debbie barker and alison hopper · suggested reading john hancock (2007) yes, but can they solve...
TRANSCRIPT
Rethinking the teaching of Trigonometry at
KS3&4
Debbie Barker and Alison Hopper
A huge thanks to our sponsors
What can we learn from the research about the best way to teach
trigonometry?
Why is transition from Key Stage 2 to 3 important and why is
trigonometry a crunch point for misconceptions?
How are MEI’s new materials addressing these issues?
What can we expect from these materials?
Rethinking the teaching of Trigonometry at
KS3&4
What can we learn from the research?
What can we learn from the research?
Insecure prior learning.
Less-effective teaching
approaches.
Low teacher confidence.
Too fast.
What can we learn from the research?
Insecure prior learning.
Less-effective teaching
approaches.
Low teacher confidence.
Too fast.
1. Make connections.
2. Teach for understanding.
3. Support teachers
4. Take time. Expose
misconceptions.
Where does it start in KS2?
Understanding
decimals
Understanding
calculations
Multiplicative
relationships
Triangles
… and circlesAcross the
maths
curriculum
Where does it start in KS2?
Trig?
Understanding
decimals
Understanding
calculations
Multiplicative
relationships
Triangles
… and circles
12 × 2 = 2412 = 24 ÷ 2
12 =24
2
0.8 > 0.796
24 ÷ 2=1248 ÷ 4 = 1224
2=48
4
Properties and
vocabulary
What does it say in the National Curriculum?
Trig
Understanding
decimals
Understanding
calculations
Multiplicative
relationships
Triangles
… and circles
Solve problems involving
similar shapes where the
scale factor is known or can
be found
Identify the value of each digit
in numbers given to threedecimal places and multiplyand divide numbers by 10,
100 and 1000 giving answers
up to three decimal places
Solve problems involving the
relative sizes of two quantities
where missing values can be
found by using integer
multiplication and division
facts
Solve problems involving addition,
subtraction, multiplication and division
and a combination of these, including
understanding the meaning of the
equals sign
Solve problems involving multiplication
and division, including scaling by simple
fractions and problems involving simple
rates.
Use simple
formulae
Express
missing number
problems
algebraically
A ‘perfect storm’ of misconceptions?
How will students
encounter this?
KS2 Sat’s 2019 Paper 3
How will students
encounter this?
KS2 Sat’s 2019 Paper 3
Solve problems involving the
relative sizes of two
quantities where missing
values can be found by
using integer multiplication
and division facts
KS2 Sat’s 2019 Paper 2
How will students
encounter this?
Express
missing number
problems
algebraically
Pearson EDEXEL Higher Tier P3 2018
Solve problems involving the
relative sizes of two quantities
where missing values can be
found by using integer
multiplication and division facts
90
18 18 18 18 18
B = 54 A = 36
Use simple
formulae
Express
missing number
problems
algebraically
What can we learn from the research?
Insecure prior learning.
Less-effective teaching
approaches.
Low teacher confidence.
Too fast.
1. Make connections.
2. Teach for understanding.
3. Support teachers
4. Take time. Expose
misconceptions.
4. Take time
1. Make connections
2. Teach for understanding
2. Teach for understanding
3. Supporting teachers
3. Supporting teachers
3. Supporting teachers
Suggested reading John Hancock (2007) YES, BUT CAN THEY SOLVE RIGHT-ANGLED TRIANGLES?
Doug French (2004) Teaching and Learning Geometry.
Walsh, Richard, Fitzmaurice, Olivia, O'Donoghue, John (2017) What Subject Matter Knowledge do second-level teachers need to
know to teach trigonometry? An exploration and case study.
NCETM (2019) 3. Multiplicative Reasoning https://www.ncetm.org.uk/resources/53532
Cos Dabiri Fi (2003) Preservice secondary school mathematics teachers’ knowledge of trigonometry : subject matter content
knowledge, pedagogical content knowledge and envisioned pedagogy.
Ozcan Demir (2012) STUDENTS’ CONCEPT DEVELOPMENT AND UNDERSTANDING OF SINE AND COSINE FUNCTIONS. A
New Theoretical and Educational Approach.
Hülya Gür (2009) Trigonometry Learning
What next?
Register at https://mei.org.uk/stay_informed to be kept up to date.
Explore the unit circle at https://bit.ly/IntroUC.
Send your thoughts to us at [email protected] and