TAI #3 - Whole Class Teaching in Mathematics

Focusing Inquiry
For a long time now, since professional learning in 2003/2004 under the Numeracy Project training, I have used grouping systems for my teaching of Mathematics, specifically number strategies. These groups have been based on ability.
Some number knowledge teaching has been more whole class where appropriate as has the teaching of strands. Within this whole class teaching however there has always been the flexibility to work with individuals, small groups etc as needed.
With the professional learning I have been doing throughout the year I have been wondering if this is the best way to organise my Maths programme. Some thoughts...

• I have noticed that little progress is made with low ability students. This has occurred over a number of years despite intensive small group teaching.
• This year I have a small group of students who struggle with addition and subtraction mental problems - they lack the ability to solve even simple problems.
• Students who are always in the bottom group - does this turn them off Maths? They are always in the bottom group, therefore they do not improve, therefore don't bother trying? (The Self-Fulfilling Prophecy).
• These students are never exposed to higher order thinking, more advanced strategies or the rich discussion that comes from more able students as they are always in the bottom group.
• The research shows that students teaching students is one of the most effective ways for children to learn themselves. If students are supported to learn through a variety of methods then maybe doing away with ability groups and using whole class teaching will support and accelerate progress.
• Low expectations of students = lack of progress, low attainment

Teaching Inquiry (Possible strategies to meet the focus)
Focus students: DR, HL, GL, AW, EG, EP
I would like to try using a whole class approach with students developing knowledge for themselves, seeking help as necessary, students supporting each other, students booking in/self selecting teacher support as necessary. The following structure will be used:

• Introduce the Learning task, typically Figure It Out series (Rich Tasks). Read through. 
• Students to self assess whether they have the understanding to complete
• Students can then choose whether to complete work or attend a teaching session
• During the teaching session students are responsible for sharing how they solve problems and teaching others as much as possible
• Students have the chance to solve problems independently, then explain and discuss with a partner and then sharing with the group/whole class
• I am free to meet with other groups to extend, support one-on-one, clear up misunderstandings etc
• Provide feedback as much as possible on progress and effort (Mindsets)

Other ideas:
Find research that supports this approach - Maths Symposium notes/references, Best Evidence Synthesis

Teaching
Began new approach week 4 - have gone back to addition and subtraction strategies.
Used Figure It Out "Strategy Strut" 
Students read through, discuss and develop their own understandings of strategies
I will work with individuals, pairs, groups as needed
Allow time to students to speak as much as possible rather than myself. Students learning by "Talking their Thinking aloud."
Hold mini-workshops as needed to target strategy needs
Explain the strategies using Explain Everything

Learning (11th November, Week 5)
More of a focus from students making their own meaning of strategies.
Students thinking through and working out how the strategies work rather than me modelling
Students are becoming more aware of when they can work out a problem mentally and when they need to write thinking down
Students more articulate at explaining
In my quick fire problems at the beginning of Maths more students are able to take part, solve problems quicker
3 of 6 students have now accurate strategies that can be used mentally (HL, AW, EP). 1 student has been away (EG). 1 student needs more support to understand the strategies (GL). 1 student can now use the strategies recording his thinking on paper (DR)

Learning Inquiry (Impact)
Most students in the target group have made pleasing gains - perhaps look at some data collection next time to prove this?
It would appear that this approach works better for these students
Need to ask students whether this is a better way of learning - why or why not?
Implications for the rest of the class (Mid/Upper ability)

• How can I use this system to make sure they are being exposed to new strategies, rich thinking? I have spent a lot of time with lower ability students and need to also make sure these others receive quality time
• Will the learning be sustained (say in a month?)
• How can I build in maintenance of the new strategies?
• How can I continue to move the "Locus of Control?"

TAI #2 - Rich Questions in Maths

Focusing Inquiry
I have noticed that some of my students struggle to think for themselves when posed with open-ended questions in Maths. While they may be able to solve equations, when faced with a "good question" they struggle to interpret what information they need to answer the question, struggle to identify what information in the question is needed to solve it and also struggle to question themselves e.g. "What do I already know?", "What do I think this is asking?"
These observations have been made after attending the Maths symposium in the July school holidays on "Good Questions".

Teaching Inquiry
Attended Taranaki North Math Symposium (July Holidays)
Reading “Open-ended Maths Activities(Peter Sullivan)
Discuss enjoyment of Maths and ways to solve problems
Begin to use questions in class – start with a small group, extend to whole class
Use the teaching approach mentioned in the book

Teaching
I have begun to pose open-ended questions at the beginning of Maths lessons. Whilst some students are working on Maths goals, half the class are with me whilst we talk through a problem. 
Initially they have found this very difficult. Some students sit muddled, others attempt.
I am using the following process:

• Pose a question
• Allow individual time for thinking how to solve and calculate
• Discussing the problem and how to solve with a partner
• Sharing of strategies - whole class
• Paired teaching when appropriate

Learning
Students will be able to:
Identify what a question is asking
Identify the information needed to answer the question - if sufficient information is not given, identify this and ask for the information
Attempt to find a way to solve a problem - using whatever strategy and knowledge they do have
Develop new knowledge and strategies to solve a problem


Learning Inquiry
Observations:
Students have initially found this difficult - are they not used to being asked open-ended rich questions? I am thinking that the more they are exposed to this the easier it will become?
I have noticed that less able children do not understand the question or explanations from other students. I know need to make sure that these children have an easier problem that they can interpret (but mathematically similar) to allow them success but also to provide a way of solving the original harder problem. The idea is that the easier problem will naturally lead them on to the harder question.
I am also not catering for the students that do solve the problem quickly - these students need harder problems. Or could possible be writing the problems for other students?
A small selection of students are quickly identifying that they need to ask for more information - very pleasing.
I think modelling of how to solve the problems may be necessary.

Next steps and implications for Teaching

• Continue to use rich questions on a regular basis - adapt programme so they are used more regularly in Maths lessons not just at the start. I am reminded that this is not a stand alone programme but supplements current programme. More practise will helpfully hope students to develop deeper thinking.
• Use the approach above across Maths - Pose a problem, individual thinking time, discuss with someone, sharing, paired teaching
• Work with less able students to model and discuss how to solve these types of problems - these students need to become aware of their own thinking in Mathematics. 
• Set students the challenge to solve the problems 2 ways
• Begin using images/photos as described in the Maths symposium - "Find the Maths"

Further thoughts
Do I need to have more thorough evidence that the teaching practice is making a difference? If so, how?
I have also learnt that TAI's are ideally centered around a small group of target students - 5-6 is the magic number.