professional development guide for 21 century … · 21st century competencies in the mathematics...

21st Century Competencies in the Mathematics Classroom

Restricted – for Reference by Staff of MOE Schools 1

Professional Development Guide

for

21st Century Competencies in the Mathematics Classroom Video

This video outlines an example of how the 21st Century Competencies, specifically

Critical and Inventive Thinking (CIT), enhanced by Self-Directed Learning (SDL)

processes, are deliberately developed in a Primary 3 Mathematics classroom. (A

brief description of 21CC, as well as SDL and Collaborative Learning (CoL), is found

in Annex A. The unit plan can be found in Annex B.) As you watch the video, you will

notice the following strategies being used by the teacher:

1. Use of thinking routine: Think-Puzzle-Explore

Generates students’ interest

Allows students to take ownership of their learning

Develops students’ information literacy skills

2. Use of 5Ws and 1H

Guides students to formulate questions

3. Use of ICT

Facilitates the gathering of different viewpoints

4. Use of thinking routine: “What makes you say that?”

Prompts students to:

i. Describe what they see or know

ii. Construct explanations

iii. Exercise evidence-based reasoning

5. Use of thinking routine: “I used to think… Now I think…”

Facilitates reflection on students’ thinking process

Helps students recognise cause-and-effect relationships

Encourages students to learn from each other

6. Use of Project Work

Facilitates transfer of learning in a new and authentic situation

7. Use of Presentation

Develops communication skills

Assesses students’ understanding



As you watch the video, take note of…

How the strategies presented in the

video apply to your classroom

Ideas with which you agree or

disagree

Share your thoughts and ideas with your discussion group.

After watching the video once or a few times…

What connections do you draw

between the teaching & learning

practices seen in the video and your

own teaching experience or what

you already know?

What new ideas did you get that

extended or broadened your

thinking in new directions?

What challenges or puzzles have

come up in your mind, which were

triggered by the ideas and

strategies presented?

Adapted from Thinking Routine “Connect-extend-challenge” Source: Ritchhart, R., Church, M., Morrison, K. (2011). Making Thinking Visible. San Francisco, CA:

Jossey-Bass.

Questions for discussion within your group:

Strategies to Develop Emerging 21CC through Mathematics Lessons

1. The emerging 21CC that the teacher aims to develop through the lesson is

Critical and Inventive Thinking (CIT).

a. What are some strategies you have used to develop CIT in your

current classroom teaching & learning practice?



b. How do / can you create a classroom environment that is rich in

thinking?

c. How do / can you as a teacher model critical thinking when facilitating

classroom discussions?

Use of ICT

2. ICT was used in this lesson to collect data from the class to generate bar

graphs.

a. (for Mathematics teachers) Which ICT tool/s would you choose to

teach this topic and why?

3. ICT was also used to capture students’ thinking and reflections, thus making

students’ thinking visible.

a. What ICT tool(s) would you use to document students’ thinking? What

are the advantages of doing so?

b. How would you use the reflections written by students to inform you

about their learning?

Discipline-Specific Skills

4. One of the objectives of this lesson was for students to learn the following

discipline-specific skills:

Read scales Read and interpret bar graphs in both horizontal and vertical forms Complete a bar graph from given data Solve problems using information presented in bar graphs Read, interpret and present information in written, graphical, diagrammatic

and tabular forms (in the first lesson, students will only be able to interpret information)

Use mathematical language to communicate mathematical statements accurately and logically

a. Do you have an alternative way of teaching these skills while

developing 21CC in your students?

b. To what extent, in your view, are the featured lesson activities effective

in achieving the intended objective of helping students develop the

abovementioned skills?



Next Steps

You may wish to use the following learning plan to plan your next course of action

after this PD session.

Questions Responses Next Course of Action (If Applicable)

1. What is the immediate next step you need to take?

2. What further information do you need?

3. What specific actions will you take to get there?

4. What specific support will you need?

5. What evidence will you look for to demonstrate growth and progress in your teaching?


Jointly developed by CPO, CPDD, ETD and CHIJ St. Joseph’s Convent (2012) A-1

Annex A

Introduction to 21st Century Competencies (21CC), Self- Directed Learning (SDL) and Collaborative Learning (CoL) To help our students thrive in a fast-changing world, MOE has identified

competencies that have become increasingly important in the globalised world of the

21st century. These competencies will enable students to tap into rich opportunities

present in the emerging digital age.

