Car Caravan: How many minutes will it take to create this?

After watching a video of the students’ discussion from Day 1, we decided to use our target student’s one mathematical wondering below and present it as the challenge of the day.

The challenge: How many minutes will it take to create this?

We presented this challenge at the end of community time and invited those interested to work together to solve it. I brought the students to the drama area since it had the most room. We cleared out the furniture and sat down to get to work. Here is a documentation of our conversation below.

Teacher: What do we need to create this?

Student 1 : Marbles

Student 2: Little pieces of red/orange

Teacher: Of what exactly?
Student 2: Paint

Student 1: Wood

Teacher: We need to use what we have in class so have a look around or if you’d like we can look in our storage room as well.

Students were very excited.

Student 2 ran to get a picture of pattern blocks made into the alphabet.

Teacher: Oh wow that`s interesting.

Student 1: It`s too big

Student 3 went to get more pictures of the pattern blocks and talked about making a rocket.

Teacher: Do we need the pictures of the blocks or the blocks?

I noted they were getting side-tracked

Teacher: How do we know the pattern blocks are good materials?

Student 1: No, we don’t have pink.

Student 2 grabbed the chips of red and yellow.

Student 1: It`s not the same colour.

Student 3: Grabbed a puzzle.

I noted they were very unfocused and needed guidance to choose a material and move forward.

Student 1: It`s too big (shouting).

Student 3: Same size

Student 2 got the pencil crayons.

Student 3: Yes!

Student 1: No, it`s too big.

Teacher: Let`s compare!

Student 2 got more pencils and started to build.

Student 3: Let`s get started.

Teacher: Prompted to clean up what wasn't being used and help gather more pencils.

Student 1: Pencils are not good because we don’t have a lot of yellow.

Teacher: Where else can we get pencils?

Prompted them to make a list of what they needed using the colour words in class to copy the name in French. They only listed yellow and we went to ask two other classroom teachers to borrow their yellow pencil crayons. I encouraged them to count how many they took and write it down so we could make sure to return the right amount. During this time one student lost interest but two others joined to help start to create the image.

We took a snack break and then it was almost clean up time so I decided to take them in the hallway so we weren't distracted and I could take a video. I then took a video of them building it and gave my phone to one student to keep track of the minutes. In the end, I said all students needed to give a thumbs up to show they agreed it was complete. One student was not happy so I prompted him to explain why and for them to fix the issue before stopping the time. He claimed they needed purple.

In the end I encouraged one student to write down the number. I noticed he had trouble writing it down because of the colon and decimals. So I asked all four of them to try to copy down the number.

Next step: Present our video to the class and the next challenge will be to debate the answer to our challenge question after looking at their written results of the time it took to create the image.

Collaborative Math Inquiry: Car Caravan Math Task Results

After completing the Car Caravan task with our students, our primary team gathered to discuss the results. Click on the titles below for the detailed Kindergarten learning stories.

Kindergarten Class A: I see, I think, I wonder...

Kindergarten Class C: How many minutes will it take to create  this?

What similarities did we encounter when presenting this problem?

• The problem was very open-ended and we had trouble getting students to developing mathematical wonderings.
• Students both in Kindergarten and Grade 1/2 needed lots of prompting to develop mathematical wonderings.
• Most primary students noticed the colours first, the floor and some talked about the shape.
• The main observations were about the colours and shapes.
• Regardless of the Grade, students in both Gr. 1/2 and in Kindergarten came up with wonderings that were mathematical at all.

• When the Car Caravan was presented in a small group to target Kindergarten students, educators found that they were distracted easily.
• Some students were overwhelmed by their own questions.
• Students observations demonstrated their fixed mindset Ex. Insisting that their observation was correct and was not open to others’ ideas.
• We discovered students’ comfort level in using counting strategies.

What strategies worked?

• It was best to take the small group out of the classroom to help students focus when presenting the Car Caravan photo and to be able to discuss their wonderings.
• Students needed prompting to get them thinking more mathematically:
• What mathematical question do you think I’m going to ask you?
• You see circles? How many circles do you see?

Teachers Successes:

• Presented the challenge so that students had a voice
• Gave students the liberty to discuss their wonderings without any time constraints
• Clarified their answers by repeating their answers so all could hear and think about it.
• Gave everyone the opportunity to join at any point (kindergarten)
• Praised them for the time and effort put into their work or for any participation or idea suggested whether great or small.
• Allowed students to choose any materials to show their thinking
• Set up the materials as a tabletop activity with the intention of allowing them to build the car caravan in their own way

Next Steps:

• Grade 2s responses seemed to list various possible counting strategies but didn’t show any reasoning for choosing those strategies. We decided that they needed to continue to extend their thinking by doing a third lesson and asking:
• Which counting strategy is the most efficient? Why?
• What other strategies /prompting/questions can we use to help students develop their mathematical wonderings?
• Educators will continue to work on using more language to help pull out the proportional reasoning

Collaborative Math Inquiry: Car Caravan Findings K-8

We gathered with teachers from our school board from Kindergarten to Grade 8 to discuss the results of the Car Caravan Math Task. Here is an account of our findings.

What struck you?

• Students seemed very frustrated they couldn't just apply one formula
• students not used to open ended questions and seemed overwhelmed
• Need to narrow down the wondering in order to be able to tackle it and move forward
• Teachers also at times frustrated that students were not thinking deeply and not producing questions or taking the problem very far.
• Some teachers were surprised that some ESL students were very engaged and using math language to talk about the colours and the proportional language used : ex. more than
• The task was so open it pushed us to think about what we were documenting and pushed us to think about how we question students and focus on presenting more open-ended questions.
• Teachers found students were debating a lot and had trouble working in groups and collaborating.

