Teacher Only Day 20.07.18

Effective Pedagogy in Mathematics

By Glenda Anthony and Margaret Walshaw

1. Creating a safe environment for learning
2. Allowing group discussions and individual thinking time to solidify learning
3. Building a students thinking;
   Relating interests to the learning, hands on tasks, incorporating prior knowledge. Pitch the learning at a reasonable level, reduce complexity of the task to ensure students are still successful. No "busy work", you tend to fall back on worksheets that they already know the answers to; there is no valuable learning happening here. Mixed ability approach supporting inclusive maths environment. Using misconceptions and errors as building blocks. Natural to make conceptual errors, but instead of telling them they're wrong, we should use it as a basis of discussion and talk about alternative solutions. Focus students on their thinking and tasks so they are not just doing busy work. We need to know the next steps and mathematical progressions in order to propel their learning forwards. What activities will help to assist their learning. 
4. Worthwhile mathematical tasks.
   The tasks that the teachers set develop student understanding. Teachers need to ask open ended questions to allow mathematical thinking to develop. Changing the mindset around play in maths for senior teachers. Students being positive risk takers and giving them time to practice, using knowledge in social contexts. Challenges are knowing capabilities of learners, active participants vs hesitant participants. Knowing how to respond to students' questions. Our own dispositions negatively affecting our ability to teach and students' learning. "Teachers need to develop a mathematical identity to help students do the same."
5. Making connnections
   Effective teachers support students in creating connections between different ways of solving problems betweehn mathematical representations and topics, and between mathematics and everyday experiences.
   Applying maths knowledge and concepts to everyday and meaningful experiences.
   Linking different areas of maths, rather than teaching it in isolation. e.g. using a ruler to measure the graph which you are going to plot your statistical investigation on. Shows students the purpose of maths. Building knowledge in small steps, learning place value before next steps, explicitly teaching students that all mathematical concepts are related is crucial. 
6. Using effective and varied assessment for learning
   Looking closely at different ways to assess, might be as simple as asking/answering a question. Assessment in the moment is more valuable for the learning because it helps to progress the learning. Teacehrs already have good effective teaching practices; by asking open ended question. More important to focus on the journey rather than the destination; how did you get there? Don't give them solutions to work out the problem, but encourage them to think of other ways to solve the problems.
   The importance of self and peer assessment and becoming a regular part of maths sessions. The challenge of regular peer and self assessment is that students need to know what is expected of them.
   Found it interesting that visible actions helps our learners, how does this relate to ESOL learners. 
7.  Mathematical Communication
8. Mathermatical language: effective teachers explain in different ways
   Using maths vocab right across schools and classrooms. Students from all classrooms should understand what is being talked about because of common vocabulary being used.
   The importance of accurate explanations being used. comparing something brought from home, half an apple, 1 out of 2 halves. Incorporating home language e.g. "what do we call half in your language?"
   Teachers understanding of mathematical concept is strong before you can teach students adequately.
   Challenges are to be aware of the variations in terminology. ESOL learners.
   Use of home language and incorporating this in your maths lessons. 
9. tools and representations: effective teachers carefully choose tools
   Children are drawing on their own
   Teaching using symbols etc to promote understanding, using materials to further understandings.
   Challenges are to find the appropriate materials when working with larger numbers, using appropriate technology and applications on iPads and knowing what is out there. Using materials in the correct way, knowing how to use the resources you have available to you. Teaching the same concept in a range of ways. 
10. Teacher Knowledge
    Teachers need to have the knowledge to teach and extend. See students using a mathematical concept but understanding where to go next. Recognising teachable moments as they arise and planning in response to them to ensure students are benefiting from this. We are good at understanding our students and their needs.
    Challenges are having access to good PD, observing the practice of others.
    Interesting points are having a strong level of pedagogical knowledge at all stages. JAM assessments; teachers will better understand the strand knowledge, about us knowing the next steps in order to get our students there. 

Junior School Chat with Andrew

Pink Books

Book 4 for whole class warm ups. Aim for E/CA activities. 

Book 5 small group activities. 

Long Term Planning - NZ Maths

Long Term Planning

How to use materials and equipment