Figure 1 – Framework for 21st Century Competencies and student outcomes

As reflected in figure 1, the framework is anchored in core values that shape the

beliefs, attitudes and actions of a person. The middle ring signifies the Social and

Emotional (SE) competencies which are necessary for students to recognise and

manage their emotions, develop care and concern for others, make responsible

decisions, establish positive relationships, as well as to handle challenging situations

effectively. The outer ring of the framework represents the emerging 21CC

necessary for the globalised world we live in. These are: Civic Literacy, Global

Awareness and Cross-Cultural Skills; Critical and Inventive Thinking; and Information

and Communication Skills.

SDL and CoL can be seen as learning processes that students engage in, through

which they acquire essential 21st Century Competencies that lead to the

realisation of the desired outcomes of education. In SDL, the student exerts effort to

gain knowledge and skills, both for personal development and to explore ways to

contribute to his community. Students engaged in self-directed learning will exercise

ownership of, as well as manage, monitor and extend their learning. In CoL, students

are engaged in social interactions that help them achieve better understanding about

a concept or phenomenon, or to co-create a piece of knowledge or solution to a

problem. Students who learn collaboratively will engage in effective group processes

and be committed to both individual and group accountability for their learning.

Figures 2 and 3 provide detailed explanations of the constructs of SDL and CoL.



Figure 2 – Constructs of SDL



Figure 3 – Constructs of CoL

Both SDL and CoL enable students to acquire skills and competencies to learn

and work effectively in the 21st century knowledge-based environment. ICT provides

many new possibilities to facilitate SDL/CoL, e.g. students could systematically

search for information and expert help, and use various online tools to synthesise

and represent the data (SDL), or engage in a shared task that is constructed and

maintained by and for the group (CoL).


Jointly developed by CPO, CPDD, ETD and St. Andrew’s Junior School (2012) B-1

Annex B

Math Lesson Plan

Subject: Mathematics Level: Primary 3 Topic: Bar Graphs Duration: 60 minutes per lesson

Desired Results

(for the entire unit)

Established Goals (from syllabus documents):

Acquire the necessary mathematical concepts and skills for everyday life, and for continuous learning in mathematics and related disciplines.

Develop the necessary process skills for the acquisition and application of mathematical concepts and skills.

Enduring understanding

Students will understand that…

Bar graphs are used to represent data and information in everyday life.

Essential Questions:

Why do we use graphs to represent a set of data? How does a set data get represented in graphs?

Knowledge

Students will know that….

Graphs are used to represent a set of data or information.

Graphs can be presented in both horizontal and vertical forms.

Skills

At the end of the lesson unit, students will be able to…

(Subject-specific skills)

Read scales Read and interpret bar graphs in both horizontal and vertical forms. Create a representation of a bar graph from given data Solve problems using information presented in bar graphs



Read, interpret and present information in written, graphical, diagrammatic and tabular forms (in the first lesson, students will only be able to interpret information)

Use mathematical language to communicate mathematical statements accurately and logically

(Critical and Inventive Thinking Skills) in particular to this lesson

Explain his or her reasoning and decisions explicitly and precisely using mathematical language to demonstrate understanding of the concept of representation using bar graph (CIT 2.1a)

Sequence Resources /

Materials

Evidence of 21CC

(CIT)

Evidence of SDL

Lesson 1

(15 min)

Teacher begins lesson by introducing students to the concept of bar

graphs by priming students’ prior concept of graphs when they learned

picture graphs

Discuss the concept of ‘graphs’ as a class

- Link picture graph (learnt in P2) to bar graph - Real world examples (ACE pedagogy) - “Why are we studying graphs?” - “Why are graphs important?” “How are graphs useful?” “What are




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

the advantages of graphs?” - “Where are you likely to see graphs?” (this could be something for

students to find out over the week)

SDL: Ownership of Learning

(10 – 15 min)

Teacher asks students to do a T-P-E (Think-Puzzle-Explore) (SDL:

Ownership of Learning) on Google Form and tabulates the students’

responses using word cloud. Students are to fill in the ‘T’, ‘P’ and ‘E’

parts.

