Introduction to Differential Calculus Presentation Secondary School Listowel (1)

8/9/2019 Introduction to Differential Calculus Presentation Secondary School Listowel (1)

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Maths CountsInsights into LessonStudy

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Presentation SecondarySchool: Listowel:

• Jacqueline Normile, Norma Dowlingand Elaine Hickey

• Si!th "ear

• #ssociating deri$ati$es with slo%es o&tangent lines

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Insights into Lesson Study

• (ntroduction: )ocus o& Lesson

• Student Learning : *hat we learned a+outstudents understanding +ased on data

collected• -eaching Strategies: *hat we noticed

a+out our own teaching

•

Strengths . *eaknesses o& ado%ting theLesson Study %rocess

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Introduction• Topic investigated:

Associate derivatives with slopes of tangent lines.• How we planned the lesson:

Maths Team got together and we looked at anddiscussed!lanning lesson !rior knowledge"hat we wanted to teach"hat we wanted the students to know at the

end.• Interested in:

Strategies to improve learning and understanding.•

#esources used:The Teaching and Learning !lan the sylla$uswhite$oards rulers pencils coloured markersactivity sheet and !ower!oint%s.

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• !rior &nowledge:oStudents understand:

• #ate of change and slope are

e'uivalent.• The di(erence $etween the average

rate of change and the instantaneousrate of change.

• Transformation of )uadratic *unctions.

Introduction


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2

Introduction

• "hy did we choose to focus onthis mathematical area+ –

The class had started the calculussection of the course and thisTeaching and Learning planprovided a solid foundation from

which to continue.


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Introduction

• ,nduring understandings: – Students will $e a$le to analyse this

information and present their -ndingsin mathematical form.

– The aim of this lesson study was forstudents to understand why weassociate derivatives with tangentlines.

– Students should $e a$le to apply theirknowledge and skills to solve pro$lems.

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Learning 4utcomes:

• Students will understand: – The slope function of a 'uadratic

function allows us to predict the slope

of the function at any point. – Slope functions may $e determined $y

eamining the pattern of the slopes of

tangents to the function. – Slope functions may $e determined $y

a simple rule.

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#e/ections on theLesson

• Student Learning : *hat welearned a+out studentsunderstanding +ased on data

collected

• Teaching Strategies: *hat wenoticed a+out our own teaching

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Student Learning

• Data 7ollected &rom the Lesson:

1 #cademic eg sam%les o& students

work

' 8oti$ation

/ Social 9eha$iour

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#cti$ity &rom -.L Plan

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We handed this activity to the class and told them they were to fill in the

table, individually, and see if there was a discernible pattern.

Then they collaborated in pairs and in small groups.

One person then reported from each group on their findings.


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7ommon misconce%tions: 1

• Students &ound the slo%e o& the

secant o& two ad;acent %oints, ratherthan the tangent

See ne!t ' slides

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1/


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7ommon misconce%tions: '

• Students &ound the slo%e o& the

secant &rom the origin to the %oint o&interest, rather than the tangent

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See ne!t ' slides


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7ommon misconce%tions: /

• *hen students used the &ormula,

they took run as a negative distance, rather than a negative mo$ement

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See ne!t slide

Slope =rise

run

Slope = riserun

± ÷


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16


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Student 0nderstanding:1

"hat we learned a$out the waydi(erent students understand thecontent of this topic+

• Students saw two points andfound the slope using these twopoints rather than the tangents.

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See ne!t 0 slides


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'2


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Addressing


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AddressingMisconceptions•

#ecommendationsIn future when we teaching rates ofchange we should put more emphasis on

1 -he idea o& a constant rate o& change

' -he secant line is used to


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*urther #ecommendation

• 3efore teaching this lessonagain the students should havegood prior knowledge of

– !atterns – Slopes of linear functions

– #ates of 4hange

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Teaching Strategies

"hat did I notice a$out my ownteaching+

– To $e /uent in the correct mathematical

language. – To $e organised 5 timing resources.

– Increased level of sound.

– "ait time 5 give the students time tocomplete activity and then discussactivity and -ndings.

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Teaching Strategies

"as it di6cult to ask 'uestions toprovoke students% deep thinking+• "e circulated the classroom and listened to

the progress.

• "e encouraged students to ask each other'uestions.

• "e noticed di(erent mem$ers of a group haddi(erent results.

•"e asked them to discuss this with eachother.

• Students had to tease out which piece of workthey thought was correct.

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Teaching Strategies

How did I assess what students knewand understood during the lesson+• A mem$er from each group reported $ack

with their conclusions using the visualiser.

Some )uestioning used during thelesson –

"hy did the group decide that this wasthe $est answer+

– "hat was wrong with the other answers+

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Teaching Strategies

How did I put closure to the lesson+• Having seen eamples of work we asked the

class which piece of work they thought wascorrect.

• "e also asked what were the commonmisconceptions.

• "e then showed a fully correct eample ofthe activity on the visualiser including thecorrect pattern for the slope function.

• "e then graphed the f%89 2 function andasked the class what type of function thiswas.

• The class recognised it was linear.

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Teaching Strategies• Homework:

• ,ach student was asked to -ll in theta$le formulate a pattern i.e. slopefunction and graph the slope

function for di(erent 'uadraticfunctions such as:

• x2 + 1

• x2 – 1

• 2 x2

• 2 x2 + 1

•

2 x2

– 2 /2

u en omewor :


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u en omewor :,ample 1

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f ( x ) = x 2 + 1

u en omewor :


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f(x) = x 2 – 1

u en omewor :,ample 2


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f(x) = 2x 2 + 1

,ample ;

u en omewor :


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f(x) = 2x 2 – 2

u en omewor :,ample <

N t L


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– Students used the visualiser to

display their homework – They noticed that all 'uadratic

functions gave rise to linear slopefunctions

– "e asked students could they comeup with a general formula forderiving the slope function $ased

on the homework – "e then introduced the derivative

formula as a simpler method for-nding the slope function.

– =erivative function Slope function01

Ne!t Lesson

> ? ti L St d


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>e?ections on Lesson StudyProcess• >reatly improved

communication colla$orationand collegiality $etween

mem$ers of the Maths Team.• Increased my con-dence.

• Increased my knowledge of more

varied teaching methodologies.

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>e?ections on Lesson Study


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>e?ections on Lesson StudyProcess

#ecommendations as to how LessonStudy could $e integrated into aschool contet. –

"ritten lesson studies are very timeconsuming.

– "e found it to $e a great learningeperience.

–

It has thought us the importance ofsitting down and talking a$out thecontent of a topic and how to teach it 5even for -ve minutes.

– Sharing of la$our.

– The im ortance of a common a roach.0/

P t ti S d S h l


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Presentation Secondary School:Listowel:

Thank ?ou

@ac'ueline 7ormile 7orma =owling and

,laine Hickey.

Documents

Introduction to Differential Calculus Presentation Secondary School Listowel (1)