How Can Make Their Own Reflections Every Time They Implement A Mathematical Task As A Framework?

The author explains how many students, especially those in the focused-upon second grade class, have difficulty explaining their “mathematical thinking process”. While they may provide correct answers using memorized calculations, they are unable to demonstrate their conceptual understandings or explain how they achieved the right results. As stated by the researcher, “it is important for students to be able to demonstrate their mathematical thinking as well as their method of solving a problem” (Kostos & Shin, 2010, p.223).

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

This artifact addresses the standards of content/subject matter, diverse learners, instructional strategies, and methods of teaching in several different ways. The artifact deals with the content of 8th grade math, in this particular artifact it deals with slope, proportionality, and slope intercept form. With using these concepts, I used a variety of strategies including creative thinking and problem solving to make questions. I was also able to create opportunities for diverse learners in this lesson with the strategies and methods of the 8th grade math content. When creating this lesson it was not my goal to interconnect these four standards, it was after reflecting on the lesson that I observed I connected these four standards in my lesson

Essential aspects that underpin the professional and dedicated educator include the revising of knowledge and experience, reflection, and an effort in understanding their students. Within mathematics, these skills are informed by the curriculum chosen, the students involved, and the pedagogy that is selected, that create the professional judgement cycle (as seen in Appendix One) (Department of Education and Training Western Australia [DETWA], 2013a). The more teachers understand about their students, the more they can adapt the learning environment to cater for these different learning approaches (Burns, 2010).

For this observation, I was in Mrs. Dye’s 5th grade math class when the students were learning how to add and subtract decimals. Mrs. Dye started the class with having the students write a math prompt about explaining how to add decimals. After about 5 minutes she asked one of the students to read their prompt out loud to the class. Then the class were told to work out the daily question and it was about adding decimals. She asked another student to come and work the problem out on the smart board and to explain it step by step. Then Mrs. Dye would read problems out of a work book that she would ask the students to work out on their own sheet of paper, but then ask other students to work them out on the board again explaining the problem step

The Standards for Mathematical Practice are essential tools that will ensure a student has everything they need to improve in their knowledge and understanding in mathematics. Thus, it is highly important that all level mathematical educators try to implement these standards into their classrooms. Ultimately, there are two sections called, “processes and proficiencies” in which the standards are derived from. The practices are depended on these two standards in the mathematics education. For the reason being, that they provide strategies that will help develop a foundation that students may rely on to comprehend and approach a problem. In other words, the standards do not show step-by-step ways on how to solve a problem, but rather help a student feel comfortable and confident in approaching, analyzing, and finishing a problem. The process standards defined by the National Council of Teachers of Mathematics emphasizes a way of problem solving, reasoning and proof, communication, connections, and representations. The proficiencies identified by the National Research Council include, adaptive reasoning, strategic competence, conceptual understanding, productive disposition, and procedural fluency. Knowing how beneficial the Standards for Mathematical Practice is for students, it is clear that as a future teacher I will implement these strategies in every classroom so that all my students may have a chance to prosper.

As a result of implementing any of the ten lesson plans, the students will learn about quantities and their relationships. Moreover, the students will use their curiosity to explore and learn about the world around them. For example, they can learn about how and why leaves change colors. As a result of developing and implementing this artifact, I learned that educators need to ask and respond questions to help foster students’ inquisitiveness and scientific thinking. I also learned that teaching mathematics can be done through interactive activities, and not through hand outs. To improve these lesson

The purpose of the study is to identify how varying ways of knowing mathematics manifests in the use of the core practice of facilitating classroom discourse. I am interested in better understanding how teachers use their mathematical knowledge for teaching to facilitate meaningful discourse. Gaining greater understanding it this area will aid in assisting teachers in developing the skill of facilitating meaningful discourse. The ability to engage students in mathematical discussions that enhance student learning has continued to be a topic in mathematics education and is viewed as a major component of mathematics education reform. It is vital that teachers, novice and experienced, develop the skills necessary to create a learning environment

Van De Walle, Karp, & Bay-Williams (2013) describe the importance of using visual representations such as Area, length and Set models to consolidate fractional concepts. Observations of students representing fractions through the use of the three models allows teachers to gauge if learners have a real understanding of the fraction concepts. Area models represent fractions as part of an area. Circular or rectangular pieces, grids or dot paper, pattern blocks, geoboards and paper folding are examples of this type of model (Van De Walle, Karp & Bay-Williams 2013, p. 293). Length or number line models permit for the comparison of lengths or measurements instead of areas by either drawing and subdividing them or through the comparison of

We approach teaching in five dimensions: verbal, mental, written, visual, and hands-on, with emphasis on verbal and mental math interaction. By discussing the how and why of math, students build an understanding of how they learn. Metacognition is an approach that stimulates multiple senses and engages students more effectively. For more information about our teaching methods, check this YouTube video and review the curriculum here.

When teaching mathematical concepts it is important to look at the big ideas that will follow in order to prevent misconceptions and slower transformation

In the article, “How Should Elementary Math Class Look and Sound”, I learned that math can be taught in ways where the teacher do more than just tell them the steps to solve a problem. Teachers can inhibit students to figure out the steps to take when solving and equation or a word problem. For instance, making the students read a word problem out loud and disaggregating the word problem piece by piece. Moreover, I also learned that by doing so it let students deepen their thinking about math and can sometimes help with the understanding. In addition, I have seen in the reading classroom I’m observing my cooperative teacher using a similar method. For instance, she will tell the students to tell her what they think the story they are about to

According to Hand (2012), teachers can become powerful agents to improve the inequities within classrooms for students. This research indicated that when classroom instruction supported wide students’ participation, students seemed to feel comfortable engaging in mathematical dialogue with each other and the teacher (Hand, 2012). When teachers’ engage a wide range of learners, they essentially are inviting students to “take up space” in the mathematics classroom instruction (Hand, 2012, p. 238).

At the end of each day students can write reflections on how their understanding of math has changed or improved from earlier discussions. Music is another way to improve mathematical concepts.

According to the teachers’ standards (DfE, 2012) “teachers make the education of their learners their first concern, keep their knowledge up to date and are self-critical.” Therefore, this reflection practice will guide me towards the improvement on my lesson planning strategies and delivery. In addition, it will also make an enormous difference in my teaching and learning practice which is vital for teacher training.