T: “What do you think you know about graphs?”

P: The teacher may need to give an example of a question first – e.g. “I

wonder what graphs are used for?” Then from there, the students would

know what ‘puzzling’ questions are and can generate their own. The

teacher also needs to clarify what ‘puzzle’ means, to ensure everyone is

on the same page

“What questions or puzzles do you have?” Push the thinking further by

inviting the students to wonder more about the topic with additional

questions, such as “What would be interesting to investigate and learn

more about? What are you wondering about? Are there things about this

topic about which you are curious?”

Thinking routine: T-P-

E (Think Puzzle

Explore): Setting the

stage for deeper

inquiry




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

E: “How can we explore these puzzles?” Ask students to identify a puzzle

from the list, or at times teacher may want to highlight a couple of puzzles

for the class, and ask students how the class or an individual might

explore those puzzles further. “Whom might you ask? Where could you

get further information? How would you frame your search key words?

What sources would be worth tapping? How could you find ways to

answer your own puzzles?”

Teacher gathers a few responses from students and shares them with

class. Teacher takes notes of students’ questions and refers to them and

addresses them as he teaches the lesson on bar graph.

Lesson 2

(30 min)

“How many of you have made a decision today?” or “How many of

you have made a decision in the past week?”

Teacher to ask students this question to get them thinking about what

decision making is, and help them realise that they make decisions every

day. This will set the stage for the lesson as they will be engaged in skilful

decision making.

Task:

From 21CC Standards

and Benchmarks for

P3:

The student is able to

explain his/her

reasoning and




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

Teacher to prompt students to recall previous lesson on graphs and

set the context for the task to be completed on this lesson on bar

graph

“Your class is going to organize a games day for all primary 3 students in

the school. However, we can only play 3 games on that day. How can

you, as organisers, decide which 3 games to play? How can you find out?

You will need to explain your decision to your teacher and convince him

that the 3 games you chose should be played on games day, explaining

the criteria (CIT2.1a) you used to decide on the choice of game ”

Class discussion( teacher facilitates this)

Understanding the task

Teacher asks the class what they understand of the task. “What do you

think we are supposed to do here?” Teacher guides the class in the

understanding of the task - students have to make a decision on the

choice of games for games day.

Teacher facilitates a class discussion for coming up with a few criteria for

helping to choose the games to be organised. “What kinds of criteria

1:1 computing

Show the challenge

statement on

powerpoint slide or

write it on the board.

decisions. (CIT2.1a)




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

should we use to decide on the choice of games?”

(Some examples: most students play this game (popularity), availability

of facilities/ equipment for the game, safety, time, team/individual games

etc.)

Deciding on the method for collecting information/ data

Teacher asks the class what kinds of data the class would need to gather.

“What kind of information do we need to help us decide?”

Teacher asks for suggestions on the methods for collecting the data

needed.

Students to submit their suggestions on Google Form which will be

collated and presented on Wordle.

Teacher acknowledges all the suggestions in a word cloud (“We have

many ideas from the class such as…”) and discusses the feasibility of the

more popular suggestions (words in bigger font) with the class.

“Do you think this is a good way of collecting the information we need?”

Google Form

Wordle

(www.wordle.net)

http://www.wordle.net/




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

“How else could we have done it?”

The teacher looks at the ideas on the interactive whiteboard and

facilitates the class in evaluating the effectiveness of each idea with the

help of a graphic organiser (Appendix B1). Teacher may wish to

explain the concept of pro/con to the class at this point. Teacher

proceeds to participate in weighing the effectiveness of the ideas and

coming to a decision whether to accept or reject the ideas. For each

pro/con, teacher puts a +/- sign against the idea. (CIT2.1a)

“What do you think of idea A? Why? Why not?” (Listing pros and cons)

“Student X, what do you think of idea B?”

“Student Y, how about idea C?” and etc.

