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Teaching Students To Write Mathematics

Kevin HoustonUniversity of Leeds

[email protected]

www.kevinhouston.net

Outline

The problem.

My solution(s).The way forward.

Outline

The problem.My solution(s).

The way forward.

Outline

The problem.My solution(s).The way forward.

The problem

ExampleYear 1 question: Is {1, 2, 3, 4, 5, 6, 7}under multiplication mod 8 a group?

Student answer: not closed. setcontains 0.

The problem


Student answer:

not closed. setcontains 0.

The problem


Student answer: not closed.

setcontains 0.

The problem


Student answer: not closed. setcontains 0.

Writing mathematics

Forces thinking.

Fantastic skill to have.Marking is a joy.

Writing mathematics

Forces thinking.Fantastic skill to have.

Marking is a joy.

Writing mathematics

Forces thinking.Fantastic skill to have.Marking is a joy.

Myth

Myth:

Learning mathematics teachescritical thinking andlogical thinking

Myth

Myth:

Learning mathematics teaches

critical thinking andlogical thinking

Myth

Myth:

Learning mathematics teachescritical thinking and

logical thinking

Myth

Myth:

Learning mathematics teachescritical thinking andlogical thinking

Myth 2

‘Tell students to write their work so thatsomeone else can understand it’.

If only it were that simple.

My approach

Teach thinking.Teach writing.

My approach

Teach thinking.

Teach writing.

My approach

Teach thinking.Teach writing.

Thinking and writing

To write clearly, students need to thinkclearly.

To think clearly, students need to writeclearly.

Reasons

A good university education preparesa student for life.

Writing well is an extremely usefulskill.Students choose mathematics asthey do not like writing essays.Low hanging fruit: Small effort givesmajor boost for student.

Reasons

A good university education preparesa student for life.Writing well is an extremely usefulskill.

Students choose mathematics asthey do not like writing essays.Low hanging fruit: Small effort givesmajor boost for student.

Reasons

A good university education preparesa student for life.Writing well is an extremely usefulskill.Students choose mathematics asthey do not like writing essays.

Low hanging fruit: Small effort givesmajor boost for student.

Reasons

A good university education preparesa student for life.Writing well is an extremely usefulskill.Students choose mathematics asthey do not like writing essays.Low hanging fruit:

Small effort givesmajor boost for student.

Reasons

A good university education preparesa student for life.Writing well is an extremely usefulskill.Students choose mathematics asthey do not like writing essays.Low hanging fruit: Small effort givesmajor boost for student.

How to write mathematics

How to write mathematics booklet.

Chapters 3 and 4 of my book.

Copies of samples on my website.

www.kevinhouston.net

What the students are told

Write in sentences.

This advice hasprecedence over all others. This canreally change the way you presentyour work.Use punctuation. That means acapital letter at the start of sentencesand a full stop at the end. Doing thismakes your work so much clearer.


Write in sentences. This advice hasprecedence over all others. This canreally change the way you presentyour work.

Use punctuation. That means acapital letter at the start of sentencesand a full stop at the end. Doing thismakes your work so much clearer.


Write in sentences. This advice hasprecedence over all others. This canreally change the way you presentyour work.Use punctuation.

That means acapital letter at the start of sentencesand a full stop at the end. Doing thismakes your work so much clearer.


Write in sentences. This advice hasprecedence over all others. This canreally change the way you presentyour work.Use punctuation. That means acapital letter at the start of sentencesand a full stop at the end. Doing thismakes your work so much clearer.


Use grammar correctly.

Common error: ‘Mathematics ishighly symbolic so if I just providesome mathematical symbols I’mdoing maths.’ This is wrong.Symbols are merely shorthand forcertain concepts; they need to beincorporated into sentences for thereto be any meaning.


Use grammar correctly.Common error:

‘Mathematics ishighly symbolic so if I just providesome mathematical symbols I’mdoing maths.’ This is wrong.Symbols are merely shorthand forcertain concepts; they need to beincorporated into sentences for thereto be any meaning.


Use grammar correctly.Common error: ‘Mathematics ishighly symbolic so if I just providesome mathematical symbols I’mdoing maths.’

This is wrong.Symbols are merely shorthand forcertain concepts; they need to beincorporated into sentences for thereto be any meaning.


Use grammar correctly.Common error: ‘Mathematics ishighly symbolic so if I just providesome mathematical symbols I’mdoing maths.’ This is wrong.Symbols are merely shorthand forcertain concepts; they need to beincorporated into sentences for thereto be any meaning.


