The Theory Of Multiplication As Equal Groups Through A Familiar Context

[In lesson 1 at time stamp 2:44, I illustrated a Math Mountain and asked students, “What Math Mountain is that?” A student gave an answer of six. I elicited the student’s response by asking, “How do you know that (name)?” The student responded by telling the class that one more than five is six. I continued to build on the students’ answer and circled the six at the top of the mountain. I explained that this was our big total, a vocabulary phrase. I ask students to raise their hands and tell us what the word total means. Some students were hesitant in defining this word, so they did not raise their hands. I went back to what a student mentioned earlier and circled the numbers as I spoke, “(Name) said that five plus one equal six. What do you think total means?” The same student gave the answer, “All of the numbers together.” I paraphrased their response and added to it by motioning my arms in a big circle while repeating, “Big total, it’s going to be the biggest number.” I also had the class repeat the word big total.

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).

In Section D, Daniel demonstrated a primary understanding of the multiplication and division concepts. Daniel can count group items by ones. He also counts one by one to find the solution for involving multiple groups when all objects are modeled. Daniel was able to use different strategies to count the cars in the boxes as he said, “I can count them by twos because there are two cars in each box,”

The lesson plan 3 was about “Time by the hour” for math. Throughout the time in my placement field, I get to observe and teach in my cooperating teacher’s 1st grade class. I had learned so much about the students and enjoyed working along with everyone. At the end of every planned lesson plans, I have learned so much and gained some useful information on how to become a better teacher in the future. In this lesson plan 3, I had reflected on my past mistake and learn to grow from it.

The math concepts taught in this lesson are teaching the students how to use certain math formulas, and practice addition and multiplication. It is beneficial for students to know what tools to use for capturing and displaying information that is important to them (Davis, 2011). The science concepts taught in this

Upon observing your class, we have learned a lot about the methods you utilize in order to help the students with mathematics and about how the students learn. Observing your class was both an honor and a learning opportunity for us, as you are an important, and well-respected faculty member in the school system. However, while we appreciate your goals and tactics to make learning mathematics easier for the students, we have discovered some flaws in the use of mnemonics, rules, and tricks for helping students understand the subject material.

During fourth period on Thursday, January 28th I observed Dee Hertzog’s Honors Geometry class. At the beginning of class Dee went around checking to see which students completed their previous night’s homework assignment. While this was going on students were expected to work on the warm-up problems that were projected on the Promethean Board. After Dee was done checking in with each student on the homework assignment she asked two students to work together to put their work and answers to the warm-up problems on the board. This warm-up was then reviewed with the class. While reviewing the warm-up problem, Dee activated prior knowledge by asking the students if they remembered using the Pythagorean Theorem. She asked the students what they

The teacher gathers students on the carpet and draws a circle with a dot at the center on the IWB and questions children about their feedback on it and expects for mathematical terms circle, round, one, center, radius, diameter and circumference. She concludes that a single picture represents more mathematical concepts.

For each of the categories listed below (2a–d), describe what you know about the focus learner’s strengths and challenges as related to the lesson objective(s) of the learning segment. Cite evidence of what the learner knows, what s/he can do, and what s/he is learning to do in relation to the learning goal and any relevant planned supports.

b. How does the tutoring reflection demonstrate your knowledge of the major areas of exceptionality in learning?

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

Another point the author makes, he criticizes the way school mathematics, like the treatment of mathematics instruction as a race of poor educational practices. The art of mathematics is finding the true answer, it’s the explanation or the argument of the process to get the true answer. In addition, Lockhart’s explanation of mathematics is “Math is not about following directions, it’s about making new directions”, however many schools will not educate more dense mathematics or give more imagination of creative aspects of mathematics. The section “Instrument of the devil”, has another Lockhart’s criticism about how the education is forcing students to follow the rigid format and giving their proofs or solutions. In addition, his view is that a proof is like a work of fiction or a poem in that its goals is to satisfy. Lockhart shares that the way of teaching students about the concepts of mathematics, can decrease the amount of connecting or understanding to other science, engineering, and technology ideas. Mathematics brings a fantasy to the students, which it will be a meaningful human experience in the

During a given day in Mrs. Bakers classroom, student enter and exit the room quite frequently. Students come and go from their classroom to Mrs. Bakers room back to their classroom; some students do this twice a day. During the school day, Mrs. Baker taught ten students. When students arrive, they are greeted and then told what they were to do for that day. On the day of observation, tests were administered for assessment and records. All ten students did

Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.

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,