What are the big ideas we discovered by presenting this problem?

• Big idea: Getting students to justify their thinking. Often the questions used were:
• How do you know?
• Can you prove it to me?
• Are you sure?
• Students ended up first trying to use strategies and concepts that were taught in the previous couple weeks.
• Learning context has a huge impact on the students. Some important questions to ponder prior to planning to help focus on educators’ intentions:
• Are we letting them struggle with a problem or giving them the strategies too quickly?
• What kind of student groupings will be best?
• Are we providing materials that are consistent?
• Ex. on the computer it may look different than when it is printed.
• How does the environment affect their wonderings?
• Ex. The lighting

Kindergarten Small Group Discussion:

• Difficulty getting out the math until educator seemed to find the right questions
• Ex. It`s race track! If it`s a race track , which one is winning?
• Some KG students talked about cars, colours, it`s a rug.
• Lots of talk about what the picture represented.
• Some noticed the background first.
• They were trying to figure out what it was versus wondering
• Focus on colours: ex. 2 shades of blue
• Some discussion about shape
• Teacher asked : Are there a lot of car? - provoked their thinking about what is a big number. One student remarked that they would need to “count fast” - and he started to count by 10s.
• Asking questions was challenging for the teacher because the students went on many tangents in their discussion and it was hard to bring them back and focused.

Kindergarten discussions after viewing Students' work from K-8:

-

• You could see all the strands covered across all the grades
• The problem could be presented at the beginning of the year and brought back again to ask other questions and reach other strategies
• EQAO years – affect their answers and wonderings
• We heard other teachers commenting on kindergarten inquiries saying that in Kindergarten it seems to be more of an exploration
• Noticed how kindergarten students were drawn to colours but that math can be integrated later

What would you do differently?

• Some of us wanted to rethink the questions we were using to figure out how to draw out more math
• Need to MODEL more mathematical wonderings

Collaborative Math Inquiry Lesson Plans: Car Caravan Math Task

As part of the Collaborative Inquiry in Learning Mathematics (Funded by EOSDN), we have been given some PLC days in order to plan for our math tasks. Today, our primary team met to discuss and plan for the Car Caravan task. This task has been given to all teachers in our board from Kindergarten to Grade 8. We will be gathering documentation on target students and coming together to analyze our findings with the goal of promoting a growth mindset, more positive attitude towards Math in general and encouraging the development of proportional reasoning.

Here are our plans for the Car Caravan Task:

Day 1 

1) Introduce the Car Caravan problem by showing a small group (including the target students) the following photo and asking:

• What do you see?
• What are you wondering?

Document their wonderings with video and/or anecdotal notes. Videos can be shown to the whole group for discussion.

(Gr. 2 students willl all be put into small groups to work on their own.)

Our intention: to allow target students to develop a wondering. By presenting in a small group, the target students may have more confidence to speak and  share. This will allow them to have a voice and develop a more positive mindset versus potentially withdrawing  if the problem was presented in a whole group and feeling intimidated.

2) Present the problem to the whole class and present the video of the small group’s wonderings and discussion. Ask the whole group if they have any other wonderings.

3) Analyze documentation and list of wonderings. Choose a wondering to focus on for the following day, based on target students’ interests. Gather potential materials to assist in solving the problem tomorrow.

Day 2

4) Challenge of the Day: Present the chosen wondering of the day at the end of community time as an optional centre time activity, guided by the educator.

**If the target students do not willingly join the challenge, (perhaps they are hungry and want to go to the snack table right away), the educators will invite them to join later. If they are resistant, then give them time to do another activity and invite them back later. Document their response and engagement.

5) Provide the small group with the photograph and the specific wondering (written on a paper). Ask them what materials they need to solve the problem. And guide them to discuss and attempt strategies and work on a solution.

6) Consolidation: During sharing time, we will have small group of students present their strategies either orally or through a video/pictures.

Pedagogical Documentation Look-Fors:

• Describe what you see and hear.
• Do they have a curiosity about the task?
• Look at their understanding and ability to explain their thinking.
• Look at their persistence.
• What other factors contributed to the students’ engagement : Did anything else happen that morning? or the night before?

• What materials did the students suggest.
• What language are you (the educator) using to pull out the information?

Next week we will meet for another PLC day as a primary team and use the following success criteria to analyze and evaluate both educators and students learning. We are very excited to put our plans into action and discover all the learning that will take place!

Kindergarten Success Criteria

Success Criteria Teachers	Success Criteria for Students
Using descriptive feedback more than just saying wow and passing it along	Having them explain their thoughts and they can have a voice – they can be the teachers too
Planning open ended activities for all entry levels	Demonstrates interests and curiosity by taking risks and attempting to solve problems in play areas
Praise the students based on their abilities rather than their output	Shows willingness to collaborate with others when solving problems.
Allow the students to use their own strengths to communicate their thinking	Displays persistence when facing challenging problems and when experiencing failure
Using intentionality in placing the manipulatives and allowing the students to be creative in their explanations.	Seeks opportunities to extend their mathematical learning and make connections to real life situations
Using your language to help pull out the proportionally reasoning language (You can go and wash your hands if you are wearing more red on your shirt than any other colour)	Allow the students to use their own strengths