iec conference 2011 - literacy/maths/high challenge-high support
DESCRIPTION
PowerPoint about the literacy demands of mathematics, focusing on geometry, shape and measurement.TRANSCRIPT
Mathematics – Mathematics – high challenge with high challenge with high supporthigh support
A focus on shape A focus on shape and geometry and geometry
High High SupportSupport
Test and re-test vocabulary until students reach a Test and re-test vocabulary until students reach a
pre-determined standard.pre-determined standard.
Irregular hexagonal prism
perpendicular height
Research says:
If it is tested, its important!
High SupportHigh Support Continually emphasise spelling Continually emphasise spelling
When words are removed in maths, the remaining words need to be spelt correctly to retain meaning. When words are removed in maths, the remaining words need to be spelt correctly to retain meaning.
This is very important in geometry, because theorems This is very important in geometry, because theorems are always abbreviated.are always abbreviated.
High SupportHigh Support Encourage correct language use.Encourage correct language use.
e.g.e.g. Don’t accept ‘I minused 50 Don’t accept ‘I minused 50oo.’! .’!
xo50
o
Solution:
xo + 50
o = 90
o (a right angle is 90
o.)
xo = 90o 50
o
xo = 40
o
Teacher: What is the answer? Student: The answer is 400.
Teacher: How did you get 40o?
Teacher: Why did you subtract 50o from 90
o?
Student: I subtracted 50o from 90
o.
Student: Because a right angle is 90o.
High SupportHigh Support Create scaffolds where correct language can be practisedCreate scaffolds where correct language can be practised
The diagonals
opposite sides
opposite angles
adjacent sides
of a rhombus are equal.
parallel.
perpendicular.
bisect each other.
its angles.
meet at right angles.
Emphasise: ‘The’ means ‘all’.
True or false: The opposite sides of a trapezium are equal.
Click here for more on
articles.
High SupportHigh Support Include non-technical languageInclude non-technical language
The ‘little’ words often get missed.
between
From………. to
4
Vocabulary is only about Vocabulary is only about 40% of the problem, so…40% of the problem, so…
……how can we improve how can we improve reading and writing reading and writing outcomes?outcomes?
Maths
High support – high High support – high challengechallenge
Identify large descriptive noun groupsIdentify large descriptive noun groups
Note: The most important adjective is always next to the noun.Note: The most important adjective is always next to the noun.
When students are ready, introduce complex sentences.
and…… but……
High support – high High support – high challengechallenge
Encourage use of clauses. Encourage use of clauses.
A triangular prism, A triangular prism, which is a solid shapewhich is a solid shape, has , has two congruent triangular faces and three two congruent triangular faces and three different rectangular faces.different rectangular faces.
Modelled description:
The triangular faces The triangular faces have a base length of 3 cm and perpendicular have a base length of 3 cm and perpendicular heights of 4 cm. The height of the prism is 6 cm.heights of 4 cm. The height of the prism is 6 cm.
Draw the diagram and write these Draw the diagram and write these measurements in the correct place on your measurements in the correct place on your prism.prism.
3 cm
4 cm6 cm
High support – high High support – high challengechallenge
Writing in a detailed descriptive way usually Writing in a detailed descriptive way usually helps the ability to read for detail.helps the ability to read for detail.
eg cloze, dictaglos, matching activities, barrier games,…etc
Use any ESL strategies suitable for your class,
High High supportsupport – high – high challengechallenge Practise reading descriptions and drawing diagrams.Practise reading descriptions and drawing diagrams.
Mathematical descriptions usually shrink into one paragraph!
High support – high High support – high challengechallenge
In English: → In maths:
First paragraph = First sentence
Subsequent paragraphs
= The next sentence(s) give extremely accurate detail.
Here’s how descriptions shrinks.Here’s how descriptions shrinks.
Writing reinforces reading, and thus, we hope, understanding.Writing reinforces reading, and thus, we hope, understanding.
High support – high High support – high challengechallenge Show students how to think, before writing.Show students how to think, before writing.
High support – high High support – high challengechallenge
OR
High support – high High support – high challengechallenge
Pronoun reference and other referencesPronoun reference and other references
References are quite detailed in maths.
High support – high High support – high challengechallenge Plurals are easily missed!Plurals are easily missed!
Difficult Pluralsaxis axesvertex verticeshalf halves
High support – high High support – high challengechallenge
Mathematics abbreviates immediately when words become Mathematics abbreviates immediately when words become repetitive! repetitive!
In geometry, ‘because’ occurs too often and theorems become In geometry, ‘because’ occurs too often and theorems become repetitive!repetitive!
EllipsisEllipsis
High support – high High support – high challengechallenge
50o
xo• •
• •
A B
C D
xo + 50
o = 180
o (coint ’s, AB//CD)
xo = 180
o 50
o
xo = 140
o
Solution:
…..because cointerior angles are supplementary in parallel lines, AB and CD.
