~~NOTOC~~ {{:2018:mathematics:mathematical-thinking-banner-790x50.jpg |Mathematical Thinking Banner}} ====== NESA Mathematics K-10 ====== [[http://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/guide-to-the-new-syllabus/|NESA 2018 - Guide to the new Mathematics K–10 Syllabus]] === NESA 2018 MATHEMATICS (All Stages): OUTCOMES === ++++ Working Mathematically - Students... | develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning ++++ ++++ Number & Algebra - Students... | develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation ++++ ++++ Measurement and Geometry - Students... | identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying formulas, strategies and geometric reasoning in the solution of problems ++++ ++++ Statistics and Probability - Students... | collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgements. ++++ * NESA Outcomes: http://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/outcomes/ ---- === NESA 2018 MATHEMATICS (All Stages): CONTENT === ++++ Number & Algebra ...| Whole numbers, Addition, Subtraction, Multiplication, Division, Fractions, Decimals, Patterns and Algebra ++++ ++++ Measurement & Geometry ...| Length, Area, Volume + Capacity, Mass, Time, Three-Dimensional and Two-Dimensional Space, Position (+ Angles for ST2 and ST3) ++++ ++++ Statistics & Probability ...| Data and Chance ++++ ++++ Work Samples ...| **Stage 1 (Years 1 and 2) Sample Activities** - Chelsea at the zoo - Students use words and/or pictures to record ways in which ten monkeys could hide in two trees. - Making number patterns - Students make a number pattern that increases or decreases, explain it in words, then create another number pattern that has a particular number in it. - Time of day - Students draw pictures of events or activities that happen at particular times of day, and record them on analog and digital clocks. - Wake up - Students work out how many eggs are in a basket from the number outside the basket and record results using pictures, numerals and/or symbols. **Stage 2 (Years 3 and 4) Sample Activities** - What could the question be? - Students work out a variety of ways in which addition, subtraction, multiplication and division of different numbers can arrive at a given answer. - Ordering fractions and decimals - Students order fractions, decimals and percentages on a number line and record their reasoning. - Recording my strategies - Students mentally solve addition and subtraction problems and then record their strategies. **Stage 3 (Years 5 and 6) Sample Activities** - Mixed operations - Students express each of a selection of numbers in two different ways using a mix of operations. - What's the problem - Students record a variety of questions, including word problems, number sentences and questions that involve more than one operation to arrive at a given answer. ++++ * NESA Content: http://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/content/ * NESA Work Samples: http://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/work-samples/ ---- === TEACHER BACKGROUND INFORMATION === * '**A schoolgirl making the decision to not study maths**, as early as high school, is unknowingly precluding herself from access to the jobs with the highest growth rates and the highest future earning potential.' ABC News 06/02/2018 ((http://www.abc.net.au/news/2018-02-06/stem-subjects-australian-education-system-jobs-atlassian/9373456)) * '**Students taking advanced maths in Year 12 at its lowest-ever level** - A new report shows that students are increasingly turning away from more challenging mathematics subjects in the last years of high school. The number of those studying advanced mathematics in year 12 is at its lowest level in two decades – and the biggest drop-off is amongst girls. ABC News 08/03/2019 ((https://www.abc.net.au/radio/programs/worldtoday/students-taking-advanced-maths-in-year-12-at-lowest-ever-level/10883462 )) * '**Quite simply, if a learner’s thinking is superficial**, biased, weak, lacking depth or breadth then **his learning will be superficial**, biased, weak, and lacking depth or breadth. **Thinking and learning are inextricably linked**' - Lane Clark ((Lane Clark - http://www.laneclark.ca/interview-by-rodrigo-santodomingo-for-revista-magisterio-may-2015/ )) * '**It is not what you cover, it is what you uncover that is most important**.' Prof. Walter Lewin (( https://www.youtube.com/watch?v=El3g9XtZ-iA )) \\ {{ youtube>pzfwBkqftRc?640x360 |Five Principles of Extraordinary Math Teaching - Dan Finkel (13min)}} === Video 1: Five Principles of Extraordinary Math Teaching (13min) === * IF UNABLE TO ACCESS YOUTUBE VIDEO, TRY:[[http://viewpure.com/pzfwBkqftRc|Five Principles of Extraordinary Math Teaching - Dan Finkel]] \\ Five principles to encourage mathematical thinking: - Start with a question (or a misconception). - Students need time to struggle (make effort). - You are not the answer key (do not give answers) - Say 'yes' to student ideas (it's not the same as saying 'you are correct or wrong' - what if 2 + 2 = 12 and we explore the consequences?) - Play ('the highest form of research' - N. V. Scarfe) ((https://quoteinvestigator.com/2014/08/21/play-research/)) ====== A Private Universe In Mathematics - Project Overview ====== **The workshops** are the outcome of unique, longitudinal classroom research (over twenty continuous