The Challenges Of Mathematics Teaching And Learning

Taught not as a static subject, but an interactive one. Our students should start with applicable math, using objects, angles and visual learning to reinforce the lessons. Children should be shown how math is in every part of our lives, and see real-world examples of how math affects their daily life to encourage excitement and curiosity. Math is the foundation of all of our science, teaching children how to see math in everyday life will lead to greater understanding of the world around them, and why math is important. It is currently taught as a very dry subject that has no connection to their real life outside the classroom, we need to change our approach so they see math as part of daily their

Teachers play an important role in fostering mathematics skills. In the “play dough” (Appendix A) episode, the educators can push student thinking and place the burden of thought on the student. Strategic questioning can really promote higher order thinking a natural integration between math and play (National Council of Teachers of Mathematics [NCTM], 1999). Questions such as “How can you tell which one is the biggest/smallest? How do you put them in order? Teachers should be encouraged to think about, not only the questions they are asking as children are working but also the frame that sets students off to larger problem solving and mathematical discoveries – measure and compare the lengths and capacities (ACARA, 2016). It is important for teachers to think about the questions that are embedded in the task itself but must also analyse the questions to ensure that children are set on a path to deeper understanding of the concept being taught rather than rote regurgitation – as evident in the play dough experience chosen. When it comes to questioning, educators “need to know when to probe, when to wait for answers and when to reinforce responses and when not ta ask questions” (NCTM, 1999, p.187). As seen in the ‘play dough’ (Appendix A) activity chosen, educators can introduce the mathematical concept of measurement and connect new knowledge with old through the use of effective questioning which crates a “link between actions and the language” (Knaus, 2013,

First, the interviewer presented the problem as difficult when reading the problem. Once the child had solved, the interviewer immediately went to the 7 in the hundreds place and questioned what that number represented (i.e. identifying the place of error). The interviewer pushed the child to re-examine place value, and was able to get the child to realize it should be larger numbers that sum to 1000. However, when the child didn’t automatically try to fix the other numbers, the interview pushed the child to fix the other numbers by again prompting towards place value application. Once the child said ten-hundred, the interviewer pointed back to the previous thousand and questioned why they were different—then asked “Really?” when the child showed a

What preparations have you made to anticipate students’ prior mathematics knowledge, students’ differentiated responses and knowledge, and their evolving mathematical thinking throughout the lessons?

Matthew Misiura is a math teacher at Susquehanna Community High School. Mr. Misiura explains that he always pushes for “content mastery” in his math classes. However, Mr. Misiura’s teachings are more than an average algebra and precalculus class. Mr. Misiura pushes for students to learn about the real world. He pushes for students to always work to their full potential. In a year in his classroom, I not only learned precalculus and trigonometry, but I learned how to view situations from a different perspective. Some students, when given back a test in which they failed, would cry, act childish, or simply complain. Mr. Misiura was able to reinforce the belief that the only way to learn is to make mistakes. He often stated that, if you already

Another idea to improve mathematics performance in elementary level is to encourage the student to link the existing knowledge and the new knowledge effectively while working math problems/examples. A worked example is “a step-by-step demonstration of how to perform a problem” (Clark, Nguyen, & Sweller, 2006, p. 190). This will prepare the students for similar problems in the future as they bridge the connection between the problems and the examples. In many cases, students are encouraged to link the informal ideas with the formal mathematics ideas that are presented by the teacher to be able to solve problems. When students examine their own ideas, they are encouraged to build functional understanding through interaction in the classroom. When students share among themselves on differences and similarities in arithmetic procedures, they construct the relationship between themselves hence making it the foundation for achieving better grades in mathematics. Teachers can also encourage students to learn concepts and skills by solving problems (Mitchell et al 2000). Students do perform successfully after they acquire good conceptual understanding because they develop skills and procedures, which are necessary for their better performance. However, slow learning students should engage in more practice

The Case of Randy Harris describes the lesson of a middle school mathematics teacher, and how he uses diagrams, questions, and other methods to guide his students to a better understanding. Throughout his case study, Harris’ methods could be easily compared to that of the Effective Mathematics Teaching Practices. There are eight mathematical teaching practices that support student learning, most of which are performed throughout Randy Harris’ lesson. Harris didn’t perform each teaching practice perfectly, despite doing the majority of them throughout his lessons. The following are examples of how Randy Harris implemented the eight mathematical teaching practices into his lesson, and how the ones that were neglected should have been

