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I have been struggling with the process of getting students to ask each other questions. I recognize that a lot of this has to do with not having practiced it, nor have the students had much experience with it. Our first grade group had a good discussion on what we could do to make this process more inclusive, fun and interactive for ALL. Based on this, I will do a type of game, where students have a number on their back and they have a partner with a similar number based on an algorithm taped on their back. (10/partner 1 & 5+5/partner 2). They need to learn their number by asking YES/NO questions. Is my number greater than 50? Less than 50? etc.... Once they learn it, they need to find their partner that has the same # as them. This person has been moving throughout the room, asking similar questions, hopefully. Once they make a match, they then can sit down or they win. I haven't figured out the ending quite yet. IN any case, this seems like a great way to get the class involved while giving each individual student exposure to asking questions. I am excited to try this experiment. Tune in for more !
Eileen, Katherine, myself and Debra Mattson, experienced a special math lesson last Friday that I'm writing about because it incorporated the use of the mathematical practices cards with questions that we used in our class. It was a very powerful lesson for both reinforcing concepts and using cooperative group skills. We started by modeling with the 4 teachers how to work cooperatively in a group. The math concept we were working on was graphing and the students with linker-cubes task were to organize the linker-cubes into 2 different types of graphs, after which they would write word problems using greater than, or fewer than language. The first would be the tally chart, and the next would be a graph of their choice( bar, line plot, pictograph etc.) The emphasis was on learning to work in a group and do so cooperatively. Showing the difficulties of sharing tasks , the students watched the teachers with interest and focus. The modeling that prefaced their group work was invaluable, especially as it was 4 adults and the students benefitted so much as evidenced by the language they were using in their group work. We also gave out the math practice cards which they all used to great success. We witnessed students changing behavior and work as a result of asking the questions on the cards and doing so cooperatively. The result was an incredible array of graphs and word problems to go with them, without very much teacher intervention. My conclusion definitely will lead me to much more modeling for even an activity that I assume students should be able to do. Of course we all decided that having 4 teachers in a room with 18 students is amazing but not having that luxury we could use other students for the modeling. Taking that time, even when it seems unnecessary is invaluable….my take-way.
My class continued working on the open number line, but this time in a small group during math centers last week. I was pleased with the dialogue that the groups were having. For example, one discussion started with the typical, "How did you solve that problem?" The student talked about how he added the tens and then the ones. He added the ten made from the ones to the other tens and then added the total tens and the ones. Another student responded, "I didn't think about that!"
I had a couple of students solve their cards but would randomly place them on the number line. (I think theses students may have been overwhelmed with either having to memorize what the answer to the previous cards were or resolving them.) A student would quickly disagree and make a statement such as, "I respectfully disagree with that because 44 is bigger than 25." I would step in at moments like this and ask, "So, are you saying that 44 is greater than 25?" to reinforce mathematical terms.
I think it helped a great deal to have used the same equations for the number line because it allowed the students to see them solved in a different way by different people. Along with the review, the smaller group also gave both the strugglers and the quieter students an opportunity to practice other aspects of a high quality discourse--where to stand so as not to block the number line, how to hold the card and showing the others without covering it up, projecting one's voice, being an active listener, etc.
I plan on doing a juicy problem of some sort at the end of the week and I am going to challenge myself and the children by using some of the MP question stems.
On April 22nd, my students and I continued to defy odds with a juicy problem supplied by our school’s math coach, Kim Duncan. She came to lead the session and we practiced mathematical strategies 3 (I can explain my thinking) and 5 (I can use math tools).
Three math tools were given to the students (cuisenaire rods, unifix cubes, and base ten blocks) with the question as follows:
Sam counts 48 wheels in the parking lot. How many cars does he see?
One student chose unifix cubes and others soon grabbed them as well to work. Three students with probing questions from Kim and I began to group cubes by “4” to show one car has four wheels.
I noticed how one less confident student keenly observed a peer sitting close by and imitated groping cubes in 4’s to start solving the problem. I could not help but to think then the words, “Imitations is beginning of imagination!”
Solving the juicy problem was difficult for my students especially when it came answering “Can we explain how we solved the problem?” or “What is the evidence that supports our solution?” However, Kim and I were thrilled to see all students persevering in using their gifts of drawing or using manipulatives to show mathematical knowledge even if words did not come naturally. They also managed to speak up and express their understanding provided a few words or phrases.
