âMathematical Knowledge for Teachingâ VOLUME 2 - AMESA

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Conclusion:I hope that learners would realise that statistics can be integrated with other learningoutcomes and other learning areas.References:• Maths4Stats – 2006• Pretorius, Potgieter & Ladewig : Mathematical Literacy (2006) Oxford UniversityPress. South Africa.• National Curriculum Statement.• Wikipedia22
THE BIASED INTERPRETATION OF DATA USING MEASURESOF CENTRAL TENDENCYMamoshibudi MabaleCapricorn District: LimpopoThe presentation is one that I have used when I workshop FET Mathematics andMathematics Literacy educators on the concepts of measures of central tendency. Thepresentation does not focus so much on how to calculate the measures of centraltendency but on how people interpret a calculated measure of central tendency. Italso addresses bias when presenting or interpreting data by using Circuit results.ASSESSMENT STANDARDSThe following Assessment Standards for Grades 10 – 12 mathematics andmathematical literacy are covered by this presentation:MATHEMATICS:10.4.1 (a): Collect, organise and interpret univariate numerical data in order todetermine measures of central tendency (mean, median and mode) of grouped andungrouped data and know which is the most appropriate under given conditions.10.4.3 (a), 11.4.3 (a) and 12.4.3 (a): Identify potential sources of bias, errors inmeasurement, and potential uses and misuses of statistics and chars and their effects.10.4.3 (b), 11.4.3 (b) and 12.4.3 (b): Effectively communicate conclusions andpredictions that can be made from the analysis of dataMATHEMATICAL LITERACY:10.4.3; 11.4.3; 12.4.3: Understand that data can be summarised and compared indifferent ways by calculating and using measures of central tendency for more thanone set of data, inclusive of mean, median and mode10.4.4; 11.4.4; and 12.4.4: Critically interpret data in order to draw conclusions onproblems investigated to predict trends and to critique other interpretationsINTRODUCTIONWhile the purpose of the first part of the workshop was to help teachers to calculatemeasures of central tendencies, the rest of the workshop was used to help teachers tointerpret the calculated values.Exam results were presented to the teachers. What was important was that theyshould use the same data to calculate the median, mean and mode so that they couldsee how the same data can be interpreted differently. I also wanted to show them howtheir interpretations of the results and their conclusions could lead to misconceptionsdepending on which measure of central tendency was used.23
Page 1 and 2: Proceedings of the15 th Annual Cong
Page 3 and 4: Foreword“Mathematical Knowledge f
Page 5 and 6: ContentsHow I teachAuthor Title Pag
Page 7: Scheiber, JackieThe interpretation
Page 10 and 11: SKETCHING A CUBIC FUNCTIONTRADITION
Page 12 and 13: of the first computer games, Pong,
Page 14 and 15: Although this genre of computer gam
Page 16 and 17: He played on and off all day until
Page 18 and 19: [10] Butgereit, L, “Thumb Tribe M
Page 20 and 21: 2) Use the information given in the
Page 22 and 23: ConclusionSince these terms were fa
Page 24 and 25: EXAMPLE: The table below represents
Page 26 and 27: Five-number summaryMinimum = …; Q
Page 28 and 29: ACTIVITYIn an experiment to measure
Page 32 and 33: ACTIVITYBelow is a summary of a cir
Page 34 and 35: REFERENCESScheiber, J. 2003. Data h
Page 36 and 37: MOTIVATION FOR RUNNING WORKSHOPThis
Page 38 and 39: CONCLUSIONThese are not the only te
Page 40 and 41: n(E)• P(E) = 1 if event E is cert
Page 42 and 43: DETERMINING PROBABILITIES OF COMPOU
Page 44 and 45: Calculate the relative frequency of
Page 46 and 47: HOW I TEACH SCATTER PLOTSDUNGILE MA
Page 48 and 49: • It is clear from the above grap
Page 50 and 51: A STATISTICAL INVESTIGATION INTO HU
Page 52 and 53: • Does the activity relate to han
Page 54 and 55: MEASURES OF CENTRAL TENDENCYTHABANI
Page 56 and 57: 1) Determine the mean, mode and med
Page 58 and 59: HOW I TEACH MATH USING VIRTUAL MANI
Page 60 and 61: The Balloon ModelIs this game fair?
Page 62 and 63: Virtual manipulatives can be both s
Page 64 and 65: References• Moyer P., Bolyard,J.