years) by educators from universities and institutions including Rutgers, Harvard, MIT, The Smithsonian Center for Astrophysics and Annenberg Media. This is the longest study of its type ever undertaken. **The research** follows an 'ordinary' group of learners from first grade through high school and beyond, concentrating on their work on a set of mathematical (especially combinatorics) tasks. **The data** drawn from this research, illustrates and explains how teachers and student groups work collectively to build mathematical ideas over time. **The classroom videos and journal entries** show how reasoning that takes the form of proof can evolves and can be promoted from early childhood. **Assessment example** Print out a class list with at least one column for each week/lesson (or create an Excel or Google sheet). During each session, allocate a numeric value (say 1, 2 or 3), to refelect the level of understanding that a student may demonstrate in that session. At the end of the assessment period, sum the totals for each student and normalise the result. Ascribe a comment for each student, based on their score. Cross-check by browsing through each student journal/notebook as an alternative/supplementary method of evaluation. {{ youtube>Vj2qtZlCXRI?640x360 |Introduction - A Private Universe in Mathematics (3min)}} === Video 2: Introduction - A Private Universe in Mathematics (3min) === * IF UNABLE TO ACCESS YOUTUBE VIDEO, TRY:[[http://viewpure.com/Vj2qtZlCXRI|A Private Universe in Mathematics (3min)]] \\ The study has produced over 4,500 hours of video, detailed transcripts and related on-line resources and investigates how students’ reasoning evolved from elementary and high school years to college and beyond. These resources are an invaluable tool not only for primary- and secondary-school teachers of science or mathematics, but also for anyone involved in teacher preparation. === MATHEMATICAL THINKING - K-6 + High School & Beyond === * Source - The Private Universe Project - http://www.learner.org/workshops/privuniv/pup03.html * What improved outcomes does this workshop offer? {{ youtube>Vgbo91z1u6U?640x360 |A Private Universe in Mathematics (7min)}} === Video 3: The Research - A Private Universe in Mathematics (7min) === * IF UNABLE TO ACCESS YOUTUBE VIDEO, TRY:[[http://viewpure.com/Vgbo91z1u6U|A Private Universe in Mathematics (7min)]] \\ The theme of these Workshops is "how to develop authentic mathematical thinking by and for those who may have little mathematical training and/or confidence. This is done by blending long-standing teaching research and effective strategies within the context of new technologies". Both teachers and learners are encouraged to develop new metaphors for their roles in the classroom. Students are urged to see themselves as something other than "sponges" soaking up the teacher's information. ====== RANDOM MATHS RESOURCES: ====== {{ youtube>CxC161GvMPc?640x360 |Mathematics helps us understand 'The Tragedy of the Commons'(15min)}} === Video: How Mathematics Helps Us Understand 'The Tragedy of the Commons' (5min) === * IF UNABLE TO ACCESS YOUTUBE VIDEO, TRY:[[http://viewpure.com/CxC161GvMPc|'The Tragedy of the Commons' (5min)l]] Nicholas Amendolare ---- === EXTENSION: More Challenging Maths Activities: === * [[https://ed.ted.com/lessons/what-is-the-tragedy-of-the-commons-nicholas-amendolare|How does 'The Tragedy of the Commons']] relate to mathematics? * [[http://www.mathematicshed.com/hard-sums-shed.html|The Maths Shed]] Dara O' Briain 'Hard Sums' Homework Problems. * [[https://www.youtube.com/watch?v=407wRiuewNY&t=1440s|School of hard sums - Maths for pirates]] - Dara O'Briain (([[https://www.youtube.com/playlist?list=PLuCLp4gEmHzrTmxeK3mmGOvOf7CWgtZS-|School of Hard Sums - Playlist]])) * [[https://www.youtube.com/watch?v=wUP5rtwvsUI|Vedic Mathematics: My Trip to India to Uncover the Truth]] - Alex Bellos * [[https://www.youtube.com/watch?v=DeJbR_FdvFM|Trigonometry, Pi & Infinity]] - Marcus Du Sautoy (([[https://www.youtube.com/watch?v=pElvQdcaGXE&list=PLm1X3gNOVk2a223QtfbdMjoMl7im6XSJA|Marcus Du Sautoy - Popular maths documentaries]])) * [[https://www.youtube.com/watch?v=f1QXrbWtbKQ|The Secret Mathematicians: Jorge Luis Borges]] - Marcus Du Sautoy * [[https://www.youtube.com/watch?v=9rIy0xY99a0|Making sense of random patterns]] (([[https://www.youtube.com/watch?v=XPo3G4IWuHM|Probably not!]])) * [[http://mathforum.org/library/drmath/view/56492.html|Making sense of Pascal's Triangle]] and on-line [[https://www.dcode.fr/pascal-triangle|calculator]] ---- === REFERENCES === Find out more about the Harvard-Smithsonian Center for Astrophysics here: www.cfa.harvard.edu - Learn more about Annenberg Media and browse the resources and workshops they offer to teachers: www.learner.org - To watch //A Private Universe// video: www.learner.org/resources/series28.html - To watch //Minds of Our Own// video: www.learner.org/resources/series26.html - The //Private Universe in science// project videos: www.learner.org/catalog/extras/puptwsup.html - To watch the //Private Universe in Science// workshop videos: www.learner.org/resources/series29.html - The //Private Universe in mathematics// project videos, see: www.learner.org/resources/series120.html - The //Private Universe in mathematics// project [[http://www.learner.org/resources/freevslicense.html|K-12 License]]