によって WY Lim 10年前.
535
WZ ICT Cop
Understanding percentages is often challenging for students, especially when the base is non-conventional. This can lead to confusion, particularly in word problems involving discounts, GST, and interest.
によって WY Lim 10年前.
535
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ICT for Maths
Use of GSP and Padlet
Easy to replicate figures via GSP
Lesson 2: Circumference Investigation
Lesson 1: Pi
Use ICT to vocalize students' thoughts, hands on learning, enhance visualization skills, ritualize thinking routine
Finding relationships of circles within circles
Versus: ICT (more accurate values)
Traditionally, hands on paper-cutting
Learners' Difficulty
What challenges do students face?
Scaffolding strategies
Aim of activity is to see the relationship between radius and diameter. Next activity is to see the relationship between big and small diameter for circles within circles of varying sizes.
Use a platform to discuss their exploration strategy. Hide the column and find out what they come up with
Metacognition is important
guide them to specific columns
Ask them to seek trends between values in the columns
relationship between circumference of small circle within big circle
Generate multiple cases to see a pattern
Using GSP, understanding value of pie.
PK: Current pedagogy of teaching?
Concerns
Cut and paste, shifting of shapes
cut and paste is more challenging in general
which is more suitable?
Based on last year's PSLE circle question, surprised teachers
Increasing the alternative problem solving methods?
Has to emerge in eventual lesson. Giving them a range of problem solving methods. Draw on affordances of visualization, supported by technology to see the mathematical relationship. Through GSP applet, designed activity to elicit what is/is not the relationship
Yes
Make assessment. To discard existing practices?
Not the case.
GSP
Still in midst of developing the platform
create a context for students to use that tool to justify certain things.
Aim is for students to discover the relationship
Discover relationship and pattern through GSP
Using TPACK to see relationships more efficiently
Without GSP, currently help them see basic shapes/patterns. For more challenging problems, break down the question into smaller portions.
PK: How teachers teach this sort of problems?
Relationship between the radius and the diameter
cut short alot of time on calculation and help with visualization
cultivate alternative way of thinking about such a problem
Using formula and prior knowledge
Concerns: time consuming esp in exam context
CK: Content knowledge not an issue. Concern is students not adopting the most efficient solution.
Proposed solution: 1) part by part 2) short cut
Concerns: time consuming to draw so many figures and manually calculate. GSP enables various diagram and auto calculate. Pupils focus on analysing the data instead of the calculation. Gives more examples in a shorter period of time.
Use GSP to derive shortcut
Able to convert percentage to decimal and vice versa, given any context
exploratory, inductive
Assess their level of understanding. Sift out their misconceptions and addressit accordingly
Instil skill ofgenerating patterns
PCK reasoning: by establishing the r/s and see for themselves that base of percentage is 100, and r/s to decimal, their knowledge and then be transferrable
Use the mathematical conversion platform, guided by Cynthia.
Concept of relationship between decimal and percentage. Vice versa
Use of questioning
Encourage students to justify their thought processes
address miconception through questions
Help students make overt their reasoning
Leverage on ICT tools
Use multiple representation to encourage student discussion
Connecting communication to concepts
Authentic learning
From the point of view of the learner
Encourage student articulation/discussion, reasoning
Potential ICT tools
Excel folder using formulas
Exchange rate
differentiated tasks
Fraction is a pertinent issue among students
Ratio
Relative quantity
Big idea behind Fraction/thinking skills involved/mathematical reasoning
How to link fraction to ratio?
Action needed to help students understand the concept of fraction
Visualization
See equal parts
Reasoning
Consistency of familiar words
Importance of communication
Connection gets disrupted if discourse/instructional words between topics changes. Students may then find it challenging to draw the link moving from topic to topic
Manipulative methods
Inability to relate to real life scenarios/Dissociation with real life
Solution: inter level connectedness between topics.
How to help students understand the link?
Instruction design: guide student through conversation and action to see the link via multiple representation through ICT tools. Importance of teachers' questioning.
Fraction(P5): added dimension- part of the same and different whole. Students find it challenging to grasp this concept
Relate to real life applications
Solution: ratio of syrup and water needed to make drinks.
Eg: exchange rate. Students are not familiar
solution: use more concrete and physical examples (concrete manipulatives). Eg: mass, money
students find it challenging to grasp abstract concept
every fraction is anchored by a whole
students get hands-on experience, kinaesthetic learning
Technology
What is the underlying concept of fraction?
Comparison of 2 or more quantities
equal parts of a whole (fraction/ratio)
quantities are of equal part
Derived from equal division/sharing
Equal parts of a whole
Ratio->fraction->percentages
Related representations
Relevance to real life situations
relationship with other topics. Fractions, percentages. Craft task to relate all 3 topics. Multi representation of ratios
At P4 level, able to leverage on decimal to see the link between ratio and fraction
sketch and geogebra reasoning
Schoology
Use of manipulation
Use of Edmodo
Upload to youtube
Use of geogebra platform
Use of screencast-o-matric to record the process
exposure to various shapes
Measurement specific
Practise their construction skills
Construct what they intend to construct
Developing a platform to discuss each others' thinking process/reflection
especially useful for problems with multiple solutions
Parking the cognitive artifact
Questioning: seeing the part whole relationship
Proportional reasoning
Using comparisons as a form of scaffolding
Presentation videos
P5 HA group: 50% found the answer. P5 LA group: made assumptions that led to obstacles, brainstormed and eventually was able so solve
Implemented with 2 classes in CCK
1 Ha, 1 Ma
Learning through failure
Use specific structure to justify their reasoning
Improve confidence. Enhance logical thinking process. Improve the way they structure their thought processes on paper
Understand their problemsolving process
Why agree/disagree
App to capture their discourse
Verbalise problem solving process in proper mathematical language
Screen Cast Omatic. Allows teachers to select any screen of choice on the laptop. Play, record, over ride. Can publish it out on the website. Similar function to what was suggested
Concerns: platform for students to showcase thought processes?
learning as a class
more vocal students can give constructive feedback
student presentation to class
share ideas and learn from each others' mistakes
to surface misconceptions
What is the anticipated misconceptions?
