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Showing Auxiliary Science. 7. Learning through examination: Spotlight on chance and variability. Module 7:. Layout of module 7.

Showing Secondary Mathematics 7 Learning through examination: Focus on shot and fluctuation Module 7:

Outline of module 7 • Links to Department assets • Variability instinctive thoughts and experience • Digilearn – Spinners • Short-run variety and long-run soundness: 5.0 • Teaching Strategies o using ICT o investigations • Links to Principles of Learning and Teaching P–10

Mathematics Online Interview Mathematics Developmental Continuum Improving Student learning in Mathematics Scaffolding Numeracy in the Middle Years Assessment for Common Misunderstandings Effective Mathematics Teaching DVDs Dice Duels Coin Tossing http://www.education.vic.gov.au/studentlearning/teachingresources/maths/default.htm

Variability: Intuitive Ideas and Experience Where do understudies experience changeability? What encounters and thoughts do they convey to the classroom? What words do we utilize when we examine changeability in science?

Variability: Intuitive Ideas and Experience

American Broadcasting Commission News Does the house dependably win in Sin city? Inconstancy: Intuitive Ideas and Experience Many speculators trust that you can beat the chances and win, in the event that you know the privilege strategy. (ABC news) http://abcnews.go.com/2020/story?id=3102356

Does the house dependably win in Sin city? Inconstancy: Intuitive Ideas and Experience By JOHN STOSSEL and FRANK MASTROPOLO May 1, 2007 Gamblers are a superstitious breed. They've made heaps of myths about betting, as there are approaches to beat the chances and win - in the event that you simply know the correct system. Obviously, individuals do win cash. Be that as it may, consider the chances. It costs groups of cash to pay for all the captivating structures, astounding attractions, every one of those workers and all the fat benefits that clubhouse make. They don't profit by losing to you. American Broadcasting Commission News

Digilearn Spinners-A flexible asset http://www.eduweb.vic.gov.au/dlrcontent/4c33353436/ec_002_utah_045/index.html

The Mathematics Developmental Continuum: Short-run variety and long-run security: 5.0 Knowing your understudies: Diagnostic assignment A reasonable coin is hurled. Which of the accompanying is more probable, or would they say they are similarly likely? Give your reasons From Continuum – MCD - 5.0 - Illustration 1

The Mathematics Developmental Continuum: From Continuum – MCD - 5.0 - Illustration 1

The Mathematics Developmental Continuum: Why are the wrong answers engaging? What misguided judgments do understudies bring into the classroom? From Continuum – MCD - 5.0 - Illustration 1

The Mathematics Developmental Continuum: Why utilize examinations in arithmetic? Investigative learning by understudies expands their ability to: Predict Gather information from a genuine trial Gather information from a recreation Observe – Analyze - Explain Share and talk about outcomes

The Mathematics Developmental Continuum: Small quantities of trials display incredible variety Predict How many 3's in 12 moves of a kick the bucket? Most extreme number of 3's?, least number of 3's? Lead explore In sets , roll a pass on 12 times (or move 12 dice at the same time!). Record the quantity of times each face 'comes up' Discuss Variation in results. Contrast number of 3's and expectation Calculate Relative (Frequencies partitioned by 12) Discuss Experimental probabilities acquired and how they change. What this implies in genuine circumstances e.g. playing recreations, translating insights in the media, and so on Small quantities of trials display awesome variety Predict How many 3's in 12 moves of a kick the bucket? Most extreme number of 3's?, least number of 3's? Direct examination In sets , roll a bite the dust 12 times (or move 12 dice at the same time!). Record the quantity of times each face 'comes up' Discuss Variation in results. Contrast number of 3's and forecast Calculate Relative (Frequencies separated by 12) Discuss Experimental probabilities got and how they shift. What this implies in genuine circumstances e.g. playing recreations, translating measurements in the media, and so on

The Mathematics Developmental Continuum: Exploration of 60 trials Predict How numerous 1,2,3,4,5,6 if a pass on was hurled 60 times Experiment Toss bite the dust 60 times and record results (in fours, work cooperatively to do this productively) Discuss Variability Compare numbers with expectations Calculate Relative frequencies Discuss Experimental probabilities acquired. Contrast these and the outcomes from 12 rolls

The Mathematics Developmental Continuum: (cont) Perform numerous trials utilizing the spreadsheet To create a recreation of rolling a kick the bucket 60 times, press CTRL = . Examine the inconstancy in various gatherings of 60 trials.

Two arrangements of results from hurling a bite the dust 60 times The Mathematics Developmental Continuum: It is critical that understudies see the connections amongst genuine and virtual tests!

The Mathematics Developmental Continuum: Exploring long-run relative recurrence, trial and hypothetical likelihood with a Using the Coin-hurling reproduction gave : (spare to neighborhood circle first) Experiment, investigate Generate comes about for rolling the kick the bucket 600 circumstances. Create comes about for rolling the bite the dust 6000 circumstances. Watch, record Results and components of the charts Discussion

Comparing relative frequencies for tests containing 600 and 6000 trials The Mathematics Developmental Continuum:

The Mathematics Developmental Continuum: Exploring long-run relative recurrence, trial and hypothetical likelihood with an irregular generator Compare changeability in short and long runs Experiment, Observe Graph indicating recreations for 60, 600 and 6000 moves of a kick the bucket on one arrangement of tomahawks Graph demonstrating the outright distinction between the long-run relative frequencies and the hypothetical likelihood Discuss Variability in long-run relative frequencies for 6000 moves of a bite the dust contrasted with 60 and 600 moves of a pass on Note : Even for 6000 trials, there is still some fluctuation in the relative frequencies and henceforth the exploratory probabilities. Continuum – MCD – 5.0 demonstrates to utilize a spreadsheet to produce probabilities

Graph indicating recreations for 60, 600 and 6000 moves of a kick the bucket on one arrangement of tomahawks

Teaching Strategies and Goals utilizing: ICT gives great conceivable outcomes to learning science, however educators require particular educational abilities. What understudy abilities ought to instructors know about with a specific end goal to utilize ICT assets profitably?

ICT: Other Resources Measurement, Chance & Data: A basic way to deal with summary insights and diagrams: 4.75 Working Mathematically: Carrying out examinations: 4.5 "Suggesting conversation starters from an informational index" Structure 5.5: Exponential capacities: 5.5 " Guitar frets" spreadsheet Australian Bureau of Statistics Australian Consumers' Association

Principles of Learning and Teaching P-12 The exercises advanced in this module interface unequivocally to the Principles of Learning and Teaching P-12 especially Principles 1, 2 and 6 The learning condition is steady and profitable The learning condition advances freedom, reliance and self inspiration Learning interfaces emphatically with groups and practice past the classroom

Principles of Learning and Teaching P-12 Discuss with your gathering how the exercises: Promote autonomy, relationship and self inspiration Connect firmly with groups and practice past the classroom How could instructors help understudies to see the pertinence of these tests to their own particular lives?

End of Module 7 This is the last slide of the module Further inquiries… studentlearning@edumail.vic.gov.au Subject field-Teaching Secondary Mathematics

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