Page 66 and 67: WHAT ARE MISLEADING BAR GRAPHS?If a
Page 68 and 69: CONCLUSION:It is a well known fact
Page 70 and 71: MISLEADING AVERAGESThe mean, median
Page 72 and 73: e) Do you think any of the averages
Page 74 and 75: ANALYSIS OF QUESTION 10.2 OF THE NO
Page 76 and 77: CONCLUSIONThe midpoint curve is TRA
Page 78 and 79: called a sample. A sample is any su
Page 80 and 81:
This demonstrates that the larger t
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Consider the marks 32 ; 56 ;With 32
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SOLUTIONStep 1: Collect the data in
Page 86 and 87:
HOW I TEACH TALLY TABLES TO LEARNER
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In a survey, 50 people were asked t
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At the end of the first “branches
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Let A denote an odd and even number
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ADD THE ANGLE TO THE 2- and 3- DIME
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……………………………
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Enlarge the following objects90
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MathematicsGrade: 6Learning Outcome
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A B CD E FGMathematicsGrade: 6Learn
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INVESTIGATING 3-D SHAPES: ANALYSING
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When we arrange objects according t
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Sphere:Cube:Prisms, pyramids, cylin
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a Now complete the table below:pris
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27 Now look at the different spatia
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elationships algebraically; and rep
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• How do analytical and global th
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Adults must not be shy about asking
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In fact, if a pupil asks a research
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INVESTIGATING BALANCING POINTS OF P
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DATA HANDLING IN THE FOUNDATION PHA
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NUMERACY ASSESSMENT STANDARDS AND M
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FUNCTIONS AND INVERSES IN CONTEXTMa
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ARRIVE ALIVE!!!When a motorist brak
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BACTERIA!!!Food goes rotten when th
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Suppose we want to make x the subje
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REGRESSION MODELLINGPaul LaridonRAD
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table. Then press [AC]. The screenc
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3.2 The PendulumThe diagram represe
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3.2.5 and comment on how good or ot
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THE VERSATILE USE OF PATTERN BLOCKS
Page 146 and 147:
AN INTRODUCTION TO FUNCTIONAL RELAT
Page 148 and 149:
USE OF MATHEMATICAL GAMES AS AN ALT
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the teacher’s ability to choose t
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method. This will be followed by a
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mathematical concepts, (2) develop
Page 156 and 157:
TEACHING AND ASSESSING SPACE AND SH
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Grade R Grade 1 Grade 2 Grade 3•
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3.2Grade R Grade 1 Grade 2 Grade 3R
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have a lid that can roll, andPeople
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Grade R Grade 1 Grade 2 Grade 3•
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Page 168 and 169:
Page 170 and 171:
WORKSHOP: TWO HOURSTARGET GROUP: GR
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PROBLEM SOLVINGFOUNDATION PHASE MAT
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5. Guess the number I stand for.•
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ASTROS? OR SMARTIES? ASTROS? OR SMA
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It is important to note that volume
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Part 1: The Great Bicycle Race (30
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IDEAS AND ACTIVITIES TO MAKE YOU A
Page 184 and 185:
WHAT IS THINKING? (15 MIN)An import
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EXPLORING GRAPHS THROUGH TABLESDORY
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• Use the constant -3 to decide o
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Explain the error in line 7.6. Draw
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SOLVING EQUATIONS & FACTORISING AN
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Simple GrowthYear Amount1 R11000234
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3. Solve for x :3 24x - 4x - 7x - 2
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2) QUARTILESA quartile is any of th
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‣ The lower quartile corresponds
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ACTIVITY:Answer the following quest
Page 204 and 205:
SETTING A MATHS LITERACY EXAMINATIO
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are soup tins usually cylindrical?.
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Part 4: 30 minutesIn groups: Make y
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DEVELOPING ALGEBRAIC THINKING IN TH
Page 212 and 213:
WORKSHEET 2Activities to develop le
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3.Fig. 1 Fig. 2 Fig. 34.Fig. 1 Fig.
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2. Another brick wall:Repeat questi
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2.1 Are the methods of all three le
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2.3 Is there an opportunity here to
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1.3 Is there an opportunity here to
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Investigate whether the following i
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Kieran, C. 1989. The early learning
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Motivation for doing the workshopOu
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• Paired cards• Crack the code
Page 232 and 233:
• Separate tests were developed f
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Enlighten Education TrustBaseline T
Page 236 and 237:
Enlighten Education TrustSchool Ave
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âMathematical Knowledge for Teachingâ VOLUME 2 - AMESA