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.

Lewis work blog week 14

The past couple days we have been working on developing patterns and predicting where the pattern will be in the xth stage.  My mentor teacher and I will present the first three sequences of a pattern, ask the students to recognize the rule, then apply that rule in order to find out the a specific part of the pattern further down the line. In one problem, the students were presented with the following problem. 

This problem was taken from the quick check the students were given at the end of class.  This problem is simpler than predicting a pattern far past the next unit of the pattern because it is simply asking how many blocks will be in the next tower.  One of my students had the misconception that the next tower would have four blocks in the fourth row.  From what I can tell, she is confusing the number of the column with the number of blocks in each column.  When I reviewed this problem with the student I asked her to draw out each part so she could see the addition of two more blocks to the second row each time.  This helped her to recognize the pattern. She then counted up the total number of blocks with the fourth row added and arrived at the answer of 20 total blocks in all.  

More, Less and Equal Values- Kayleigh Robb

After moving on from my measurement unit, my students are diving into comparing numbers 1-20 and deciding if certain values are more, less or equal. I began by having a whole class review of the numbers and then began to demonstrate, with cubes, a pair of numbers. I coordinated the numbers by color and asked which color group was “bigger” (more) and “smaller” (less). I did this several times, gradually giving students more say in what we compared and how we compared them. I then asked student to compare the number of 6 blocks to another group of 6 blocks. “Which is more? Which is less? Turn and talk to you partner about!” Although I was not hoping to, I did not trick them. Students responded when I called them back that, “No, Ms. Robb, they are the same!” I responded with “Yes! When we make comparisons, boys and girls, we call that equal.”

 Then I passed out the cards, 1-23 (the number of students in my class) and asked students to go around and talk to their peers with their cards. The students told each other what their number was and then said, “I have more than you.”, or, “I have less than you.”

I went around and acted as “the zero”. I wanted to interact with individuals as well as groups.  I observed this several conversations first. There were several excellent discussions. The following is one that really stopped me in my tracks:

Student 1: holding 19 “I have 19.”

Student 2: holding 13 “I have 31.”

Student 1: “No. You don’t have that.”

Student 2: “I have less than you. This is less.

Student 1: “I have 19 and I have more but that’s not 31.”

Teacher: “Student 1, what do you mean? Can you show student 2?”

Student 1: “Well, 31 is a 3 and a 1. And that is a 1 and a 3. I think its, 13? Ms. Robb?”

Teacher: “Yes, it is 13! Is 13 less than 19?

Both students: “Yes!”

Teacher: “Excellent, I think you both made very good comparisons!”

            Here, I see that some of my students need background knowledge concerning the explicit naming of the numbers, 1-20. This student was not the only student to “misname” their number. But I can see in this students thinking that they recognize that in the order of the numbers, this number comes before 19, and therefore is “less” than 19. I can tell this because the student is able to determine that their number is less than the number that their partner has before their partner has an opportunity to say that she has “more”.

Student Work Blog- Week 13

Different symbols and ways of Writing Division Problems

            As students approach division,  they are introduced to different ways of writing division problems. It is important for students to be able to recognize different division symbols in order to know what to do when they are solving math problems. The activity that students had to do in class was to solve division problems. The division was not hard for the students however writing their solutions in different ways seemed to be a challenge for students. Some students were used to seeing the ÷ when they were doing division. Students got all of the division problems that included this symbol correct. However, students were not able to solve division problems set up like this: 4|¯24. Students had never seen a division problem set up like this so a lot of students did not attempt this problem which caused their score on the activity to go down. What this says about their current mathematical understanding is that they understand what it means to divide. Although they may not know all the symbols for division, they can successfully carry out division tasks. Based on the activity, the gap in mathematical understanding is that there can be different signs that mean the same thing. At this point it seems that students have not been introduced to different signs for division. Students have been accustomed to solving division problem in different ways. Two activities that students can do to further their mathematical understanding would be to practice solving division problems in various ways using different symbols this will help students become more familiar with various types of division. Another activity would be to practice division problems using different symbols. By practicing writing the symbols different ways students will become more familiar with how to write division problems and be able to recognize to recognize different division signs when they see them.                                                                                                                                                                                                               

Student Work- Jones Week 12

There is not Student Work Blog this week because of Thanksgiving! Happy Turkey Day!

