âMathematical Knowledge for Teachingâ VOLUME 2 - AMESA

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A STATISTICAL INVESTIGATION INTO HUMAN BEHAVIOURNokwanda MbusiWalter Sisulu University(Senior Phase / FET Band)This presentation was inspired by the desire to give learners an opportunity to beactively involved in their learning, as well as the belief that learners learn better in arelaxed atmosphere where they interact freely with each other. Appropriate datahandling activities can give learners this opportunity, as it will be illustrated in thepresentation. Learners will collect, organise and interpret data using practicalactivities that involve parts of their bodiesINTRODUCTIONThe articulation between mathematics and everyday life is a phenomenon that needsto be investigated and recognized (Ensor & Galant, 2005). Data Handling, as one ofthe Learning Outcomes in the National Curriculum Statement, has a major role toplay in achieving this articulation. Here, learners develop the skills to collect,organise, display, analyse and interpret information, thus enabling them to participatemeaningfully in, among other things, social activities. A statistical investigation intohuman beings’ everyday activities and behaviour would give learners and teachers anopportunity to explain this articulation within a familiar and interesting context…andthey will have fun too!In this presentation, participants will collect information on how they fold their arms,clasp their hands, open bottles and peep through holes. Although the sample would betoo small to generalize findings, and chances of possible biases are never ruled out,the following investigations will give learners an opportunity to collect, organise,analyse and interpret data that relates to their own daily life. This presentationaddresses Learning Outcome 5, Assessment Standard 5 in Grade 9 from the RevisedNational Curriculum Statement, which states that “the learner should be able tocritically read and interpret data with awareness for sources of error, andmanipulation in order to draw conclusions and predictions about characteristics oftarget groups (e.g. age, gender, race, etc.)”.ACTIVITIESThe investigations that follow were done for the purpose of trying to answer thequestion: Is there a relationship between the handedness of a person and the way heor she does most of his or her daily physical activities?42
Learners were asked to summarise the data, display it in tables and analyse it bylooking at the numbers (frequency) or percentages of observations in each category.Assessment Standard 10.4.2 in the Mathematical Literacy subject statement requireslearners to be able to use a variety of methods to summarise and display data in, forexample, tables. Assessment Standard 10.4.3 (b) requires learners to be able toeffectively communicate conclusions and predictions that can be made from theanalysis of data.INVESTIGATION 11) Participants observe each other while they fold arms. Specifically, they need tonote if the right or left arm is on top.2) Next they should clasp their hands and observe whether the right or left thumb ison top.The observations should be recorded in a table as follows:Participants’nameGenderHandedness(left/right/both)Arm on top(left/right)Thumb on top(left/right)Possible questions that could be asked:• Are the above activities (arm on top and thumb on top) related?• Do they relate to handedness?• Do they relate to gender?INVESTIGATION 2Small water bottles are supplied to each group and the participants observe andrecord which hand is used by each of them to open the bottle.Participants’ namesHandedness(left/right/both)Hand opening the bottle(left/right)Possible questions that could be asked:43
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 30 and 31: Conclusion:I hope that learners wou
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 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
Page 82 and 83: Consider the marks 32 ; 56 ;With 32
Page 84 and 85: SOLUTIONStep 1: Collect the data in
Page 86 and 87: HOW I TEACH TALLY TABLES TO LEARNER
Page 88 and 89: In a survey, 50 people were asked t
Page 90 and 91: At the end of the first “branches
Page 92 and 93: Let A denote an odd and even number
Page 94 and 95: ADD THE ANGLE TO THE 2- and 3- DIME
Page 96 and 97: ……………………………
Page 98 and 99: Enlarge the following objects90
Page 100 and 101:
MathematicsGrade: 6Learning Outcome
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A B CD E FGMathematicsGrade: 6Learn
Page 104 and 105:
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
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AN INTRODUCTION TO FUNCTIONAL RELAT
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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
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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:
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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
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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
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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
Page 228 and 229:
Motivation for doing the workshopOu
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• Paired cards• Crack the code
Page 232 and 233:
• Separate tests were developed f
Page 234 and 235:
Enlighten Education TrustBaseline T
Page 236 and 237:
Enlighten Education TrustSchool Ave
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âMathematical Knowledge for Teachingâ VOLUME 2 - AMESA