Arithmetic Skills ,Geometric Skills , Interpretation of graphs and HOT Skills

1. MATHEMATICAL SKILLS

2. ARITHMETIC SKILLS
Arithmetic
 “Mathematics is the queen of
sciences and Arithmetic is the
queen of Mathematics “
 Greek word
 The science of numbers and art
of computing
 Oldest branch of the subject

3. Early Math Skills
Before starting
school, most
children develop
an understanding
of addition and
subtraction
through
everyday
interactions.

4. Key Math Skills for School
• Number Sense (forward and backward)
• Representation (mathematical ideas
using words, pictures, symbols, and
objects )
• Spatial sense (Geometry, ideas of
shape, size, space, position, direction and
movement.)
• Measurement (finding the length,
height, and weight of an object )

5. • Estimation (more, less, bigger,
smaller, more than, less than. )
• Patterns (learn to make predictions,
to understand what comes next, to
make logical connections )
• Problem-solving (using past
knowledge and logical thinking skills to
find an answer )

6. Top 4 Basic Math Skills Students
Should Learn
• Problem solving (to develop
analytical thinking)
• Applied Math (applying math in
everyday situations)
• Estimation and approximation (to
use almost everyday)
• Necessary computational skills

7. Fluency
• Math fluency is defined as the
“ability to recall basic math facts.”
• By enhancing fluency, one can
develop more confidence and less
dependence.

8. Tips for speed and accuracy
• Do speed addition and subtraction tests
( 50 problems in 3 minutes)
• Memorize multiplication tables up
through 15 (extend to 15)
• Recall your multiplication tables for
division
• Simplify calculations into smaller, easier
calculations

9. Fundamental Arithmetic Ideas
• Addition
• Subtraction
• Multiplication
• Division
• Fractions
 Latin word
 ‘break’
• Decimal Fractions
 Simon Stevin,Belgium,1584
 Decimal point by Napier,1617

10. • Ratio
• Proportion
• Percentage
• Simple interest
• Compound interest
• Area
 Square /Rectangle
 Parallelogram
 Triangle
 Cross roads
 Circular roads
 Circle
• Volume
 Cylinder

11. Geometric Skills
Geometry
 Greek word
 ‘earth measurement’
 The science of lines and figures
(or) The science of space and extent
 Deals with the position ,shape
and size of bodies.
 It is the picturized arithmetic /
algebra

12. 3 stages of teaching Geometry
• Practical Stage
 common geometrical concept
• Stage of Reasoning
 to prove theorems and exercises
• Systematic Stage
 acquisition of mastery in reasoning

13. Traits of mathematically able children
 Ability to make and use generalizations often quite
quickly.
 Rapid and sound memorization of mathematical
material.
 Ability to concentrate on mathematics for long
periods
 An instinctive tendency to approach a problem in
different ways
 Ability to detect unstated assumptions in a
problem

14. Graphs
 Graphs are especially useful for presenting
quantitative data.
 A graph is a visual form of data from a table.
 Graphs are ideal for communicating scientific
information.
 A graph can make it easier to analyze and
interpret the information you have collected.

15. Features of a graph
• title
• grid
• horizontal axis or X-axis
• vertical axis or Y-axis

16. Different kinds of graphs
1) Line graphs
 to show how one variable affects another.
 Line graphs are useful in that they show the
relationship between two variables.
2) Bar and column graph
 both used to show categories of data that has
been counted.
 In a column graph, the height of the column
shows the number of individuals.
 In a bar graph, the length of the horizontal bar
represents the number of individuals.

17. 3)Histograms
 Histograms look similar to column graphs but
are different because each column represents a
group of related data.
 The height of the column shows the number of
individuals counted, like a column graph.
4) Pie graphs
 Pie graphs are useful for showing the
percentage composition of various categories that
are unaffected by each other.
 Computer programs can present pie graphs in
many different, interesting shapes

18. 5)Scattergrams
 Scattergrams are graphs that are used to
find patterns in some kinds of data.
 The information about each individual or
test is plotted as a separate point.

19. Choosing a graph type
Each time you need to draw a graph, think
about the different kinds of graphs. Decide
which kind of graph will make your data the
easiest to analyses and interpret.
Sometimes there are several kinds of
graphs that would be suitable.
For example, usually you can use a bar graph, a
column graph or a pie graph to Present the
same kinds of information. A line graph and a
histogram can show the same data.

