Slides for Flipped Classroom

Slides for Flipped Classroom : Click here

How to Improve Your Students' Mastery of Math?

If you are a teacher who is finding it hard to engage your students in class, you are not alone. Many teachers in the other schools and generations of teachers before them, have faced the challenge of getting their students interested in this traditionally dry academic subject.

All is not lost. There is light at the end of the tunnel. You can turn those unmotivated students into eager learners. By following the suggested techniques listed below, you just might turn your math class into the most anticipated class in their schedule.

1. Make students’ thinking and learning visible through Web 2.0 tools

With the popularity of the internet and Web 2.0 tools, students today are constantly using online platforms such as facebook and twitter to express themselves and reach out to the world.

By incorporating online discussions and providing opportunities for students to share their learning online, you make learning a more interactive and social process for the students. Most importantly, you begin to communicate in their language and they will respond positively.

2. Spice up the lesson with multimedia.
Include elements of fun in your lesson to break up the monotony in class. You do not have to deliver instruction and content in front of the class all the time. Make your math lesson more interesting by incorporating math games, music, videos and other online activities into your learning activities. By skilfully wrapping these interesting activities around a mathematical concept, you can achieve your lesson objective and yet have fun.

3. Relate learning with authentic real life examples.
Students are constantly exposed to tonnes of information daily. If they are not able to connect the math concept with their lives, they will find it hard to understand and are unable to retain the lesson taught. By showing how math concepts can be applied to real life examples, students begin to see the relevance and will be more likely to remember it.

4. Try flipping your classroom
When you are introducing a new concept, consider creating a short online package with videos to illustrate the concept and a short survey to check their understanding. Encourage students to view these contents prior to class. By analysing the result of the survey, you will know what are the common misconceptions faced by the students before the start of the lesson. You can spend more time addressing these learning gaps and answering students’ questions as they are engage in learning activities that elicit high order thinking skills.

5. Encourage students to create learning artefacts
To help students transfer their learning, you can design some end-of-topic activities that involve students creating a simple math game, composing a song ,creating a video or slideshow to illustrate their understanding. The purpose of these activities is to give students the opportunities to apply their understanding of the concept to create meaningful learning artefacts. Besides conceptual understanding, students will need to apply creativity and high-order thinking skills to communicate their ideas across to their target audience. These are certainly desirable outcomes of learning.

6. Stretch your gifted students.
As a teacher, you have a tendency to spend a more time helping weaker students who do not understand a concept. This will take time away from the gifted students, who would benefit from an additional challenge to stretch their ability. By designing self-directed online math modules that take the mathematical concept to the next level, the gifted students in your class can be actively engaged while you continue to narrow the performance gaps for the rest of the class.

7. Provide additional online resources to aid the weaker students.
In general, some students would need a little bit more time and space to understanding a concept and they would definitely benefit from differentiated instruction methods. To support this group of students without delaying the rest of the class, you can consider assigning the weaker students to review online learning materials such as self-directed online lessons, videos and online assessment as part of their homework.

By incorporating all of the above tips into your math lessons, you will better capture the attention of your students and increase their mastery of math. Give them a try today!

Improving Math with 8 simple steps

Throughout my teaching career, I have many students who are overwhelmed by this fear of math. “Math is hard” and “Math is boring” are common phrases in school. When I was a beginning teacher, getting them interested in the subject is one big challenge. Are they generally weaker then other students? Why are other students able to excel? Is there a secret formula that is waiting to be uncovered? So what does it take to help these students overcome this fear?

Thus I began this journey to look for answers. After interacting with many experienced educators and reading numerous articles, I realised that the main difference between the 2 groups of students is attitude. Students with a positive attitude are always actively looking for solutions and they ask a lot of questions. On the other hand, students who adopt a poor attitude towards learning give up easily when faced with problems and they seldom ask questions.

Learning is all about attitude. Instilling a positive attitude in our students is critical to their developmental success. Having a good attitude makes learning easier. To be able to excel in math. you can start by adopting a positive attitude towards the learning of math.

