Cling to the main vine, not the loose one.
Kei hopu tōu ringa ki te aka tāepa, engari kia mau ki te aka matua

Thoughts on Teaching and Learning of Mathematics
Team and Problem Based Learning
Lesson #11 • Revised 25/1/20

- to learn that team based work is a powerful opportunity to build learner knowledge
- to see problem based team work as future focused and empowering for learners

I am suggesting here that by calling this "TEAM" and "PROBLEM BASED" that these are in fact two separate parts. "TEAM" and "PROBLEM BASED" are two different parts in the development but become intertwined in the execution. Two aspects of the same thing. A chicken and egg problem of which was first!

The TEAM needs careful development to ensure that students learn what a team is, how it operates and how the jobs of a team weave to form synergy. Synergy is a lovely word that means the result is greater than the sum of its parts. "Two heads are better than one!" comes to mind. Sharing a problem or by verbalizing  thoughts increases clarity and a better understanding often develops. A team is essentially a business entity with employees and a purpose which all models future pathways as adults.

The PROBLEM BASED learning connects to investigation as a learning pathway to generate knowledge. PROBLEM BASED learning is more focused on a developing a solution but shares the many different ways mathematical investigation can proceed. Problem solving techniques include "listing all possibilities", "connecting to previous knowledge", "simplifying" just as investigation. The two concepts involve the same skills.

My approach to turning my classroom into a hive of mathematical discourse and problem based learning is to develop teams FIRST. Small groups of 3 self selected students and starting with simpler problems solvable in 10 to 20 minutes. As teams develop this builds to larger problems and investigations. See the rubric for measuring team progress for teachers and students below.

TEAM Based Learning
Do not underestimate the pay off for time spent developing effective teams in the classroom. It takes a bit of setting up, not arduous sweaty hill climbing type work, but a bit of persistence and knowledge. Students love to work collaboratively and as one of the key C21 skills they need to learn how to be collaborative as well. Be generous with time and patience, noise levels and responsibility for learning in the development. Time because "it will happen but will not happen over night", (thanks Rachel Hunter).  Patience because you will need to be tolerant and move responsibility to the students increasing their self management ability. Noise tolerant because groups need to learn to listen to each other to be collaborative. The "being responsible for my own learning" is the creation of life long learners, increased self management, becoming a learner. These are some of the brave words I often see in school charters but often do not see in classrooms in those schools. Actions speak louder than words!

Here is my plan for setting up a TEAM.
1. Group
Ask students to get into a group of three. This group will be set for this term when we will have a chance to change so think carefully and agree to be team members.
It is important they self select rather than be told. Unfortunate groupings can be negotiated! The group owns the responsibility of the structure. They can always play their "Yellow Card" at any time for a change to be made.

2. Identity
The first task is to think up a team name, logo and motto. You might choose "Warriors", a picture of Zena or Spartacus, and "He who dares!"
An agreed identity is unifying and builds the team. It will also show you how collaborative the team is as a baseline.

3. Jobs
Have each group to decide what three jobs the team members will have to be a successful team. These jobs will rotate every time they meet in a group. The jobs that emerge after a class discussion and vote are usually Manager or Leader, Resourcer or Go-Getter, Recorder or Presenter.

4. Responsibilities
For each of the three jobs and the team list 5 things that that person and the team are responsible.
eg and only an example! Use what students say!
    • Manager - keeping team on task, keeping noise appropriate, time keeping, making key decisions, contact person with teacher
    • Resourcer - gets materials, does calculations, finds books, looks up on internet, keeps things tidy
    • Presenter - records findings, makes journal entries, speaks for group, presents to class, publishes
        • Team - to collaborate, be creative and solve problems, to trust and work together, to be effective as a team, to have fun learning and building new knowledge.

5. ID Tags
Each team is now to design a label to be worn as a badge or hung around the neck to show their job each time the groups operates as a team. These designs are collected and either copied or made individually as the group or class decides. This promotes responsibility.

6. Journal and Folder/Team Box
A notebook or otherwise is used to record the team name, team details and daily allocation of jobs. It has a place for the team to record an entry every time the team operates and a place for the teacher to record a comment about the effectiveness of the team.

This lesson is quickly over and students will wonder how the time went so fast.

If there is time it might be suitable to present a small and first challenge like "find the sum of all the numbers from 1 to 100. This is an example of a "low floor, high ceiling" problem Jo Boaler talks about and is accessible to any team of three students at any age or stage. They answer this in any way they choose and record an answer or progress and if time a team could be selected to present their answer. There are many ways to solve this problem and there are ways to raise the ceiling and lower the floor. Whatever happens and whatever problem it is more important they experience success working as a team.

The final action is to record a comment about "Our learning today was ..."
After the RESOURCER for each group has replaced the journal in the Team Box, or during class if appropriate, the teacher can comment about the effectiveness of the team. "I noticed the Team manager keeping everyone on task"  and "I saw you listened to each other." No judgement, just facts and comments about competencies. They can deduce your thoughts on good, bad or otherwise. It is more important that you normalize the expectation of journalling by all involved.

