Mathematics Leaders’ Video Conference Wednesday 15th Feb, 2017

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Revisit Protocols for video conferences We Will Mute the microphone when we are not speaking Speak in a normal voice and talk directly into the microphone. When you start talking, JUST KEEP TALKING! Try not to ask "can you hear me?" Listen to and show respect for the opinions of others and not engage in side conversations

Learning Intentions: We are learning to: Explore a definition of problem solving Deepen our knowledge of problem solving strategies Expand our knowledge of the teacher’s role in problem solving and implementation within my classroom Purpose of this Video conference: Ongoing conversations and observations with teachers have alerted us to the need to revisit Problem Solving as a focus for our 2017 Video Conferences. Teachers have commented after analysing NAPLAN and PAT M that a common area in which students are making errors are questions that involve more than one step in problem solving. We will begin the discussion and then encourage you to share your expertise and knowledge with colleagues.

Success Criteria: We will be successful when we can… Clearly articulate what problem solving is, based on research Identify the key problem solving strategies Reflect on the role of the teacher in problem solving

Defining Problem Solving What is your definition of Problem Solving? Participants to spend a few minutes constructing this definition independently. What is your definition of Problem Solving? We will ask 3 teachers to share

Definition of Problem Solving Problem solving in Polya's view is about engaging with real problems; guessing, discovering, and making sense of mathematics. • seeking solutions not just memorising procedures • exploring patterns not just memorising formulas • formulating conjectures, not just doing exercises. Definition of conjectures: A conjecture is a statement that appears to be true but is not yet proven An educated guess Eg Christian Goldach - 18th century conjectured that every even number greater than 2 is the sum of 2 prime numbers. The evidence indicates that this is true but it has not yet been mathematically proven.

George Polya • Lived between 1887 and 1985 • Famous 20th century mathematician of Hungarian descent • Known for many major mathematical theories • Fascinated with how people worked through mathematical problems • Famous for a quote that relates to it being better to work on one problem in many different ways rather than working on many problems in the same way

What does it look like in your school or classroom? Think Time Individually Whole Group Sharing

Polya’s Problem Solving Techniques Familiarise yourselves with “Polya’s Problem Solving Techniques” article making a connection to our previous discussion about what is happening in your school/classroom We invite you to particularly focus on Polya’s second Principle- Devise a plan as this will be the focus for the remainder of the session

What are the research based Problem Solving Strategies? Make a table Draw a Diagram/Picture Solve a simpler, related problem Guess and check- Guess and Improve Make a list Act it out Identify a Pattern Make a Model Use Concrete Materials Work Backwards Write a Number sentence Logical Reasoning Do we explicitly teach Problem solving strategies? For schools engaged in PLC the perception is that problem solving only occurs in Level 4 application. SFX, a few years ago made a continuum of Problem Solving across the year levels. We are working on developing a Diocesan scope and sequence for problem solving. - AIM to collaboratively work on this and request your input during 2017.

What is the Teacher's Role in Problem Solving? Watch Mathedology Video- FPS4 Exploring the Teacher's Role in Problem Solving 4 As Video Protocol What do you agree with? What do you want to Argue with? What do Aspire to or Act upon before the Term 2 VC Mathedology Video FPS4 - Exploring The Teacher’s Role In Problem Solving Watch - up to 7:16 What is part of the teacher’s role in helping students understand the problem solving situation? Responsibility to children to encourage a sense of perseverance, self confidence and skillfulness The teacher talks about the meaning of words with the students, what is going on, clarifying the problem While the children are working on the problem the teacher helps facilitate understanding by asking questions. The students might “act it out” and the teacher's role is to offer suggestions that will support them to be systematic, keep track of the problem. The students may draw a picture or circles and label “How might you show what is happening? Connecting lines. Teacher’s role may ask who is keeping track? - draw lines to record.”how might you tell who is who?. The teacher is the facilitator and questioner to guide the students in their problem solving- help them make progress and keep them moving with the problem.FOCUSING HINTS- DIRECTION GIVING( LAST RESORT) “WHY DON’T YOU……. 4 As Video Protocol What do you agree with? What do you want to Argue with? What do Aspire to or Act upon before the Term 2 VC

Resources Mathedology Videos - Origo SLATE Thinking Caps - Origo SLATE Reys et al(2002) Chapter 6 - Helping Children with Problem Solving Shapiro Books- “Solve That Problem” Middle & Senior Maths 300 http://www.maths300.com/ Lighting Mathematical Fires Lighting Mathematical Fires 2

Success Criteria: We will be successful when we can… Clearly articulate what problem solving is, based on a variety of research Identify the key problem solving strategies Reflect on the role of the teacher in problem solving

Actions From this meeting: What actions might/could/should be pursued? If so: –WHO will be responsible for this action? WHEN will this action be completed? By the……...I will………. So that………. Evidence………….

Evaluation A link will be sent out to all participants for feedback on the session