20. H O T Skills
‘H O T Skills ‘
- Higher Order Thinking Skills

21. History
 Human thinking skills can be classified into two major
groups:
lower order thinking skills (LOTS)
higher order thinking skills (HOTS).
 LOTS have three aspects
remembering
understanding
applying. (the first 3 of Bloom’s taxonomy )
HOTS have three aspects
analyzing
evaluating
creating . (the last 3 of Bloom’s taxonomy )

22. Why teach Higher Order Thinking
Skills(HOTS)?
• “Higher-order thinking skills are valued because
they are believed to better prepare students for
the challenges of adult work and daily life and
advanced academic work. “
- Pogrow
• Higher-order thinking may also help raise
standardized test scores.
• The revised secondary mathematics curriculum
has shifted its emphasis to the fostering of HOTS.

23. Higher Order Thinking Skills
• Higher-order thinking is thinking on a higher
level than memorizing facts or telling
something back to someone exactly the way
that it was told to you.
• HOTS is the highest part in Bloom’s taxonomy
of cognitive domain.

24. Five fundamental HOTS
i. problem solving skills
ii. inquiring skills
iii. reasoning skills
iv. communicating skills
v. conceptualizing skills.

25. 1. Problem solving skills
• According to National Council of Teachers of
Mathematics (NCTM),
“ problem solving is a process of applying
previously acquired knowledge to new and
unfamiliar (or unforeseen) situations.”
• Four phases are ,
- understanding the problem
- devising a plan of solving the problem
- carrying out the plan
- examining the reasonableness of the result
and making evaluation.

26. 2. Inquiring skills
• Inquiring involves discovering or constructing
knowledge through questioning or testing a
hypothesis.
• The essential elements are,
Observation
analysis
summarizing
verification

27. 3. Communicating Skills
• Communication involves receiving and sharing
ideas and can be expressed in the forms of
numbers, symbols, diagrams, graphs, charts,
models and simulations.
• 2 types :
oral and written
• 3 stages :
construct
refine
consolidate

28. 4. Reasoning Skills
• Reasoning is drawing conclusions from
evidence, grounds or assumptions.
• 2 types :
inductive reasoning
deductive reasoning

29. 5. Conceptualizing Skills
• Conceptualizing involves organizing and
reorganizing of knowledge through perceiving
and thinking about particular experiences in
order to abstract patterns and ideas and
generalize from the particular experiences.
• The formation of concepts involves classifying
and abstracting of previous experiences.

30. Three components in HOTS
(1) critical thinking skills
(2) creative thinking skills
(3) systems thinking skills.

31. Nine factors that comprise HOTS
• the use of mathematical concepts
• the use of mathematical principles
• impact predicting
• problem solving
• decision-making
• working in the limits of competence
• trying new things
• divergent thinking
• imaginative thinking.

32. Higher-order thinking helps
• to manipulate information and ideas
• to synthesis, generalize, explain, hypothesis
(or) arrive at some conclusion or
interpretation.
• to solve problems and discover new meanings
and understandings.
• i.e., the teacher is not certain what will be
produced by students.

33. Note the following
1) There is no simple, clear and universally
accepted definition of HOTS.
2) The five HOTS cannot be easily isolated from
each other in mathematical work.
3) HOTS can be taught in isolation from specific
contents, but incorporating them into
content areas seems to be a popular way of
teaching these skills.
4) Computer provides an excellent tool for
teaching HOTS

34. Questions and investigations
• Closed question 6 + 4 = ?
• Open question What numbers could
you add together to make 10?
• Investigation There are chickens and
calves in the farmers paddock. If there are 24
legs altogether, how many of each animal
could there be?

35. HOT and investigation
Example :
Noah counted 24 legs as the animals walked into
the ark.
What types of animals might they have been?

36. Levels of thinking
Learning of rules
and facts
Applying rules and
formulae in
standard situations
Solving specific
problems in novel
situations
Investigating
issues and
problem situations

37. Relationship between HOTS and student
performance in Mathematics
• There is a linear, positive and strong relationship
between HOTS and the GPA of students.
• Students with high level of HOTS are expected to
succeed in their next study in study program of
mathematics education.
• Students who have high HOTS tend to get high
GPA in mathematics instruction.
• Therefore, the value of HOTS can be used as an
indicator in the selection of new students.
• In order to thrive in learning mathematics,
students should have high level of HOTS.

38. To improve student’s HOTS
• To improve student’s HOTS , revise textbooks used in
mathematics learning in primary and secondary
schools.
• The mathematics textbooks used in Indonesia should
promote student’s critical and creative thinking.
• Examples and practice tests provided should be able to
train students to think critically and creatively by using
open-ended test.
• The open-ended test is a test used as an instrument in
this study to measure students' HOTS