Cling to the main vine, not the
Kei hopu tōu ringa kei te aka tāepa, engari kia
mau te aka matua
Thoughts on Teaching and Learning of Mathematics
Team and Problem
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.
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.
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
An agreed identity is unifying and builds the team. It will also
show you how collaborative the team is as a baseline.
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.
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
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
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.
You are the reason computers will never be the educator. Make
sure you promote this purpose and be an educator. Expect and
• 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
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!
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
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
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
Problem Solving Checklist
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.
Can everyone become a team player?
Is there still a place for individuals in the modern world?
literacy and numeracy website for rubrics on listening etc.
What mathematical content knowledge does a teacher need to inform
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.