Transcript Mathematics

Mathematics
NISPLAN Day 2
Afternoon Session
"The value of a problem
is not so much coming up with the answer
as in the ideas and attempted ideas it
forces on the would be solver."
I. N. Herstein
“It’s not how
many answers students
know.
It’s how they
behave when they
don’t know that counts.”
Alistair Smith (2003)
Leading Learning
Challenge
How would you do the following questions?
a)
5 – 2.37
a)
2 +3 +5
a)
4 x6
b) 37.6 x 5
a)
4.99 x 16
b) 3 x 5
a)
428 ÷ 6
b) x = √23
a)
25 x 8
b) 320 x 25
1
3
1
2
1
3
3
10
a) 2
+5
3
5
b) 5hrs 37mins – 2hrs 45mins
2
3
b) 7 ÷ 4 x 12
3
4
b) 0.75 x 0.25
Counting on /
back
a)
5 – 2.37
a)
2 +3 +5
a)
1
4
3
1
3
1
2
x6
b) 5hrs 37mins – 2hrs 45mins
2
3
b) 7 ÷ 4 x 12
b) 37.6 x 5
3
3
4
a)
4.99 x 16
b)
a)
428 ÷ 6
b) x = √23
a)
25 x 8
b) 320 x 25
3
10
a) 2
+5
3
5
x5
b) 0.75 x 0.25
Partitioning
Rounding &
adjusting
Mathematical concepts are made up of three components:
Linguistic
Conceptual
Procedural
Mathematical Language
What words do you use?
Sometimes words sound the same but have different meanings
Working in pairs try to list as many
definitions of ‘right’ you can think of.
•Right angle
•Turn right or right-hand side
•Right meaning correct
•Right meaning good or OK
•Right in terms of health
•Right wing or right-handed
•Right meaning deserved
•‘Write’ down using a pen or pencil
What can you do to help a pupil’s understanding?
Be aware of these and
similar words
Consider using a
dictionary of topic or
contextual vocabulary
for your subject
Be alert to pupils who
look confused
Promote a safe
learning environment
where pupils would be
happy to ask the
meaning of words
Pupils, their parents and teachers should be aware that there
can be a number of valid ways to arrive at an answer.
It is important that pupils are given the opportunity to explore and
share different strategies for calculating, and through discussion,
to conclude that some are more efficient than others.
Such sharing of thinking is essential to consolidate
understanding. For all pupils, reflecting on and explaining how a
calculation has been worked out is a powerful way of learning.
The teacher’s role is to encourage thinking, discussion and
explanation in order to foster in pupils a willingness to listen to
the strategies used by their peers, and consequently to evaluate
their own strategies.
What Is
Effective
Questioning?
Questions are planned and related to session objectives.
Questions are mainly open.
Teacher allows ‘wait time’.
Both right and wrong answers are followed up.
Questions are carefully graded in difficulty.
Teacher encourages learners to explain and justify answers.
Teacher allows collaboration before answering.
All participate e.g. using mini-whiteboards.
Learners ask questions too.
To help learners to adopt more active
approaches towards learning
Engage learners in discussing and explaining ideas,
Challenging and teaching one another,
Creating and solving each other's questions
Working collaboratively to share methods and results.
One day the teacher was reading the story
of Chicken Little to her class. She came to the
part where the chicken warns the farmer . “ …
and Chicken Little went up to the farmer and
said, “The sky is falling!”
The teacher then asked the class. “And what do
you think the farmer said?”
One little girl raised her hand and said, I
think he said: “Holy Sh*t a talking chicken!”
The teacher was unable to teach for the next 10
minutes
Multiplication
http://www.teachertube.com/viewVideo.php?video_id=46231
The wall of maths mastery
Mahesh Sharma
Communication
Application
Abstract
Pictorial
Concrete
Intuitive
Linguistic
Conceptual
Procedural
The wall of maths mastery
No layers above so what
supports further building?
Application
Abstract
Pictorial
No solid foundation below so what’s
going to happen?
Developing Cognitive Strategies
Use a great deal of concrete experiences
Ask a considerable number of questions
Concrete
Multiplication
Pictorial Multiplication
20
30
6
600
120
5
25 x 36
150
600
30
150
120
30
900
Algebra … Abstract??
Have you tried Algebra Tiles to
keep the area model going?
Using your Algebra Tiles
Show 3(x + 1) = 3x + 3
Using your Algebra Tiles
Show (x + 2)(x + 3) equals x² + 5x + 6
Procedural
What is eleven hours and thirty minutes take
away four hours and forty-five minutes?
As the number of minutes to be subtracted is bigger. (You have to
subtract 45 mins which is bigger than 30 mins)
Convert both times into minutes
11 hours 30 minutes is 11 x 60 + 30 = 690 minutes
4 hours 45 minutes is 4 x 60 + 45 = 285 minutes
Subtracting them gives
690 - 285 = 405 minutes
To change this into hours divide by 60
405 ÷ 60 = 6
with 45 left over
The answer is 6 hours and 45 minutes.
26
Procedural
What is eleven hours and thirty minutes take
away four hours and forty-five minutes?
- 15 mins
6.45
- 30 mins
7.00
- 4 hrs
7.30
11.30
27
http://nlvm.usu.edu/en/nav/vlibrary.html