Qn2: conveniently think of a concept that can best solve the problem. will not check for accuracy based on reasoning
within that group, students may teach each other and get the problem right.
group discussion precedes presentation by one group member to the class
use of ipad app for explanation
IT platform (software) allows recording of students' scribbles, audio and thinking process
Concerns: pen and paper first? Every group given ipad with question embedded. write on ipad and explain. recorded on ipad simultaneously. later link to projector for presentation.
recording can be edited at any point. dont have to start from the beginning
can import it to youtube/email back. look at platform via askNlearn/myCloud so that they can submit their work to us
problem solving process will be recorded
similar problem sums across the 3 classes
3 questions of increasing difficulty
Concerns: time consuming
groups of 3
randomly assigned
Each group 1 question
first question to boost confidence
conducted in 3 classes
HA, MA, LA
Pupil must do a print screen when they do the no line when they do the comparison during the comparison a+b, c-d etc--> have 2 no line
mulitple cases/ qns e.g. case 1: craft qns common cases and misconceptions then come up with generalisation
pupils must show no line / base 10- they must see and the growth of two number lines, no blocks
Pupils must be able to articulate 0.17 + 3 = 17 tenths + 3 ones i.e. 3 ones is bigger than 17tenths.
PCK-maths rationalization with use of blogs
ZPD
TPACK- no line in excel
role of the technology for the idea formation i.e. it has to be articulated
need to document in the blogs- inquiry and no sensing based on the multiple cases/ qnsmaths rationalisation- to help in the deconstruction,
reciprocal teaching
1. no line ( manipulate on online) , 2. base 10 blocks ( pictorial or concrete=the same)
PCK-multiple representation
What is common about this numbers? 0.7 or 0.75 ( pictorial/ % ) to hear the differnet representation.
To be able to tell us the next learning objective
pupils must know the comparison concept
pupils must know place values
pupils must know the literacy part- hundred/hundredths
pupils must know what are the jargons
Anchored by understanding of fundamentals such as number lines etc to diminish fear of progressing forward
Multiple representations
Cubes
Problem based learning
Deconstructive activities
Duplicate CoP (among teachers) in the classroom with students
Process and thinking- focused. Provide a platform for students to represent their thinking and discourse. After which, work with students through constructive feedback.
Inquiry based learning
Teacher scaffolding
Rationale: Able to tap and build on prior knowledge
teacher-directed. room for student practice in differentiated instructions. teacher-modelling, teacher as a facilitator. give cyclical practice opportunities (repeated practice of sense making) to help them understand the concept. modelling and telling-->student practice; teachers as facilitator, teacher gives feedback--> consolidate as a class
Rationale for variation within the numerical system: we need smaller denominations when we use money
leverage on students' prior knowledge (eg: fraction) to help students best relate to the topic of interest
Learning reveals itself through actions. Dependent on experiential learning (prior knowledge).
Which number is bigger, 7/10 or 0.75? in the number line/class blog
Linking to Fraction
making use of the prior knowledge of the mathematical words- concrete, picttorial,e.g. 7 tenths, 7/10, place values
Using a benchmark to trigger students' reasoning (more/less)
Number line
to give them a sense of a quantity
Use concept of fraction as bridge to representation in decimals (parts vs whole; equivalence)
Money
How is it connected to decimals?
Help them understand place values.
Linking money to decimals
How to anchoring of the topic--
Broaden the decimals, approx
Both money and decimal's numeration system includes base 10.
Challenges: form/structure is similar but underlying concept is different.
How to link one to tenths?
Challenges: syllabus order.
use cubes, coins
Hinders their ability to tackle non routine questions
Proposed solution: audio heuristics
Relative value
Twiddler
Online whiteboard space
Teacher explored and find it challenging
Deconstruction shown in their working
2-3 groups used model to solve. Others used percentage
Platform:Mimio (in house platform) Restrictive because one page at a time. Varying handwriting size and also challenging to write with stylus
Compare and contrast their problem solving process
Examine their thought processes as a class
Cyclical approach
Increasing level of difficulty
"OF" implies a derivation from something
Percentage is a system for comparison using the baseline of 100
Use of multiple situations
Case base pedagogy
multiple small scenarios/ iteration of knowledge to help students see patterns (easy-->difficult conversion of bases)
Ability to transfer knowledge exhibits understanding
Understanding terminologies such as discount/GST and relationship to content of maths lesson
Going back to fundamentals: concepts (abstract) embedded in contextualized activities linked to students' experiences
Meaning making of percentages
Repeated practice will potentially lead to improvement
Foundational students
Role play: Shopping with the aim of getting the best discount with a designated amount of money
Assumption: procedural knowledge is not an issue
Word problem using conventional base. Transitional activities: tightly contextualized, highly relevant to students' daily lives/experiences (authentic learning)
Foundation kiids
Subtopic
Lower ability: tackle conceptual understanding
discover relat
students focus on analyzing data rather than calculations
allows you to have various diagrams
How shapes interact through the use of ICT, but at the same time allowing them a platform to also pose questions, craft questions and share their reasoning.
Observation in pupils who are able solve: 1. Ability of pupils to simplify the question. 2. Ability of the pupils to visualize the different shapes