Learning multiplication is all repetition, something I had never learned the value in yet. By never studying my multiplication tables, I starved myself of acceleration in mathematics. I became severely far behind my peers in the understanding of the subject at hand and the coursework to follow. My discussion with 8-year-old Taylor would ensure that I knew just how essential math would be. Not only would tackling this problem help me excel in school and real life, it would have taught me the value of learning how to learn. Learning how to learn isn't necessarily comprehending the material, but the process in which one learns, ex. outlines, flashcards. Though now I am able to recognize how paramount learning these skills was to a child, my

This week I was observed during a particularly challenging math lesson. My lesson was elapsed time. My hope was to successfully try Sherry Parish’s, Number Talks method that Sabine Smead at Boulder County School for Integrated Studies, had introduced and modeled for us the week before at Friday Seminar.

When educating students, it is essential to their growth, that teachers have the ability to learn and grow with their students. Every child learns, thinks, and comprehends differently; therefore, the same material should be taught in multiple ways. For example, in my Math 106 class, all students solve the same problem, the teacher then has a few students explain and depict the different ways they received the correct answer. When a student has a difficult time explaining their method, Mrs. Graybeal provides encouragement and guidance; thus. Also, students who are having a difficult time solving the problem used one of the methods provided by a peer to help them comprehend and solve the problem. Math 106 teaches future educators the

The relationship that I have with the person that I interviewed is my father. My father had previously filled out his taxes by hand, but has recently switched over to using a tax software. He has found that although the tax software walks him through the aspects of filing his taxes, it is still challenging for him to navigate certain aspects of the computer software.

Chapter one in the book Number Talks introduces the rationale for number talks and gives an overview of the basis of what a number talk would look like in a classroom. Number talks can be conducted in a small group or whole group setting. It is used to help children develop strategies for solving math problems and to deepen their understanding of numerical relationships. The three main goals of teaching through number talk sessions are to help students compute with accuracy, efficiency, and flexibility (5). Chapter one gives examples of how to highlight different strategies.

I would start with a visual representation of the topic. To try an engage a visual learning style I would present the subject with some pie. I would start by having 2 pies each cut into eight pieces. We would talk about how each pie is composed of eight pieces and so one piece would be 1/8. We would then compare the following that 1 pie is the same as 8/8. We would then add in the second pie. We would have 2 whole pies and we would then link in that if 1 pie is 8/8 then 2 pies would be 8/8 + 8/8, and thus 2 pies = 16/8. Once this concept is grasped I would take away half a pie. Like she described in her interview we would start by describing our situation as a compound fraction. We would now have 1 and ½ pies. With that we would then count the number of slices we have, remembering that each slice is 1/8th of a whole. So we would have 8/8 + 4/8 = 12/8th. This is an improper fraction. I would hold off for now on simplifying the

The teacher prepared a lesson to do an assessment to the children about addition. This lesson was to show on the smart board different numbers with dots for counting. All children had the opportunity to participate in this activity, in which the teacher was able to observe and document what they know and what are some of their needs to help them. The teacher asked the children question such as Do you know which number represents these points? Can you represent it in the form of an addition? The child represented and wrote the addition 0 + 2 = 2.

An example of such a lesson was when I taught vertical subtraction with borrowing. I selected students to demonstrate the steps in solving the equation using MABs while I demonstrated writing the equation and working out on the whiteboard. I explained each step along the way, ensuring students understood that when borrowing the value of the number remains the same, when and why we borrow and how it works. Most students were confident at this stage and went to work on some problems. For students who were still unsure, as a smaller group we worked on equations together, with students writing on mini whiteboards and using MABs. These students were then confident to work on the equations. This allowed me to check what other students had been doing, ask questions to ensure understanding and to encourage students to find errors they may have made, praise the work of students, and provide feedback to students to best assist them in correctly solving the equations. Students concluded by reflecting on what they had learnt and strategies they had