I hope to further challenge my students on Monday, May 4th with the following questions and see where it will lead us:
Jay likes Hondas. He owns a few cars and a few motorcycles. Jay counts a total of 26 tires. How many of the Hondas are cars? How many of the Hondas are motorcycles? Please show your work and label it!
Why? My students may struggle with retaining concepts and lack computational skills to be fluent with facts. Nevertheless, four middle school students in grades 6-8 receiving Special Education Services due to cognitive deficits have also demonstrated how they can still be challenged at the highest level possible and show growth given necessary supports.
Perhaps, I will try Open Number Line in a small group like Mo during Math Centers prior to delving into our juicy problem above.
We have really been focusing on guiding questions. The students are very receptive to asking questions that will help with clarification or getting a student to the next level. I have noticed they ask questions about a previous step to get the student to talk about what they did and guide them on moving to what they should have done as a next step. They are so excited to help each other with questions! The student who is struggling is also receptive to getting the help needed to move them forward. It is really nice being the facilitator and not the one asking questions. I love how it empowers them and brings us closer as a class.
I really enjoy class. Very valuable. After last lesson with my class, I was feeling a bit discouraged. Thinking, what am I doing wrong? They aren't asking the right questions. Why don't they get it? After being in class, Eileen helped confirm my feelings that they just aren't ready to come up with deep questions at this age.They are young. We're prepping them for asking questions on their own. In kinder we have to give them the foundation. Start with vey simple, basic questions. Sentence starters and specific questions to ask.
I have learned so many different activities and ideas to bring back to my class this session. I am hoping you will offer this again for other teachers and maybe an extension to this one. I think the discussions we have had in this class with each other has taught me how to discuss with my students.
I was sorry to have to miss this class because I always come away with good ideas, and I really love talking to the other first grade teachers.
I had been working with the open number line, but I wasn't really having a lot of success with students asking questions of each other. They were either agreeing that the student had placed the card in the correct spot or pretty much telling them where it should be placed.
Since we had been working with comparison bars and using the terms more, fewer, most, fewest, I wanted to do a lesson with those concepts.
Eileen and Catherine came in and presented the lesson. I had placed the students into groups of 3 and Eileen and Catherine modeled how you would work cooperatively in a group. The students were given tubs of unifix cubes and asked to sort them. They then had to make a statement using the vocabulary words. The rest of the team had to agree or disagree and then they repeated the statement. After this stage they were given a comparison problem that they had to solve.
It was WONDERFUL having 3 teachers in the room. I got to observe and really listen to the students and what they were thinking. Usually I am moving around putting out fires.
The questioning part is still difficult for most all of the students. They want to rush in and tell others the correct answer. This is a skill, and like any other skill it will develop over time.
This year was a challenging year, starting a new program with a combination class; however, I feel I have improved my teaching strategies in math discourse. There is definitely more collaborative discussions in my classroom during math along with student board work and student generated conjectures. I need to continue to encourage my students to ask each other questions. Using the Mathematical Practice Icons with questions will help this process.
As this class comes to a close, I am left with a huge repertoire of tools to bring into my classroom. I'm realizing that students need lots of support using modeling and sentence frames. Getting students to question others and make rebuttals is a year long process that will grow deeper and develop through each grade.
I have valued this class. It was very meaningful and offered me lots of great strategies to help me implement Common Core. I will admit that it sometimes took me out of my comfort zone. I especially liked using number lines for everything. My class loved this as well. This class was very beneficial to me because I am in a new grade level this year. My favorite part was meeting and working with teachers throughout the district in my grade level. Thanks for the amazing opportunity. I hope there will be more classes offered in the future.
After our discussion in class on 4/20, we decided to work more with our students on word problems and to continue asking probing mathematical questions to further student discourse. The math problem that we asked our kindergarteners this week was, "There were 10 apples on the ground. There were 5 apples in the tree.How many apples were there altogether?" The majority of my students were able to solve this problem quickly and explain their thinking. However, when I asked them, "what do the numbers represent?" not one student raised their hand. This puzzled me. Why did they not know what the numbers in the problem represented? I had a student repeat the word problem, yet still blank faces when I asked if anyone knew what the numbers represent. When I told them that it represented the number of apples on the ground and in the tree, the whole class went "aahhhh" as if they should've known that one. I moved on to the next question, which was, "can you make a model or draw a picture to show this idea?" Many students raised their hands to come up to the white board to draw a picture and all were able to draw it in their math journals. Overall, I think the increase in mathematical discourse in my classroom due to this class, has supported my student's mathematical thinking and articulation abilities. However, I do think they need more practice with juicy problems so that they can ask each other questions about their thinking.
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