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Symbols in the Yr5 MAGs are linked to important ideas which can be reflected on Concepts and ideas
FISH process of problem solving
I Can Fish highlights success criteria Ac;vity Process: Modelling and Expecta;ons It is important to make learning expecta2ons transparent for learners. Without this learning lacks rigor.
A global learning inten;on for the learning journal. The learner develops:
u an understanding of how they think, reason and work, mathema;cally.
Before You Implement Math Journals Consider What are the needs of your learners? What type of format will be used? How will it be organised? When and how will you respond to learners in a suppor;ve environment? When will learners have a chance to share?
reasonableness of answers to calcula;ons and using instruments to measure angles
Problem Solving includes formula;ng and solving authen;c problems using whole numbers and measurements and crea;ng financial plans
Reasoning includes inves;ga;ng strategies to perform calcula;ons efficiently, con;nuing paHerns involving frac;ons and decimals, interpre;ng results of chance experiments, posing appropriate ques;ons for data inves;ga;ons and interpre;ng data sets Suggested Resources u FISH u Blue-‐lined exercise book (not A4) to be use as a learning journal u Large art book or similar for class journal u Various models u Frayer Model (small versions for journal or can be laminated for
mul;ple use) u Beach ball u iPad if available Mathema;cs Vocabulary This is dependent on what topic you would be teaching at the ;me. You would expect to see the correct language used in a reflec;on. For example, if you were geVng the students to reflect on learning about area or perimeter, you would expect to see words such as length or width.
Power Words Current math vocabulary words should be posted
somewhere in the room and a dic;onary should be developed in the learning journal.
Australian Curriculum Year 5 The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathema;cs content across the three content strands: u The proficiencies reinforce the significance
of working mathema;cally within the content and describe how the content is explored or developed.
u They provide the language to build in the developmental aspects of the learning of mathema;cs.
Key Ideas At this year level: Understanding Includes making connec;ons between representa;ons of numbers, using frac;ons to represent probabili;es, comparing and ordering frac;ons and decimals and represen;ng them in various ways, describing transforma;ons and iden;fying line and rota;onal symmetry
Fluency includes choosing appropriate units of measurement for calcula;on of perimeter and area, using es;ma;on to check the
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The idea presented here is essen;ally of the journal as a reference book that learners can go back to for defini;ons, terms and to demonstrate their understandings of a concept or topic. Teachers would need to decide what the content of the journal will be. This also depends on the model of mathema;cs teaching a teach is using hHp://www.austms.org.au/M2+-‐+Models+of+maths+learning What is assumed here and in the MAGs themselves, is that Learning Journals are part of a Thinking Classroom approach u A classroom culture where mathema;cal discussions are part of the daily
rou;ne.
u Draw learners together a]er problem solving to share, discuss and analyse strategies they have used.
u Present ‘open problems’ which have more than one possible solu;on
u Encourage inves;ga;ons of mul;ple solu;on strategies. u Exposes learners to flexible teaching strategies using FISH
u Co-‐construct criteria with learners used to support self assessment and peer feedback.
u Encourage various ways of showing evidence of thinking
u Ensure assessment reinforces the value of showing your work and explaining your thinking
Whole Class Journal-‐a model for learners Use a big class math journal, a place where you put your modelled prompts for learners to go back and refer to. This might include: • samples • strategy posters • class dic;onary of vocabulary • photographs of unsuccessful and successful problem solving • a record of success criteria • examples of using strategies efficiently
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Class Journal Ideas
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Using a Frayer Model
The Frayer Model is a strategy that uses a graphic organizer for word analysis and vocabulary building. This four-‐square model prompts students to think about and describe the meaning of a word or concept by: u defining the term u describing its essen;al characteris;cs u providing examples of the idea u offering non-‐examples of the idea
This informa;on is placed on the chart that is divided into four sec;ons to provide a visual representa;on for students. This instruc;onal strategy promotes cri;cal thinking and helps students to iden;fy and understand unfamiliar vocabulary.
The Frayer Model can be used with the en;re class, small groups, or for individual work. The Frayer Model draws on a student's prior knowledge to build connec;ons among new concepts and creates a visual reference by which students learn to compare aHributes and examples.
This strategy stresses understanding words within the larger context of a concept by requiring students demonstrate their understanding
u The first two quadrants are used to analyze the items (defini;on and characteris;cs). u The second two quadrants are used to synthesize/apply this informa;on by thinking of examples
and non-‐examples.
Beach Ball Reflec*on Use a beach ball to write the reflec;on ques;ons you would like the learners to consider. Have students stand in a circle, and toss the ball to one student. That learners selects a ques;on from the ball, reads the ques;on aloud, and answers the ques;on for the other learners to hear.
The learner then passes the ball onto another learner, who can then select a different ques;on or add to the response from the other ques;ons already answered.
Extend and Connect: An alterna;ve as an individual reflec;on could be to write the ques;ons on slips of paper and put them inside of balloons.
The students toss the balloons around, un;l ;me is called then each student selects a balloon, pops the balloon, and responds to the ques;on in their Learning Journal. Digital Learning
Reflec*ng (Teacher Resources) hHp://www.austms.org.au/M2+-‐+Models+of+maths+learning ‘Several experienced mathema;cs educa;on researchers have presented models and heuris;cs to guide mathema;cs teaching. It is an interes;ng and open ques;on -‐ what are the different ways in which students learn mathema;cs?’
hHp://www.scholas;c.com/teachers/lesson-‐plan/math-‐journals-‐boost-‐real-‐learning ‘When children write in journals, they examine, express, and keep track of their reasoning, which is especially useful when ideas are too complex to keep in their heads. By reading their journals, you can evaluate their progress and recognize their strengths and needs.’
hHp://www.edutopia.org/student-‐reflec;on-‐blogs-‐journals-‐technology ‘Although reflec;on is o]en the first thing to go when teachers run out of ;me on a project or a unit, ac;vi;es that prompt students to look back at what they've learned and accomplished isn't just busywork or an unnecessary step, educa;onal experts say. In fact, encouraging students to pause and think about what they're learning and why it's relevant to their lives is a cri;cal piece.’