Others:Readers are not psychic. Explainwhat you are doing.

Explain your assertionsUse of symbolsExpressing yourself clearly


Others:Readers are not psychic. Explainwhat you are doing.Explain your assertions

Use of symbolsExpressing yourself clearly


Others:Readers are not psychic. Explainwhat you are doing.Explain your assertionsUse of symbols

Expressing yourself clearly


Others:Readers are not psychic. Explainwhat you are doing.Explain your assertionsUse of symbolsExpressing yourself clearly

My favourite

Curse of the implication symbol.

I can understand why students use theimplication symbol:

⇒It makes a proof or the answer to anexercise look mathematical.

My favourite



⇒

It makes a proof or the answer to anexercise look mathematical.

My favourite



⇒It makes a proof or the answer to anexercise look mathematical.

Another example

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Worked example

Worked example

In the booklet students are takenthrough the errors in the example andshown how to produce a better solution.

Videos of the example are available:www.youtube.com/user/DrKevinHouston

Weekly exercises

How is this applied?

Intake 148 Home/EU and 20International.Current offer AAB, A in Maths, halfhave Further Maths A or AS level.Six tutees.Weekly exercises.

Weekly exercises

How is this applied?Intake 148 Home/EU and 20International.

Current offer AAB, A in Maths, halfhave Further Maths A or AS level.Six tutees.Weekly exercises.

Weekly exercises

How is this applied?Intake 148 Home/EU and 20International.Current offer AAB, A in Maths, halfhave Further Maths A or AS level.

Six tutees.Weekly exercises.

Weekly exercises

How is this applied?Intake 148 Home/EU and 20International.Current offer AAB, A in Maths, halfhave Further Maths A or AS level.Six tutees.

Weekly exercises.

Weekly exercises

How is this applied?Intake 148 Home/EU and 20International.Current offer AAB, A in Maths, halfhave Further Maths A or AS level.Six tutees.Weekly exercises.

Weekly exercises

No tolerance of errors?

Plenty of feedback. HTWLAM pagenumber.Too much feedback?Do they read it?Student resistance.Students dispirited.Changes to our first year. Groups of12.

Weekly exercises

No tolerance of errors?Plenty of feedback. HTWLAM pagenumber.

Too much feedback?Do they read it?Student resistance.Students dispirited.Changes to our first year. Groups of12.

Weekly exercises

No tolerance of errors?Plenty of feedback. HTWLAM pagenumber.Too much feedback?

Do they read it?Student resistance.Students dispirited.Changes to our first year. Groups of12.

Weekly exercises

No tolerance of errors?Plenty of feedback. HTWLAM pagenumber.Too much feedback?Do they read it?

Student resistance.Students dispirited.Changes to our first year. Groups of12.

Weekly exercises

No tolerance of errors?Plenty of feedback. HTWLAM pagenumber.Too much feedback?Do they read it?Student resistance.

Students dispirited.Changes to our first year. Groups of12.

Weekly exercises

No tolerance of errors?Plenty of feedback. HTWLAM pagenumber.Too much feedback?Do they read it?Student resistance.Students dispirited.

Changes to our first year. Groups of12.

Weekly exercises

No tolerance of errors?Plenty of feedback. HTWLAM pagenumber.Too much feedback?Do they read it?Student resistance.Students dispirited.Changes to our first year. Groups of12.

Conclusion

They hate itat first

but are grateful at the end.

Not very scientific.

Conclusion

They hate it

at firstbut are grateful at the end.


Conclusion

They hate itat first

but are grateful at the end.


Conclusion

Colleagues (broadly) in favour.

Can undermine.Resistance to ‘skills’.

Conclusion

Colleagues (broadly) in favour.Can undermine.

Resistance to ‘skills’.

Conclusion

Colleagues (broadly) in favour.Can undermine.Resistance to ‘skills’.

The way forward

Low hanging fruit. Big difference. Inpractice and in research.

Chapters 3 and 4 are free on mywebsites.

Leeds School of Maths.www.kevinhouston.net

Contribute examples of goodpractice. Make Latex exercisesavailable.

The way forward

Low hanging fruit. Big difference. Inpractice and in research.Chapters 3 and 4 are free on mywebsites.

Leeds School of Maths.www.kevinhouston.net

Contribute examples of goodpractice. Make Latex exercisesavailable.

Thanks

Thanks for listening.

[email protected] ... - university of …khouston/pdf/houston-talk.pdf · writing well is an...

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