons allow students to engage in a deeper level of thinking, where they can construct concepts, discover relationships between topics, and learn to apply their knowledge in various situations. In such activities, teachers are given the power to give the mathematics taught in their classrooms real world relevance, and allow students to see where and how it fits into their lives. In creating these lessons, teachers can foster motivation by incorporating students’ interests, and allowing them to have a choice in the ways in which they can display their learning, such as through a poster presentation or a physical model.
Cooperative learning activities are imperative in teaching mathematics. Working alongside peers of varying ability can afford students the opportunity to gain new understanding and appreciation by considering different viewpoints. Students in the group that need more assistance acquiring skills or content knowledge can benefit by having it explained in a different way from a peer. Additionally, attempting to break down information in alternate ways so that others may understand it can be a valuable learning experience for those in the group that are already proficient in the content.
Students need to be shown that mathematics is not only about the final product, but about the problem solving process. Problem solving is a skill that children and adults take with them and utilize everywhere they go. Mathematics is meant to teach us that when we are faced with a problem, we must first make sure we understand what is being asked of us, which may actually be the most difficult part of the process. We need to determine what is the most useful out of the information given to us, and what information is missing or irrelevant. Then, we can decide on a path to take to solve the problem, and what tools we posses to tackle it. Finally, we execute, and assess if our plan was successful. In mathematics, as in life, sometimes we fail, but the true test of success is getting back up when we have fallen down, adjusting our plan, and trying again.