Student Work-Montague

This week for math, students are practicing more with addition and subtraction. For math, we started with a number line activity. I had the numbers 0-10 written on big pieces of paper on the floor and had students come up to solve problems (as stated in the everyday math program for  unit 4 lesson 1). Next, I modeled the worksheet that my MT asked me to do with the students (on addition) and had the students do a problem with me. For the worksheet, the number sentences were already written and students were asked to draw dots to match each number and add up the total number of dots and right that number next to the equal sign.

            The worksheet that I analyzed reveals that this student has a concrete understanding of addition when using circles to match each number as in this worksheet. The worksheets were done individually and therefore, this helps me see that this student understands the concept of adding in the form of number sentences. This artifact does not reveal much about the gaps in the students’ current mathematical understanding that I can see however, it would be interesting to see if the student can do addition problems that are written vertically too (instead of all horizontal number sentences). One way that I would advance this student’s mathematical understanding would be to give him larger numbers, or to ask him what happens to the numbers when you add. Another thing that I would do would be to give him some subtraction problems so that I can see if he has a good understanding of subtraction as well. 

student work blog week 9

We have been working with identifying patterns in multiplication.  Many of the students are quickly able to identify that counting by twos entails skipping the odd numbers and landing on numbers that end in 2,4,6,8, or 0.  They can see that skip counting by fives produces multiples that end in either 5 or 0.  When looking for patterns in nines, they notice that each time the tens places increases by one and the ones place decreases by one. 

            For some students, these patterns are not so apparent.  For one student in particular, he struggled to understand the multiples of five.  He could not recognize that he was two repeatedly add five, and that the multiples would only end in five or zero.  One possibility of his misconception could be that he does not know his multiples of five.  Another possibility is that he may not recognize the difference between odd and even numbers, or the rule that an odd plus an odd will equal an even number, while an odd plus an even number will be odd. 

            One strategy I could use in helping to guide him to the correct answer would be to review multiples of five, showing him on a number line how to count up by fives.  I could also have him look for the pattern of the multiples of five by first writing them out and showing him how each multiple ends in zero, then five, and so on.  I should also ask him to explain the difference between an odd and even number.  

Week 13

This week we started to go over patterns, we discussed how we find patterns and then make a rule to extend the pattern. The first time we introduced the students to the task we presented a problem that was similar to the following:

You were hired by Jewel-Osco to make a can display. Jewel would like the display to be 10 rows high. How many cans does Jewel need in all to make the display?

The students were instructed with their partners to create a table that included information that would be helpful to answering Jewel's questions as well as write a pattern and a rule to go along with it. We provided enough cups for the students to be able to make a display with 6 rows but then would have to use the pattern to complete their table and answer Jewel's question about 10 rows.  The students had a very difficult time with this assignment. The students could not handle making their chart on their own so we brought them back as whole class and wrote the chart together then let them continue to work. Not one group was able to look for a pattern and write a rule, it did not even occur to any of the students that there could be a pattern present that they could write a rule for. By the end of the lesson all of the students were frustrated and could not figure out the problem.

Instead of giving up we re-edited the worksheet and set the problem up the same way except added to Jewel's question by asking is there a pattern to the can display. We also explictiy modeled more what we wanted them to do and how you could use the cups to make one of the pyramids and then count the cups and record the numbers you got. This all seemed to click with the kids, following the modeling the students worked together again and there was not one group who did not understand what we were trying to find out or how to find it out. I was very impressed that not only the students took the task seriously and were ready to try it again, but they took their time made each model and recorded all the data.

To me, that was one of the best parts each student had everything labeled for them to see on their paper and made it clear just exactly what they did to find the pattern so they could communicate that to the other classmates when they were called on.

Week 12

This week I noticed that one of my students although they were getting all their homework and in class problems correct could not do simply addition. This student had to count on their fingers in order to find the answer to every single problem. This was slowing down the student and hinder them from being in the extension group because although they knew the material just as well as the other students this student could not add 7 + 4 or any problem similar. As I began to show the student tricks like 10 + 8, well 10 + 10 is 20 so subtract 2 we get 18, I realized that they never actually learned basic addition skills they always counted on their fingers. I continued to look around the room and saw that many of the students in the classroom were counting on their fingers or were having to stop and think and count in their head.

