Student Work: The Final Week

          This week, I started an experiment in math with my third grade students. My students were confused about how an experiment in mathematics would work. However, after the first few days of working on this experiment, I noticed how supporting mathematical content with engaging experiments  allows students to not only be exposed to different mathematical tasks (calculating the area, importance of many trails, finding the median, graphing, etc.), but it also allows students to better understand that mathematics does not just mean computing and calculating; rather mathematics encompasses investigating, analyzing, and understanding. After this experiment, I would ask my students: What did we learn from this experiment? What are the different mathematical processes did we use in this experiment? Is it important to perform labs in mathematics?

Van Poperin- Graphing in Kindergarten

I learned a lot this week from a lesson my mentor teacher gave and the group share out my students participated in.  Meghan had the students discuss their favorite colors and group themselves accordingly and had each of them color a sticky note of their favorite color.  She then led our students to inquire about how we could display this math data, asking probing and prompting questions like "does anyone know of a way we could show this on our big piece of paper here?" We went around the rug with student volunteers sharing their ideas and a few of them made comments like "We could each put up our sticky notes with the rest of that color, like Ashley's favorite color is pink too so we would put ours together," and "we could stack them up like we did with the connecting blocks so we could count them all and then they'd all be together."  Meghan pushed their mathematical discussion even further when she asked "But is there a way we could show how many of each color without having to count each group over and over each time?"  Jamir and Calvin then volunteered their idea which was to put a number on the top of each stack of favorites.  Jade then suggested that we put numbers on the side and it would tell us how many each group had too.  I felt as though I watched my students thinking take a few turns and twists, incorporating each new person's contributions to their working theory.

Jones- Student Work, Week 14

My 3rd grade students had the task of completing the Unit 4 Progress Check because they have a test on Monday. I chose to give them the progress check in class instead of for homework because it would give me  a chance to figure out what they know and what they did not understand. I could answer questions and clear up misconceptions as we reviewed the work together in class instead of letting them fester over night. I have learned that my 3rd graders learn a lot from talking through what they do not understand. They are sometimes able to fix their own misconceptions because they are able to express their thoughts verbally. The Unit 4 Progress Check included multiplication and division word problems, completing fact families and identifying the rule (i.e. Do you multiply or divide by a number to make the number sense true. My students did well with this Progress Check. Below is a sample Unit 4 Progress Check from one of my 3rd graders:

After reviewing my students work, I learned that the current mathematical understanding shows that they understand how to multiply and can solve multiplication word problems. My students current mathematical misconceptions/ misunderstandings are with Division. When I introduced that division is the opposite of multiplication, students assumed that they could multiply numbers to find the answer to a division problems. In some cases that is true but not in all cases.
Future activities that I could have students do to help clear up their mathematical misconceptions would be to have them discuss what it means to multiply and divide. By talking through their understanding of these two concepts I can better understand where my students misconceptions lye. Another activity would have them practice doing division. By practicing division my students will be more comfortable with it and therefore overcome misconceptions.

Final Student Work Blog

This week we introduced the math concept of telling time. Students are incredibly motivated to learn this skill after a discussion about why this is important to know now and when they are older. One of the first homework assignments for this short unit involved a worksheet with students writing the time in digital form that corresponded to the analog clock to the hour or the half hour. Several students made an error with identifying the hour when the minutes hand was half past the hour. For example, when the clocked showed 12:30, one student wrote 1:30. This same student also wrote 10:30 when the clock showed 9:30, which is interesting because he put 10:30 as the answer for a clock in an earlier problem that actually showed 10:30. This shows me that students are confused when the hour hand is between two numbers and don't understand that it hasn't yet reached the next number. One next step to do with these students would be to have them use the clocks where both hands move simultaneously, so that they see the connection between the minute hand moving and the hour hand moving. Another next step would be to show him the two different clocks from this worksheet that he put the same answer for and talk with him about the possibility of them having the same answer in digital form if they look different in analog form.

Ricchio Week 14

This week in Math we are working ballpark estimates. We want students to understand how to round numbers either up or down. We introduced students to the rules of rounding. If a number in the ones place is 5 or greater, then round up to the nearest tens place. If the number is 0-4 then you round down. While most students are liking this concept because it is "easier", many are still completely solving for the exact answer. I think it's hard for them to change their thinking when they are always being asked for the "correct" answer. Although the answer is correct, this is not what the problems are asking for. The purpose is so that students get comfortable estimating, which is a skill they will use the rest of their lives (grocery shopping, restaurants, etc) . A way to further their understanding would be actually showing students the importance, so they want to use estimation. If they understand how estimation gets them closer to the exact answer, they will begin using it as a strategy.

Delise Week 14

This week, I worked individually with a student, Kimmy, who struggles in math. We were working on change diagrams. In their math journal, there was a page of fish with different weights. The problems in their math journal would say: Fish F (11 lbs) ate Fish C (5 lbs), how much does Fish F weigh now? The students would fill out the change diagram; start box, an arrow with the change and the end box. Kimmy normally does not do her math journal. She does not participate, even when called on. Kimmy is extremely shy and it is hard to get an answer or explanation out of her. For this particular lesson, I pulled Kimmy aside and worked with her. She was able to fill out the change diagrams on her own with no help, and was able to tell me how she came to her answer. I think that she works better in a small group or one on one. Since Kimmy is in my RTI group, I have established a relationship with her. The last problem in her math journal was about seeing the difference in weight between the two fish. Other students in the class raised their hands and had questions about that problem, so I left Kimmy to go help other students. When I came back, Kimmy had finished the page and the difference problem was correct. I asked her how she got the answer and she showed me how she counted up. I was amazed, not because I didn't believe that Kimmy could do the math, but because of the difference in her attitude, from giving her attention and working with her individually. I sat with her while she did math boxes and she was actually okay to do them on her own. When I went over them as a class, Kimmy raised her hand to answer every problem. I found that just giving her praise for her methods of computing the math, her attitude and confidence was dramatically changed! I am excited to continue to bring out the mathematician in Kimmy!

Maxwell-week 14

This week, my student’s have focused primarily on measurement, as it is the main focus of their current math unit. Specifically, we have been focusing on area, perimeter, standard and non-standard units, and equivalencies.  My students begin their morning with fifteen minutes of independent reading followed by a math message and daily math activities before beginning their math lesson for the day.  Yesterday, their morning math message was a question dealing with measurement equivalencies.  The question was as follows: “Imani measured the classroom door and found that it was 36 inches, Jeremiah measured the same door and found that it was 3 feet, can they both be right?” The majority of my students answered the question “no”.  They were unable to recognize that 36 inches is equivalent to 3 feet.  The math message ended up dominating the majority of our math instruction time yesterday, as it was clear that many of the students still had serious misconceptions regarding measurement. 

Our instruction highlighted how one foot is equivalent to 12 inches, therefore two “foots” are equivalent to 24 inches, and 3 “foots” are equivalent to 36 inches.  This instruction seemed to help clear up my student’s misconceptions, however, I believe these misunderstandings were valuable tools.  It is easy to understand how a student would not understand how two different numbers could represent the same amount of something.  It is valuable to keep in mind these rather obvious issues students could struggle with.