TEACHER!
You are the reason computers will never be the educator. Make sure you promote this purpose and be an educator. Expect and give respect.

• REVISIT the team responsibilities as required. (Revision and practice makes perfect)
• Keep the task MANAGEABLE while learning to be a team. (Small steps make for a long journey)
• PERSIST (Perseverance is being modeled by you)
• HAVE HIGH EXPECTATIONS (You get what you sow)
and there are many more statements like this that could be added. The computer can do none of these.
• Talk with the students about their learning and team. (Student voice, including video and snap shots to monitor the journey.)

 
PROBLEM BASED Learning
This is where teams are presented with a problem and they work on developing an answer. Teams can and usually are given different problems. Why would you have groups if they are all working on the same problem? You might need to ponder "Are my teams ready to work as teams yet?".

Giving everyone the same problem is OK as they learn to be teams but not once they are teams. The purpose might have a common element. An example is in science where the class might be presented with a "Design and build a model of a sustainable living on a hectare of fertile land". The students would interpret this in many ways naturally differentiating the problem and the resulting solution without any further input by the teacher. The teacher has the role of being a reference expert and monitor of the development of competencies such as perseverance, collaboration, critical thinking, creativity and communication.

An example in mathematics might be to ask the teams to "Come up with a fund raising plan so the class can visit go to the National Museum of Mathematics and Science". It might be that students need some technical help or concept which the teacher can supply as an expert.

Sourcing problems will not be an issue. Look in the math resource room, google math problems, look up Math competition books, old text books, Jo Boalers website, GATI "Math Starters". GATI = Go Ask The Internet or Siri. Be creative teacher!

Teachers Role
When I was facilitating workshops during the Numeracy Project 2002 to 2011 I would ask teachers to remember all the ways they had been taught by "good" teachers and "bad" teachers, teachers they liked and did not like, men teachers, women teachers, old teachers, young teachers, principals and any one else they could think of for whom they were "the student". Then I would ask that they mentally put all of these experiences into a brown paper bag, tie the bag firmly with string, knot it several times and throw the bag away. As far as they could.

I was trying to tell them that they must learn what works for them and this is a journey of discovery, a collaborative and inquiring journey, a journey of new learning and experience and it only belongs to "you".

Here are some ideas that will help progress Problem Based Learning.

1. Do not tell
You want students to become more resourceful and to persevere. What ever happens they must believe in their own thinking and hard work.

They are to experience failure and success. Telling destroys all hope of solving the problem on your own. The early experiences of this are important and I tell new Mummies off for "doing everything for their child".

I call this "The Mummy Syndrome" where a person (man or woman) prefers to do the "book looking after", "provision of scissors", "asking of questions", and worse "answering of questions" with useless feedback like "that looks nice dear" "well done" or "√".  Men are infected by "Mummy Syndrome" as well. If you want robots you will get them by telling. [I notice the internet has another twist on the same name referring to the docile brain a mother for her children causing forgetfulness and foggy thinking].

2. Have High Expectations of Every Student
Students will learn to rewrite solutions until the required standard is reached. I learned very early on in my teaching career that students will jump the bar at whatever high you set it. A PE teacher called Fran(cis) pointed this out. I then started noticing the phenomena. Personally I want completed sentences, meaningful paragraphing, essays that contain a message, explanations that are correct and clearly reasoned, good letter and numeracy construction so it can be read without issue, clear diagrams, appropriate labeling, KISS publishing (Keep It Simple Stupid!) among many others. I want students to speak clearly and engage discussion with active listening. These are the people I want to see later on in life, no one else. All students can learn anything is a worthy mantra.

3. Monitor Key Competencies
Comment on actions and leave judgement to God. These can be recorded in the Team Box or in classroom displays. Value perseverence, creativity, communication and critical reflection. Demand collaboration, agreement and reward working together. Do not be judgemental; be factual and let the leader lead. The Team Book is the place to record the voice and thoughts of all players. Remember the seeds sown here will make a crop that will be later harvested. This lesson came to me early in my math teaching with a talented group of Year 10 students. I allowed them to be noisy and call out. I regretted this to the last day of that class! Set the bar from Day 1, do not smile before Easter!

There may be more very important ideas but these will do at this stage.

Problem Solving Checklist
Check list.

RUBRIC to monitor development of both Teacher and Students.
I was going to put a 7 step rubric in here but this is a good task for teachers. The headers are the competencies such as Collaboration. Now describe the Minimum and Maximium and then the intermediate steps. An odd number of steps is best, 5 or 7.

Some questions...
Can everyone become a team player?
Is there still a place for individuals in the modern world?
Adult literacy and numeracy website for rubrics on listening etc.
What mathematical content knowledge does a teacher need to inform team development?

Teacher TASK
Try Team based work in your classroom.
Try Problem Based learning.
Can you assess a group rather than an individual?
How do you measure ENGAGEMENT?
Design a rubric for each of 5 key competencies.

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