- Free
Angles - basic
Where do students struggle with the basics of angles, where do they come from, and what can we do to help our students?
Course overview
In this course we delve into three angles related concepts:
- Estimating and measuring angles
- Angles in triangles
- Angles on a straight line
We seek to identify and understand the specific misconceptions students have in these areas, and then consider ways we can support students understanding these concepts better.
Contents
The angles challenge!
Let's get warmed up by trying to understand why these questions are troublesome
The angles challenge!
The angles challenge (image)
What students meet and when
When do students encounter the key ideas in this course?
What students meet and when
How Diagnostic Questions are used
How are the questions that the data in this course is based on used in the classroom and at home?
How are Diagnostic Questions used?
Link: Diagnostic Questions
Link: Eedi
Mistakes versus misconceptions
What is the difference between a mistake and a misconception, and does it really matter?
1. Mistakes versus misconceptions
2. Do Diagnostic Questions cause misconceptions?
Research: The memorial consequences of multiple-choice testing
Research: Multiple-Choice Tests Exonerated, at Least of Some Charges: Fostering Test-Induced Learning and Avoiding Test-Induced Forgetting
Concept 1: Estimate and measure angles
Where do students struggle with this area of angles, why do they struggle, and what can we do about it?
1. Where might students go wrong?
2. DQ 1 (question)
DQ1 (image)
3. DQ1 (answer)
4. Comparing angles, line lengths and arcs
5. DQ2 (question)
DQ2 (image)
6. DQ2 (answer)
7. Estimating the size of angles - reflection
8. DQ3 (question)
DQ3 (image)
9. DQ3 (answer)
10. DQ4 (question)
DQ4 (image)
11. DQ4 (answer)
12. Measuring the size of angles - reflection
13. What can we do - retrieval
14. What can we do - remove the scales
Resource: protractor with no scales
15. What can we do - intelligent practice
Resource: Measuring angles
Concept 2: Angles in triangles
Where do students struggle with this area of angles, why do they struggle, and what can we do about it?
1. Where might students go wrong?
2. DQ1 (question)
DQ1 (image)
3. DQ1 (answer)
4. How do different age groups get on?
5. DQ2 (question)
DQ2 (image)
6. DQ2 (answer)
7. Scalene triangles - reflection
8. DQ3 (question)
DQ3 (image)
9. DQ3 (answer)
10. DQ4 (question)
DQ4 (image)
11. DQ4 (answer)
12. Isosceles traingles - reflection
13. What can we do - include the unusual
Twitter thread on "base" angles
14. What can we do - go deep
Resource: two isosceles triangles stuck together
15. What can we do - intelligent practice
Resource: Angles in isosceles triangles
Concept 3: Angles on a straight line
Where do students struggle with this area of angles, why do they struggle, and what can we do about it?
1. Where might students go wrong?
2. DQ1 (question)
DQ1 (image)
3. DQ1 (answer)
4. DQ2 (question)
DQ2 (image)
5. DQ2 (answer)
6. DQ3 (question)
DQ3 (image)
7. DQ3 (answer)
8. DQ4 (question)
DQ4 (image)
9. DQ4 (answer)
10. Angles on a straight line - reflection
11. What can we do - be more careful with language
12. What can we do - examples and non-examples
Resource: angles on a straight line: yes/no?
13. What can we do - practice questions
Resource: angles on a straight line worksheets
14. What can we do - Frayer diagram for retrieval
The angles challenge results!
The results are in... how did you do?
1. Angles challenge results
2. How to get the data
Link: Diagnostic Questions
3. How to use the data
Conclusion
A few thoughts before we say goodbye!
1. Your takeaway
2. Resources
My online courses.mp4
Link: My online courses
Link: Diagnostic Questions
Link: Eedi
Link: Eedi Help website
About Craig Barton
Craig Barton has been involved in teaching maths for 15 years. He was the the TES Maths Adviser for 10 years and is now the Head of Education at Eedi. Craig is the author of the best-selling books “How I wish I’d taught maths” and "Reflect, Expect, Check, Explain", the host of the Mr Barton Maths Podcast, the creator of mrbartonmaths.com, diagnosticquestions.com, variationtheory.com, ssddproblems.com and mathsvenns.com, and Visiting Fellow at the Mathematics Education Centre at the University of Loughborough.