“Looking at all the + and – signs next to the ideas, which do you think is

the best way for collecting the information we need?”

Data collection

Teacher suggests gathering students’ favourite sports by collecting data




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

using an online tool (Google form) as opposed to pen/paper survey.

(Teacher may elicit some advantages of using online survey from the

class. Some reasons are: online survey saves time, students can do this

at their own time, online survey platforms also collates the results for you)

-> possible teachable moment for CIT 2.1.

At this point, the class would have decided on conducting an online

survey. The teacher will suggest to the class to conduct the survey with

their class first.

Teacher will ask the class to brainstorm on the survey question. E.g.

“What is your favourite sport?” Teacher suggests using Google Form for

gathering of data.

Teacher will set up the survey on his computer that is projected to the

class screen. Since the class makes use of 1:1 computing, once the

Google Form is completed, the students will go in and enter their

responses. The class will come together and watch the teacher collate the

responses into the table (this is auto-generated by Google).

Google Form




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

Teacher pauses at this stage (table should be shown on the screen)

and asks a few questions. Showing the table on the screen provides the

advantage of enabling the students to see the process of collating

responses and the teacher can easily point to the students the top three

choices.

“What do you think of this table?”

“Is it easy to read?”

“Is there another way of presenting this information such that it is easier to

read?”

Students respond to the questions. Teacher probes to make visible the

thinking behind students’ responses by asking “Why?” or “Can you

explain why presenting the information this way is better than the other

way?”] (CIT2.1a)

Teacher may want to point out to the students that while there are many

ways to represent the data, they need to take into account time efficiency

in representing the data at hand.

At this point, the class would have agreed to present the information in

the form of a graph or a visual diagram. (Note: It is important at this

point to point out that while graphs and visual diagrams serve the function




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

well here, other forms of visual representation will serve the function

better for other contexts. This is so as not to discount the generation of

alternative ideas by other students.)

Teacher clicks on the option to churn a bar graph from the table of results.

The screen should show the bar graph now. Teacher asks questions.

“How is this different from a table?” (visual diagram as opposed to

numbers)

“How do you read this graph?”

“We will be learning about bar graphs today”

Sound reasoning CIT

2.1a

Students are

encouraged to reason

and explore the best

way to represent the

information on the

screen

(15 min)

Students discuss the graph with their group members

Task:

From the graph, focus on the information you need to determine the three

sports to organise for sports day. (You may look at the most popular

sport, least popular sport, comparison between 2 sports, etc.) Decide, as

Sound reasoning CIT

2.1a

Thinking routine:

“What makes you say

that” (Interpretation

with justification)

ICT-facilitated CoL,




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

a group, which 3 sports to organise for games day and explain your

decision. Type out your discussion in the online forum or blog.

Teacher gives out a graphic organiser (Appendix B2) for students to fill in

based on the criteria they choose to decide on the sports to organise.

Question for students to ask one another in their groups:

“What makes you say that?”

Questions have to be clearer so as to frame the context for students to

interpret the graph

10 minutes

Teacher to call one or two groups to share their discussion and decision

with the class.

- Some questions for teacher to keep in mind. Did anyone not respond to the survey? (concept of total number)

- Which is the least popular sport? How about the most popular sport? What makes you say that?

- How many more students prefer Sport A to Sport B? What makes you say that?

- Which three sports should we organize for games day? - What makes you say that? (Asking questions so as to make

students’ thinking visible) (CIT2.1a) Teacher may wish to pose

SDL.




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

criteria to help students in their decision making process (e.g. availability of infrastructure, time constraint and popularity of the sport), in so doing capitalising on the possible teaching moment that the most popular decision may not always be the best decision for everyone

- What do you notice about the bars itself? (equal width) If students ask why they are equal, we’ll leave that as an ‘E (Explore)’ question at the end of the lesson.

- Is there another way of presenting the bar graph? (horizontal and vertical or in 3D)

(10 min)

Reflection

Teacher asks students to pair up (think-pair-share) and do some

reflection (thinking about thinking) questions:

“Was this a good way of gathering the information (data) we needed to

organise games day?”