Below are 8 simple steps to cultivate positive attitude and habits that will help to improve one's skills in solving math problems.

1 – Acquire the concept

First and foremost, we have to develop a strong foundation in the basic mathematical concept. Instead of waiting for instruction, you need to be active in your learning and ask questions to clarify your doubts. With this understanding, we can then proceed to solve more complex problems confidently.

2 – Be familiar with the Mathematical terms

The language of mathematics can be quite daunting to the average students. You are encouraged to write notes to attach meanings to these mathematical terms to gain a better understanding of the mathematical concepts.

3 – Regular practice

Mathematics; at Primary and Secondary level, is a skill-based subject. It is important to practice so that we are familiar with the strategies and patterns of questioning techniques. Make mathematics part of your daily life, look for authentic examples around you (curiosity for learning) and this will increase you aptitude of the subject.

4 - Presentation

When solving math problems, it is advantageous to present the solution in a clear and concise manner. This will help you see the steps in a logical flow and spot any potential mistake quickly.

5 – Check your work

The old saying goes “Practice makes perfect”. I would like to add that if you are not doing it correctly, practice makes the imperfection more glaring instead. To achieve perfection, we need to guidance from mentors and be able to apply the right strategies.

Accuracy means a lot in mathematics. Do make it a habit to check your assignments for accuracy. If you encounter mistakes in your work, take the effort to find out why and correct your work. This would help to eliminate those common mistakes that you often make.

6 – Read widely

To broaden your knowledge in mathematics, you need to read widely beyond the school materials (eg. Math guide). This would help you in sharpening your math skills.

7 – Work with a mentor

As with any other subjects, you would need the help of a mentor (eg. Teacher, Lecturer) , who will be able to explain the concept clearly and guide you in solving more complex problems.

8 – Change your perception

Lastly, if you have a natural dislike for math, you might want to probe deep to uncover the root of the problem. If the cause is the lack of self confidence, you will need to find ways to boost yourself. As discussed earlier, regular practice and engaging a mentor are possible solutions. When you are confident of yourself, you will be able to approach any math problem with ease.

How to excel in Mathematics?

Mathematics is considered to be a rather challenging subject to many students. For the majority in this group,studying mathematics is time consuming and frustrating.


However, there are those who love mathematics, they know that once you are familiar with the patterns in the questioning techniques, solving mathematics problems gives them a sense of satisfaction. Some said that you are either born to do mathematics, or not. I tend to disagree.


To be good in mathematics, you need to have the conceptual understanding, the strategy and the discipline to practice. Think of mathematics to be like a competitive sports like football. Firstly, you need to understand the rules of game. Then you need to have a strategy on how to win in this game. Lastly, you need to practice regularly in order to execute your strategy with precision.


Mathematics is not a passive subject. You can’t just read about it. You need to tackle and solve those problem sums regularly, in order to get real expertise and excel in this subject. Once you understand these principles, you will begin to see the beauty of this subject. As Bertrand Russell, the great philosopher and mathematician,once said, "Mathematics posses not only truth, but also supreme beauty".


Lastly, if you aspire to be at the top of the game, you need to have that passion for learning and desire to excel. Using football as an analogy again, the top footballers are able to achieve success because they have a passion for the sports. They truly believe that they can make a difference in the game. If you have such passion, you are on your way to success. If you are still struggling, fear not. You can always look for a mentor, someone who is able to guide you in your journey to excellence.

Challenging PSLE Math Question 2/2012

24 more girls than boys signed up for a holiday camp. 
3/4 of the girls and 2/3 of the boys turned up for the camp. 
20 did not turn up. 
How many children signed up for the holiday camp?

Challenging PSLE Math Problem with Video Solution

Challenging Math Problem (PSLE) with solution

•88 children took part in a swimming competition.

•1/3 of the boys and 3/7 of the girls wore swimming goggles.

