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

Professional Literature Review: Capacity Building Series (K-2) : Pedagogical Documentation

Source:
http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_Pedagogical.pdf

Summary:
Pedagogical documentation is explored in this piece of literature as a means of finding a deeper connection to students’ thinking and deepen the assessment feedback loop. It draws on inquiries from the Early Primary Collaborative inquiry (EPCI), an Ontario Ministry Program. Even though it is a primary-age based inquiry, the suggestions are useful for the junior grades as well.

The monograph suggests give main benefits of integrating pedagogical documentation into pedagogy:

1. Create shared understanding
2. Celebrate rights of individual learners
3. Recognize student ownership of knowledge
4. Actualize shared responsibility
5. Provide voice in learning for everyone

It also suggests tips for getting started:

1. Use a collaborative inquiry approach
2. Establish your primary purpose
3. Think About your audience
4. Decide on your methods for collecting information
5. Remember - There is no one right way to do it!

Other key ideas:

• Pedagogical documentation is an ongoing, cyclical process (assessment for and as learning, vs. of)
• It “needs to become a habit of classroom practice... device... for documenting... need to be available at all times to capture learning when and where it happens” (p. 5)
• Embrace it as an attitude of knowing versus a technical process/product
• Can transform education in the early years and beyond

Ontario Mathematics Kindergarten Curriculum Connections:
“Children bring with them an intuitive knowledge of mathematics, which they have developed through curiosity about their physical world and through real-life experiences.” (p. 20 Ontario Full-Day Early Learning Kindergarten Program-ELKP) Pedagogical documentation allows educators to uncover the prior mathematics knowledge that students bring with them and continue to encourage this natural curiosity about their surroundings as time goes by, not only with their interests in mind but also with their skill-level. By setting up the classroom as a play-based setting to further propel their curiosity, teachers reflect on their observations of students and continue to uncover their interests as they change, in order to plan for future materials that will engage students’ curiosity and naturally compel them to practice certain skills. “The Early Learning–Kindergarten team plays a critical role in fostering a positive attitude towards mathematics by valuing a child’s early attempts at problem solving, by sharing and celebrating the child’s learning, and by encouraging in each child a love of mathematics.” (p. 20 ELKP). By documenting students’ mathematical learning and sharing it with other students, students take pride in their mathematical abilities at an early age and develop a positive mind-set. “They should also be encouraged to begin to represent their mathematical understandings in ways that are meaningful to them” (p. 21 ELKP) By documenting students’ thinking in various ways, educators allow for different representations of learning to occur within the classroom and display all different kinds of student voice. Pedagogical documentation is significantly important in the Kindergarten classroom across several domains and as learning is encouraged in an integrated fashion across domains, mathematics can be drawn into any play area through educators’ guidance.

Personal Reflection:

• What resonated with you?

My “ah-ha” moments while reading this monograph were more like “oh yeah, that’s so true” moments. I found what I was reading was not anything particularly remarkable, but rather clarified and reinforced what I already knew about pedagogical documentation.

“In school teams, learning communities and ministry programs, such as...the Collaborative Inquiry for Learning Mathematics (CILM)... they are experimenting with innovative ways to observe student learning, study student work and gain greater insight into effective instruction”.

This phrase resonated with me since I am working with a school team on two different mathematical inquiries: one for this class and the other as part of the ministry program. This clearly outlines our main purpose for the inquiry and makes me re-evaluate the focus of my math inquiry with my other team. I believe that perhaps it is the exact same goal: to gain insight into effective instruction of mathematics by experimenting with Number Talks.

This phrase really struck me: “It is not only our students’ thinking that becomes visible through pedagogical documentation but our thinking as educators because visible as well...” (p. 2). I was so focused on students’ thinking that I forgot that as I document my process of guiding them, I am also showing my teaching practices and thinking processes.

A few other important points addressed in the monograph that I strongly agree with:
“Through documentation, the potential for engagement and learning increases because students reflect on their learning throughout the process rather than at the end... Students... become partners in the process of determining how best to express their ideas” (p. 4). When students are given the opportunity to be part of their learning process, engagement increases. As noted later besides ownership over their learning, documentation provides voice in learning for everyone: “Students and teachers alike are demonstrating ownership of and engaging in teaching and learning... bridges understanding of children and adults” (p. 4).

Giving students the chance to also play the role of the teacher is very powerful. Recently I wanted to assess how high students could rote count in French. I decided to just go up and ask them to count for me, at any time during play / table top activities. As soon as one student was counting and saw me giving praise, others were observing and were very eager to be next to show me how high they could count. Then, as students complete activities and continue to practice their counting, I am able to partner up accordingly those that strong and can play the teacher role for those students that are weaker at a certain skill.

• What challenged you?

“Pedagogical documentation stops the train of standardized expectations and slows down our thinking processes to consider some topic with exquisite care” (Wien, Guyevskey & Berdoussis, 2011) (p. 2). Clearly, it is a time-consuming process to write learning stories and it cannot be done for all students all the time. The part that I find challenging, which is not addressed in this monograph is how to conduct this documentation for all students and how to decide which students and topics to focus on. It is suggested to become an attitude/habit. But how are we to do this in a busy classroom with only 5 hours a day? How do we use pedagogical documentation and reach every student? The only suggestion to solving the overwhelming feeling that educators face when it comes to documenting is that it be a collaborative approach and that teachers should be working in teams. “...it is the team’s collective reflection on and analysis of the evidence which deepens understanding” (p. 6). Yes, working on a team is helpful and helps us find a focus/purpose and decide which students to observe and how to analyze student-work. But what about all the other students? What is the best system/approach to reach them all? Is it possible to use pedagogical documentation all the time for all topics? I highly doubt it is. I already found it so daunting that I was only able to have a few students complete our chosen task for our collaborative math inquiry. It is certainly very interesting and very engaging and worthwhile but I am still in search of how to do so efficiently and how to do it systematically in the classroom and make it a habit.

• How might this text be helpful/useful in our teaching practice?

One of the purposes of the inquiry is to develop effective instruction and this is done in pedagogical documentation by creating a shared understanding between educators, students, and parents. Through pedagogical documentation we are able to provide parents will more precise feedback on their child’s learning which will ultimately help the parents better understand and engage in their children’s learning. “Documentation encourages educators to step back to listen and allow the child to take the lead in the learning, inviting students into the learning process” (p. 3). This documentation is also tremendously helpful for planning purposes as educators not only gain insight into student interests but also better understand students’ development needs (p. 3).