→ (cointerior angles are supplementary, AB // CD.)
→ (cointerior angles, AB // CD.)
→ (coint. ’s, AB // CD.)
xo + 50
o = 180
o ….
is parallel to
Example: Calculate xo, giving reasons.
There are no BOS standard abbreviations!
High support – high High support – high challengechallenge
Use flash cards to practise speaking (or writing) explanationsUse flash cards to practise speaking (or writing) explanations
Because opposite angles of a parallelogram are equal.
High support – high High support – high challengechallenge
ExplanationsExplanations
A few rules first:
• If you feel like drawing a picture then draw it and make
it part of your explanation.
• If you feel like writing some mathematics, then write it.
• When asked to explain why something is not true,
always end with a statement about what is true.
Explanations can have just maths, just English or both.
The rules just make it easier for students.
High support – high High support – high challengechallenge
Explanations – review responses constantlyExplanations – review responses constantly
Example: Explain why a cylinder is not a prism.
A cylinder is not a prism _______ it has a ______ base and a ______ surface. Prisms have a ________ base and _________ side faces.
because circularcurved polygonal
rectangular
curved surface circular base
High support – high High support – high challengechallenge
Mathematics uses timeless present tense Mathematics uses timeless present tense
2 = 2…..yesterday, today and forever!
When to use past tense? When to use past tense?
Past tense Past tense is mostly used in:is mostly used in:
• • graphsgraphs..• • probability probability • • consumer consumer arithmeticarithmetic• • discussiondiscussion
Graphs use past data.
When When present continuouspresent continuous is used, is used, then get ready for a difficult two-stage question! then get ready for a difficult two-stage question!
Mathematical warning
My students can read and My students can read and respond reasonably well respond reasonably well so….so….
How can I use this talent How can I use this talent to improve mathematics?to improve mathematics?
To improve mathematicsTo improve mathematics Use written procedures so students answer questions in the best Use written procedures so students answer questions in the best
possible way! possible way!
To improve mathematicsTo improve mathematics Use written procedures so students think out solutions in the best Use written procedures so students think out solutions in the best
possible way! possible way!
arc
size near
To improve mathematicsTo improve mathematics
next
reasoning
Student’s ‘draft’ thinking
What is assessed!
Literacy demands of Literacy demands of mathematicsmathematics
Vocabulary – technical and other vocabularyVocabulary – technical and other vocabulary
Lexical density - large descriptive noun groups, phrases and Lexical density - large descriptive noun groups, phrases and clauses clauses
Ellipses – Words are infuriatingly missing because they are Ellipses – Words are infuriatingly missing because they are ‘understood’ to be there.‘understood’ to be there.
Definite and indefinite articles – They are part of our counting Definite and indefinite articles – They are part of our counting system. system.
Plurals – they are too small to see!Plurals – they are too small to see!
Pronoun referencePronoun reference
Timeless present tense. When to use past tense?Timeless present tense. When to use past tense?
Text types – descriptions, explanations, procedures andText types – descriptions, explanations, procedures and
information reports.
Cultural interferenceCultural interferenceSome students:Some students:
have never been allowed to use a calculator and have never been allowed to use a calculator and thus have thus have difficulty deciding when they can use it.difficulty deciding when they can use it.
come from countries that use the ‘implies’ symbol come from countries that use the ‘implies’ symbol and thus are not use to working with and thus are not use to working with equals signs equals signs underneath each otherunderneath each other..
write and speak ‘write and speak ‘because’ firstbecause’ first and then write the and then write the answer.answer.
write‘write‘11’ rather than ’ rather than ABCABC
Never been in a classroom beforeNever been in a classroom before
Mathematics – Mathematics – high challenge with high challenge with high supporthigh support
A focus on shape A focus on shape and geometry and geometry
Articles are not so easyArticles are not so easy
5544 = ‘5 to = ‘5 to thethe power power of 4of 4’’
Question: Question:
Express 625 as Express 625 as aa power power of 5of 5..
Answer:Answer:
4455? 5? 544
? 625? 62555? 625? 62544
??
50, 5
1, 5
2, 5
3, 5
4
Here are the powers of 5
Now students must choose one out of many.
Example 1:
Articles – not so easyArticles – not so easy
Write true or false: 2 and 3 are factors of 6.Write true or false: 2 and 3 are factors of 6.
: 2 and 3 are the factors of 6.: 2 and 3 are the factors of 6.
Write a factor of 20.Write a factor of 20.
Many technical words in maths have different meanings outside of maths.
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Mathematics – Mathematics – high challenge with high challenge with high supporthigh support
A focus on shape A focus on shape and geometry and geometry