Math Reflection

Literature: Read Remainder of One by Elinor Pinczes to prepare students for the lesson. “What do you think is going to happen in this story? Based on the title, what do you think this has to do with division?” Read the story. “Can anyone tell me how division was used in this book? What happened to the extra 1 person, or the remainder? We are going to learn about dividing larger numbers today and how to do it correctly.”

Students had previously covered the topic of developing fluency in multiplication by 2-digit numbers. After that topic students moved on to cover number sense, dividing by 1-digit divisors using mental math to prepare them for the following topic of my learning segment. The topic of my learning segment consists of developing fluency, dividing by 1-digit divisors. I designed my lesson as a three-day unit focusing on long division by modeling division with place-value blocks, dividing 2-digit by 1-digit numbers, and dividing 3-digit by 1-digit numbers. Students were introduced to division prior to my learning segment but the struggled to understand and comprehend division because students were only introduced to the division algorithm and were not provided with a mnemonic to help them recall the steps. Students also weren’t introduced to division with manipulatives or drawings. Therefore, I

In lesson 1, I would still use my same warm-up problem, but as mentioned above, I would want to push the students to think deeper about the problem. I would accomplish this by asking probing questions to get the students to consider the problem from a different perspective. Also, by creating a more debatable perspective, the students would have a greater opportunity to defend their thinking with mathematical reasoning. This would also challenge the students who do well in math to think even deeper about a concept that may seem obvious.

In the chapter, “Equal Sharing Problems and Children’s Strategies for Solving them” the authors recommend fractions be introduced to students through equal sharing problems that use countable quantities because they can be shared by people or other groupings. In other words, quantities can be split, cut, or divided. Additionally, equal sharing problems assist children to create “rich mental models “for fractions (p.10).

I know that students learn best by hands on activities and creating. I choice to have the students use cheerios as part of the hands on activity and to create their own arrays, equations and story problems. They were free to pick numbers of their choosing with in my parameters of numbers. This supported the rigor because I asked them to create from scratch but also gave them to freedom to choose their own numbers and stories. As a teacher this was a great lesson to visually see who understand the standards and goals and who needs more practice. Most of the students who struggled with this lesson struggle with addition. I gathered the struggling student into a small group the following day to work on those skills. The learning outcome for this

For the Kidwatching Project Part 1, I found myself interviewing a few students on the concept of multiplication and division. According to Merriam-Webster Dictionary, multiplication is defined as the process of adding a number to itself a certain number of times: the act or process of multiplying numbers. Merriam-Webster Dictionary also defines Division to be the act or process of dividing something into parts: the way that something is divided (Merriam-Webster, 2015). Multiplication and Division is a subject that many different students in early ages can grasp or struggle with because the concept of using different ways to approach these particular problems. Many kindergarten children can solve simple multiplication and division problems

Objective: Students will understand and explain the effects of addition and subtraction of fractions with like denominators. Students will be able to read and understand a word problem and determine what operation, adding or subtracting, the word problem is asking and be able to complete the operation correctly.

The child from my video is my niece Adriana. Adriana is eight years old and she is in second grade. Since, she is my niece my brother gave me permission to include her in the video. As I went through the activity I tried not to do any modifications in the instruction, I just made up the division problems as I went through the video. The only thing I change was the counters for the cubes. The student learned how to do simple division using equal grouping. I know that she learned because she worked out few problems by herself at the end of the video. She was able to recognize dividing by equal grouping is just having the same number of units in each group. Example she was able to solve six divided by two by drawing a circle for each group and

I would with one students on how to make equivalent fractions, She was very confused and did not know how. So I demonstrated the example that was written on the board. I wrote 3/6 and then wrote the division character by the numerator and denominator and then wrote 3. So then I said 3/3=1 and 6/3=2, then wrote 1/2. Then we tried to reduce 25/100, so I said, “What can you divide by 25 and 100.” She said 5 so she followed the example that I had written. So I said, what’s 100/5, she said, 20. So we knew the denominator was 20. Then I said whats 25/5, she said 5. So then I said the equivalent fraction is 5/20. She wrote done all that we had discussed above as we were finding the answer. I still think she was a little confused after, but it was time for discussion. For next time, I think I would try multiplying as another example, which I think could help the student see both. what I would have done was try multiplying instead of

Jaclyn’s grade 8 math focused on mixed numbers to improper fractions. Jaclyn’s tone of voice was clear and welcoming to all students. Jaclyn used the Smartboard and OneNote to show examples of dividing fractions and simplifying fractions. Students were engaged and focused on the questions that were given to them as practice questions in OneNote software. Jacqueline also used instructional strategies and classroom management to refocus students on the task by asking students to put down their pencils while she taught certain math steps and she asked for student feedback while proceeding through each step. Jaclyn encouraged students to work in groups of five students at each table and she monitored each group by prompting questions with each

My lesson was based on the research that I conducted on teaching multiplication. I read in the Common Core Progression Documents that students learn multiplication through equal groups and array models. In my lesson I taught both equal groups and array models, but focused on the array models. I used the array models to help the students visualize the iterating that happens in multiplication, which was something that I had read when doing my research. I had also read that students should use the models to perform repeated addition or skip counting and I had the students do skip counting in my lesson.

The pre-assessment used to establish students' baseline knowledge and skills for this lesson was a comparing fractions pre-test. Students compared the following types of fraction comparisons: unit fractions, benchmark fractions, normal fractions, equivalent fractions, improper fraction vs. normal fractions, and improper vs. improper fractions. I have taken the information and used it to figure out which types of comparisons the students understand and using it to work on increasing the students' ability to include the other types. I use the information to accommodate what the students already know about the target. It showed me that students do not understand how to compare fractions, when they have a different denominator.

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.

During the observation time I was placed in a first grade classroom. Walking into the class I began to look around and smile, there was so much color all over the classroom I could not help but feel happier. The teacher immediately stopped the class and told us what they were doing that morning and had each student introduce themselves to us. They went around and stated their name and then went back to their math workbook. When they were finished with their math worksheets they were then able to pick something to do around the room. That included reading on their own, getting to use the iPad, working on the computer, etc. Some students were together while others chose to work on things independently.

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.