“Is the information gathered good enough for us to determine which 3

sports we should organise for games day?”

“What else may we need to find out?

“Was the information accurate?”

Students are to enter their reflections as well as what they have learned




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

about graphs today in the online platform, Wall Wisher.

During this time, teacher should look through all the Ps (T-P-E) and group

them into a few categories and ask the class to choose which of these

areas they are interested to find out more about on their own at the end of

the class.

Conclusion

Teacher concludes the lesson by going through students’ reflections on

Wall Wisher to help students distil learning points. Teacher also highlights

some of the ‘P’ and ‘E’ from students’ T-P-E and poses thinking questions

for students think further. Teacher also directs students to resources to

allow them to explore the topic further.

Lesson 3: Project work (Lesson Extension) (SDL: Self-managed

learning)

(10 min)

Teacher to divide students into groups of 4. In their groups, the students

are to design a survey form using Google Form, to better understand their

classmates’ opinions on the groups’ chosen issues. Teacher to present

some examples of possible questions that students can work on, such as:

How do students travel from home to school every day?

What subjects do students like the best?

What are the popular hobbies of students?

SDL: Self-managed

learning.




Materials

Evidence of 21CC

(CIT)

Evidence of SDL

(10 min)

Students are to design survey forms in their group using Google Form to

try out this data collection process with their classmates. Teacher to guide

them by providing the benchmark of good survey questions (encapsulated

by the “CFC” guidelines – Clear, Focused, Concise). The whole class

should be surveyed.

(10min)

Students to complete the respective surveys in 10 minutes before

resuming group discussion.

(30 min)

After the 10 minutes have lapsed, in their groups, they are supposed to

present the information they have collected in the form of bar graphs and

present their findings to the whole class.

Teacher and classmates to provide feedback on the group presentations.



APPENDIX B1

DECISION MAKING GRAPHIC ORGANISER 1

CONS OPTIONS

PROS

- - - + + +



APPENDIX B2

DECISION MAKING GRAPHIC ORGANISER 2

OPTIONS

CRITERIA FOR CHOICE OF SPORTS

SAFETY POPULARITY AVAILABILITY OF

EQUIPMENT

STUDENTS’

READINESS LEVEL



Suggested Assessment Tasks

Suggested Performance Task(s):

Authentic task

(Individual work) Students present the food items they have in their

home refrigerator in the forms of a table and a bar graph. They

should include a short write-up of their work as well as, either:

Give suggestions for adding or removing food items to ensure healthy diet for their family. or

Describe a dish that can be prepared with the food item in the refrigerator and explain the cultural significance (e.g. Chinese, Malay, Indian, Hokkien, Teochew, Thai, etc.) of the dish. (CGC 3 – Displays socio-cultural awareness and sensitivity)

Teacher may ask students to present their work to the class as an

oral presentation, or put up their work on an online platform where

Other Evidence of Learning:

(E.g. quizzes, tests, academic prompts, observations, homework,

journals, etc.)

Collaborative group work: Every student is to think of a question that they would like to know about their classmates. In the next lesson, they will form groups of 4-5 and share their questions with one another and think of presenting their information as a bar graph. They should consult their teacher with their ideas. They will then gather the data from the rest of the class and present their findings as a bar graph. Some examples of the questions are, “Do you have a pet? Y/N” and “How many siblings do you have?” There can be either Yes/No answers or answers with varied responses. The groups will have to discuss with their teacher how best to present the information.

Homework (formative) “How are graphs relevant to us?” Share some examples with the class next week, with interpretation of the graphs. (ICS 2.1a)



classmates can also view and enter their comments.

Rubrics: Teacher should design appropriate set of rubrics to assess

the task. Rubrics should be given and explained to the students

before they begin their work. If presentation is part of the work, oral

presentation skills could be one of the assessment criteria.

Homework (formative) “Where are we more likely to find graphs in everyday life?” Share some examples with the class next week and explain the use of the graph. (ICS 2.1a)

Journals (formative) Students write down what they have learned about graphs (K-W-L) in the online journal

Self-assessment

Worksheets

professional development guide for 21 century … · 21st century competencies in the mathematics...

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