It seemed like none of their prior teachers had modeled how to think through these problems aloud because they all were relying on strategies that are at  a much lower rate than what is required as fourth grade. When I first saw students counting on their fingers I allowed it because I had only notice the lower students and did not think too much of it as I felt that they were probably checking their answer. However, when I found out most students were using this method and it was to find the answer and their only way to find the answer, it blew my mind.

Being that my classroom is a fourth grade classroom there is no way that we can teach addition strategies or go back to simple addition problems to model for the students how to solve. However, with out doing either of those things I feel that some of my students are really going to suffer the end of the multiplication unit as well as the rest of the year in math because addition is present in a lot of math. It is because of that dilemma I feel that I am stuck between a rock and a hard place. I wish I could do something however I do not want to take time away from the fourth grade material that the students should be learning.

Number Sense

The piece of student work that I would like to analyze for this week is not artifactual because most of the work we do in kindergarten is large group discussion with some sort of tactile or kinesthetic option.  I played a game called "Monster Squeeze" with my kindergarteners and each of them had number cards zero through twenty and I used velcro "monsters" on a number line, asking them to find a number between those two numbers or a number that was bigger or smaller.  I could tell a lot about my students' number sense and if their thinking was actually centered on which numbers were larger than others or if they understood numbers as a memorized sequence.  For example, one of my students Hayley, told me that 17 was larger than 18 and that a number between 4 and 10 was 2.  I will reteach this lesson using some way to conceptualize the meaning of each number against the number line with objects.

Behrman_Student Work

On Friday I gave my students their summative assessment for my subtraction unit. My unit was adapted from our GO MATH curriculum, and although I liked most of their chapter test, I disliked how students were never given the opportunity to show their work and generate their  own answer. All of the word problems simply had students bubble in an answer from the presented options. Therefore, I decided to modify the final two word problems so that students were not only required to show their work, but also produce an answer without being able to compare it to the list of possible answers. One of the subtraction word problems involved comparing with an unknown quantity. The problem stated, "Mario earned 35 Art Bucks at After-School. He has 6 more Art Bucks than Alessandra. How many Art Bucks does Alessandra have?"

This student, Hector*, exemplifies a common misunderstanding I observed when grading these tests. He drew 35 Art Bucks to represent what Mario has, and then added an additional six Art Bucks to find what Alessandra was. This reveals that the Hector (and many other students) still need practice with comparing two amounts. One next step I plan on taking with him, as well as my class, is to practice with some hands on examples between two students. I will distribute the same number of bingo chips to two students and have them color in on a piece of graph paper how many they have. Then, I will tell one of the students to take 4 more bingo chips from the bag, and color those in a different color on the graph. This will visually help students to see/count how many more the second child has. Also, it will allow us to discuss what the term "more" means and when we hear it used (I need more time, I want more juice, etc), so that students recognize more=the number is increasing (adding). Thus, if someone has more than you, he/she has a bigger number than you. To find out what you have, you would have to subtract.

Even more interesting with Hector's test is the answer he generated after counting up his drawn figures: 52. With Hector, in particular, I would like to sit down with him and have explain to me what his drawing shows and watch him count them to see if he is still struggling with one-to-one correspondence or is skipping numbers when counting. Since most of my students are ELLs, they sometimes skip numbers or say them out of order since they aren't as exposed to these number words in English.

Delise Week 13

This week, the students took a unit assessment. Although this unit had not covered math facts or adding/subtracting with two digit numbers, they threw some in the assessment. This particular student has not struggled in math so far this year, so when I saw his assessment, I found it pretty interesting. the picture on the left shows this student who was able to solve c and d correctly, but did not solve a and b correctly. For c and d, this student added the two numbers horizontally. For a and b, this student subtracted, but upside down. He subtracted 7 from 8 and 4 from 6. His answers would have been correct if those were the problems, however, they were not. I am curious to see if these problems were written horizontally, how he would have done. In the picture on the right, the same student was given a two digit subtraction problem. Instead of subtracting, he added. It is kind of hard to see, but his answer was 66. Once again, if this was an addition problem, he would have gotten the problem right. I wonder if this student doesn't know what it means to add or subtract. I am also thinking that if he is able to put together numbers in some way (although it is wrong),  that he probably just needs some reasoning behind addition and subtraction. I would like to work with him to see how he does these problems, and start with him on a smaller scale, working up to double digit addition and subtraction.