Student Work- Jones Week 11

Multiplication and Division- How are they related?

            As I continue to work with my third graders, I continue to see how they relate different subjects. As students left Unit 3 and Measurement and entered Unit 4 which focused on Multiplication and Division, I had the chance to see how students thought about  Multiplication and Division. One of the first activities students did in Unit 4 was completed a Fact Triangle. A fact triangle consisted of three numbers that could be multiplied and divided be each other and not have a remainder. A Fact Triangle  for 5 and 25 would be (starting at the top, going down to your right, across to your left then back to the top) 5 times 5 is 25; 25 divided by 5 is 5;  5 divided by 1 is 5. Student would have to know multiplication and division in order to solve these Fact Triangle. Students had to complete Fact Triangle provided by their Math Journal, then they had to create a Fact Triangle of their own. This work sheet showed that students are able to multiply with ease however not all of the see that  multiplication is  the inverse (opposite) of multiplication. The fact that students do not see that multiplication is the opposite of division shows a gap in their mathematical understanding. Students should see that if they are able to multiply that they are able to divide. Although students may not be able to immediately see the connection between multiplication and division, students should be able to see that there is a connection between the two. Two future tasks that I could have students do to help their mathematical understanding of the connection between multiplication and division would be to have students work on word problems involving multiplication and division and to set up problems that allow them to use multiplication to help solve division problems. Through the problem solving and the setting up of number models, students will get used to seeing multiplication and division together and therefore making the concepts more concrete for them.

Student Work- Jones Week 10

Relating Circumference and Diameter

            We have worked on circles in my classroom. More specifically, how circumference and diameter are related. For classwork, students had to measure the diameter of circles and apply the 3 times rule to find the circumference. The three times rule was very interesting because it is connecting multiplication and circles. When students heard “three times” most of them thought that they had to multiply but they did not know what they had to multiply. We discussed the three times rule. The three times rule stated that the circumference is three times the diameter. When I first introduced this to students, they seemed skeptical that this idea could actually be true. After showing them examples, student believed the idea and were ready to try it on their own. Student were successful with this task. While walking around and watching students as they approached the activity with the three times rule, some students actually measured the diameter  of the circle and wrote out the multiplication problem to show their work. For example, if students measured a circle with a diameter  of 3 inches, they would write “3 X 3= 9, so the diameter is 9 inches. Other students did not need to do this because multiplication is a concrete concept for them and they are able to do multiplication in their heads. Some of the students were also able to think of the circumference as a straight line that when they measure it would be 3 times their diameter. This activity showed that students can take a concept that they understand such a multiplication and relate it to a not so familiar concept such as the circumference and the diameter of a circle to help it make sense. This shows that students current mathematical understanding is at a point where they can connect different concepts together which will be valuable to them as they continue in their academic career. The gaps that appear in their current mathematical understanding seems to be viewing circles as a concept in itself. Students wanted to connect circles to something that they knew which was wonderful however, I do not feel that students view circles as a concrete idea at this point. Students will need to do more work with circles so that circles will become its own idea and student will know when and where to use different ideas to find different parts of a circle such as its area. Based on this activity and what students took from it, two potential activities I could do with students to further students understanding of circles would be to have students define circles to make sure that they understood what a circle is. Some students view ovals as circles, but ovals are not circles. By having students have a solid understanding of what a circle is, students will be more likely to understand different aspects of circles in the future. Another activity would be to have students draw circles and find the diameter and circumference of circles that they draw. By doing this, they will see that in order for formulas of a circle to work, you have to have a perfect circle. What I mean when I say a perfect circle is that the students do not have any dents or edges. If a circle had these things and a student attempts to measure the diameter of the circle, the diameter will be wrong. Students need to see this for themselves so that in the future they will be able to understand circles and recognize circles and non circles when they see them.