Download Document

Empowerment
O the process of unleashing the full potential
uCan fuel thinking to empower students too!
of students for them
(a) to achieve and grow, and
Chua Boon Liang
NIE, NTU
Mathematics Teacher Conference 2016, Singapore
(b) to take on greater responsibility in their
learning.
1
Mathematics Teacher Conference 2016, Singapore
Empowerment
2
Empowerment
O The students as the “empoweree”
O the aim is to develop students to become
O The teachers as the “empowerer”
self-directed, independent , and
confident learners
--- key 21st Century Competencies
O Within a nurturing learning environment
How can teachers then empower students?
Mathematics Teacher Conference 2016, Singapore
3
Mathematics Teacher Conference 2016, Singapore
4
Empowerment
Illustration
O Topic: Expansion and Factorisation
O place greater emphasis on students
developing critical thinking, problem solving
and metacognitive abilities, and
O Aim: develop instructional tasks that
promote mathematical reasoning and
justification to empower students
O build character attributes such as curiosity,
courage and perseverance
(To empower, be empowered, by Yeap, 2005)
Mathematics Teacher Conference 2016, Singapore
O When planning a lesson, take into account
some good practices of effective
mathematics teachers.
5
Mathematics Teacher Conference 2016, Singapore
6
A framework for Planning Instruction
SG Maths syllabus
O Expansion and Factorisation
Level
1E
2E
Analyse Learners
Content
(a) Expand a product of a monomial and an algebraic
expression: e.g., 3(x + 2), –a(x + 2y) [1NA, 2NT]
(b) Factorise algebraic expressions where the terms contain
common factors [2NA, 3NT]
Conduct
Topic/Unit
Analysis
(a) Expand a product of binomials [2NA, 3NT]
(b) Factorise quadratic expressions [2NA, 3NT]
(c) Factorise linear expression of the form ax + bx + kay + kby
[3NA]
Establish
Learning
Objectives
Design
Instructional
Tasks
Reflect/Revise
Instruction and
Instructional
Tasks
Implement
Instruction
[Adapted from Reiser & Dick (1996)]
Mathematics Teacher Conference 2016, Singapore
7
Mathematics Teacher Conference 2016, Singapore
8
Analyse Learners
Topic / Unit Analysis
O Personalities, motivation, interests, language proficiency,
Level
attitudes towards learning Mathematics
O Thinking, manner in which info is organised and processed
O Prior knowledge: state factors, simplify algebraic expression
O Mathematical abilities: anyone took Foundation Maths at
PSLE?
Students’ background provides info for
decision making about the development of
instructional tasks, choice of approaches/
strategies and so on.
Mathematics Teacher Conference 2016, Singapore
1E
(a) Expand a product of a monomial and an algebraic expression:
e.g., 3(x + 2), –a(x + 2y) [1NA, 2NT]
(b) Factorise algebraic expressions where the terms contain
common factors [2NA, 3NT]
2E
(a) Expand a product of binomials [2NA, 3NT]
(b) Factorise quadratic expressions [2NA, 3NT]
(c) Factorise linear expression of the form ax + bx + kay + kby [3NA]
What are the key concepts and skills to develop?
Be familiar with the entire topic/unit even when you are teaching
only a particular level.
9
Topic / Unit Analysis
Mathematics Teacher Conference 2016, Singapore
10
Topic / Unit Analysis
O Skills
O Key concepts
* what method to use for expansion (monomial and
algebraic expression, two binomials), factorisation (with
common factors, quad trinomials, ax + bx + kay + kby)
* how to present the solution
* how to explain algebraic expression (linear,
quadratic), expand, factorise – definitions?
* what examples and non-examples to use
* what modes of representations to use
For you to think about:
* why learn special products (a + b)2, (a – b)2 and
(a + b)(a – b)
* do students have to memorise the three identities?
e.g., how would you explain “expand” to students?
Mathematics Teacher Conference 2016, Singapore
Content
11
Mathematics Teacher Conference 2016, Singapore
12
Design Instructional Tasks
Establish Learning Objectives
Consider:
O Based on the topic/unit analysis, state the
O Teach for conceptual understanding: e.g., use the area model
SIOs to focus on learning
O Inform students at the start of the lesson
Mathematics Teacher Conference 2016, Singapore
to explain expansion of monomial and algebraic expression
[x(x+3)], discuss limitation of the area model when the
expression involves subtraction, suggest using the
multiplication frame to replace the drawing of rectangles
O Build procedural fluency from conceptual understanding
O Make connections among different mathematical ideas: e.g.,
how is expansion of product of two binomials [(x+2)(x+3)]
related to expansion of product of monomial and a binomial
[x(x+3)]?
O Use and connect different mathematical representations: e.g.,
use algetiles to illustrate x(x+3), draw out the model, write
down the answer using mathematical symbols
13
Mathematics Teacher Conference 2016, Singapore
Design Instructional Tasks
Implement Instruction
Consider:
O
facilitate meaningful classroom discourse:
- clear explanation, instructions, engage students in learning,
- synchronise your gestures with your verbal instruction/
explanation,
- provide opportunities for students to discuss and explain the
different methods used to solve a problem
O
ask purposeful questions: e.g., what do you notice about the terms in
the opposite corners (for expansion using the multiplication frame), in
which box do you place the quadratic term (for factorisation using the
multiplication frame).
O
elicit and draw on student thinking , encourage students to think aloud
the strategies they use to solve a problem
O
teach one skill at a time, ensure mastery before moving on to next skill
O
be supportive and encouraging of struggle/failures in learning Maths
1. Arrange the tasks in increasing order of level of
difficulties in terms of content, skills.
2. Offer a few tasks similar to examples for individual
practice
3. Use guided practice: iDo, weDo, uDo (i.e., teacher
demo one example, then guide students to work out
second example (What is the first step we have to
do, what’s next?), followed by individual practice)
Mathematics Teacher Conference 2016, Singapore
14
15
Mathematics Teacher Conference 2016, Singapore
16
Implement Instruction
Revise Instruction / Tasks
O Students should become competent in the
O Are students confused by the teachers’
various mathematical skills,
instructions?
O Why do students make the errors?
O but the practice of such procedural skills
should not be done mindlessly and overemphasised without understanding the
underlying mathematical concepts.
O more engaged learning, emphasise
checking the appropriateness and
reasonableness of answer
Mathematics Teacher Conference 2016, Singapore
17
Thank you
Comments and feedback
are welcome.
To get in touch, please
contact me at
[email protected]
No one cannot do Maths (for less able students)
No one cannot score As for Maths (for more
able students)
Success breeds confidence, and vice versa
Mathematics Teacher Conference 2016, Singapore
19
Mathematics Teacher Conference 2016, Singapore
18