Lou Henry Elementary Last Time Reflection

Learners may also have difficulty in understanding that a fraction of a group can be found when more than one object is represented, two fractions can be equivalent even with different denominators and that objects that are not the same shape can still be the same fraction. In terms of comparison students may have difficulty in comparing bigger fractions to smaller ones and in associating the size of the fraction to the size of the whole. Furthermore students may have difficulty is grasping all of the representations of fractions and the concept associated with fractions greater than one.

During this activity students were very engaged, they created their own figures using the pattern blocks. Below there are some of the examples of the figures that students come up with (see fig.1&2). After creating these figures, they realized that they could have use tringles to make their figures instead of the different shapes. So, I ask them “Could you show me how this could work?” Some students started to make the same figures but this time only using tringles. However, I noticed that David, one of the students was not doing the same as his classmates. Instead, he was writing a key, he wrote how many triangles were in a Hexagon, a rhombus, and in a trapezoid. Then he said “I think that I need 21 triangles.” I thought that was very impressive for him to completely do something different than his classmates. Then, I saw the opportunity to allow him to continue with the lesson while the others were still figuring out how many triangles were needed to create the same figure. After everyone was done with counting how many triangles were needed for their figures, I asked them to create fractions to represent the different shapes in their figures. In order for students to see from an

When the denominator is the same he is able to partition and see what fraction is needed to make the whole. When comparing fraction pairs, Adam is using gap thinking of the fractions 5/6 and 7/8 “both need 1 of their fraction to make a whole” understanding that each numerator needs one more part to make it a whole. In saying that, when comparing ¾ to 7/9 that have more than 1 to the whole, Adam said ¾ is larger, “1 more ¼ to make 1. 2 more 9ths to make a whole” He tried to apply gap thinking, incorrectly not understanding the unit of fractions. Adam has limitations surrounding improper fractions, not recognizing that 4/2 is larger than 1 whole and is equal to 2. He has misconceptions when comparing fractions with proportional reasoning is limited. When asked to draw a fraction he automatically swaps the numerator and denominator (6/3 to 3/6) when the numerator is larger than the denominator, when considering improper fractions, rather than converting to a mixed number fraction or whole number.. This displays Adams misconceptions of the understanding of the

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

When students finish the whole set of the fraction cards, the teacher will provide them with an answer sheet and they will flip box by box and self-check their work.

Many students get confused when learning about fractions. At our grade level we teach about parts of a whole, equal shares, and partitioning.

The teacher begins her math lesson with all her students sitting orderly before her. She then explains their lesson plans for the day and reads them a story book that was associated with their lesson. The begining of her lesson was quite effective because she had all her students sit quietly before her with no distraction. Throughout her lesson she had her students participate individually, so they could understand it on their own. Using this method,

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

Mr Williams is a Grade 7 mathematics teacher at an urban school. There are 38 learners in his class. They sit in neat rows and you will never hear the learners talking in his class. Mr Williams use different tactics that he believes will get the learners to work harder. He often tells them that in grade 7 the work is very difficult and that most learners fail mathematics. He has told his colleagues that he cannot get the work in the learners’ heads even he threatens them with detention. He says that he cannot understand why today’s learners are unable see the link between the work done in class and their everyday lives. He blames the CAPS curriculum for not being up to standard.

Once I asked the students to explain to me how they got to their answers, they questioned themselves and changed their minds by rethinking. One of the students, would piggyback from the other students’ responses to explain in number form rather in the math definition form. For example; the student would say “the 1 is on the outside, with 3 on the top and 4 on the bottom”. This indicates that the students still needed instruction on understanding the numerator and denominator

Question one requires students to find 1/6 on a number scale from zero to one. The question links to the Year 5 mathematics, fractions and decimals strand, Compare and order common unit fractions and locate and represent them on a number line (ACMNA102) (Australian Curriculum, Assessment & Reporting Authority, n.d.). Students who have met this strand should be able to successfully locate 1/6 on the number scale and give the correct answer, A. Those students that answer D may hold the idea that fractions are whole numbers (Reys et al. 2012). Looking at the denominator and not taking in the consideration that the fractions are numbers, students will think of 1/6 as 6 and choose the answer furthest away from zero. To help students over come this

For the patty paper activity, several students had a hard time folding the paper. While others did not follow directions and folded the fourths and the thirds in the same directions. Once all were folded corrected and highlighted the discussion started. Students used colored chips to show ¼ and 1/3. They were not sure of themselves because they kept questioning how come ¼ has only 3 chips and 1/3 has four chips. They did several in their small group before we did them together. The same students could not see the columns and rows that created the fourths and thirds, they only saw the twelfths.

I started my lesson by pulling from the student’s prior knowledge. We worked with a board with 12 frames, which was a dozen. After we established that 12 make a dozen, the student named different things that come in 12’s. I proceeded to explain the game we would be playing for addition and subtraction. After I modeled what we were going to be doing the student was able to perform the task without assistance. As I observed the student struggling with an addition problem, I was able to use the 12 frame board to help him regroup the numbers. The manipulative helped the student work through the problems as he was able to visualize the numbers on the board. The frame and counters helped the student solve the problems. I also modify the lesson

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.

Prior to researching teaching strategies that are effective with EBD students, I taught equivalent ratios using formulas and mathematical processes. Students frequently confused steps or demonstrated confusion in conceptual ideas while working with ratios and needed frequent correction. My research guided me to choosing the JUMP Math curriculum. JUMP Math utilizes teacher -directed instruction and graduated instructional sequence to break lessons down into incremental steps. I realize I was not introducing material in a way that accounted for the wide variety of learning gaps my students can have when I compare the lessons I gave last year to the lessons in the JUMP Math teacher’s guide. It was difficult for students to connect what they knew with what I was introducing. I anticipate utilizing specific teacher-directed instruction lessons in the JUMP Math curriculum will help my students understand foundational concepts which were difficult to comprehend. While the curriculum has built in extensions and challenges, I will still need to monitor students for engagement and be conscious of students who are working at grade level or who grasp mathematical concepts easily. Students who feel the lesson is too easy will be prone to disengaging or refusing to participate in the lesson. Pre-assessment of skills will be essential in this area.