•Altogether 34 children wore swimming goggles.

•How many girls wore swimming goggles on that day?


Solution below:

Role of the Teacher in Mathematical Discourse

Teachers play an important part in orchestrating mathematical discourse in the classroom. In designing math lessons that promote discourse, the following should be considered:

1.    Problematising the content – By turning content into problems, it creates opportunities for students to discuss and present possible solutions. Instead of offering standard solutions, the teacher can facilitate learning by posing questions to elicit and challenge students’ thinking. Through appropriate questioning technique by the teacher, students would be actively engage in clarifying and justifying their ideas, either orally or in writing.

2.    Scaffolding – To support the students, teachers have to decide when to provide information, when to clarify an issue, when to model, when to lead, and when to let a student struggle with a difficulty. When misconceptions are surfaced during their discussion, teachers should seize the opportunity to turn it into a teachable moment to explain a certain concept with more details.

3.    Feedback – Providing timely feedback to students on their performance will enhance their learning. Teachers could also create opportunities for students to provide constructive feedback to their peers. Giving peer critique involves higher order thinking skills such as analysing and evaluating, which are desirable outcomes of education.

4.    Monitoring- During learning activities in the classroom, teachers should monitor students’ participation and decide when and how to encourage each student to participate. It is also a good practice to reflect after the lesson to identify what students have achieved, where they make errors, when they have misconceptions, when they are not engaged - in this way, teaching and learning can be synchronised and powerful.

With students taking more responsibility of learning, teachers would have to consider adjusting their role in the classroom to complement the change in teaching approach. From delivering instruction in the past, teachers have to assume the position of a facilitator, who will provide appropriate scaffolding and feedback to guide the students in the right direction.

What is Mathematical Discourse?

Mathematical discourse is a teaching approach that engages students in discussion about math in a manner that articulate their understanding of concepts. Through the lesson activities, students also sharpen their skills in mathematical reasoning and debate. This approach to teaching mathematics is a more constructivist and student-centered approach that involves teachers asking probing questions; think “Socratic Questioning”, to make student thinking visible by eliciting from them the steps needed to arrive at the solution and why a certain strategy was used. Through strategically designed learning activities, students are given opportunities to critique their own and others’ idea and uncover efficient solutions to mathematical problems. 

The Theory 
Classroom discourse is based on the theory of constructivism, which states that learning happens when the students interact with the environment. Through these interactions, knowledge is created. This is also aligned with the social-cultural views on learning which advocates that learning is a social process whereby students working collaboratively are able to reach new understanding that otherwise could not be achieved by working alone.

Make Thinking Visible Through Flip Classroom Model

What is the flipped classroom?

An innovative teaching model that delivers instructional content outside class through interactive, teacher-created resoruces (eg. Podcast, online digital videos, power-point presentation, etc) and interaction with the content – skill development, practice and related learning activities – is done in class. Moving lectures outside of the classroom allows teachers to spend more 1:1 time with each student. Students have the opportunity to ask questions and work through problems with the guidance of their teachers and the support of their peers - creating a collaborative learning environment.

In a flipped class, instructional activities like explanation and lecture are done at home, while homework activities like math problem sets or writing practice activities are done in class. Thus homework becomes classwork and vice versa.

What are some benefits of this method?

·   Allow teachers to spend more time to faciliate students’ learning

·   Foster stronger student/teacher relationships

·   Offers a way for teachers to share teaching resources with other teachers, students and parents easily

·   Enable students to “rewind” lessons and master topics at their own pace

·   Creates a conducive environment in the classroom that promotes collaborative learning

Engaging Students in Mathematical Discourse

Engaging Students in Mathematical Discourse
by Chris Siew


An effective mathematics programme is more than just concepts and skills. Problem solving is central to mathematics learning. The development of this ability is dependent on five inter-related components, namely Concepts, Skills, Processes, Attitudes and Metacognition(Mathematics Framework, MOE).
This article highlights the notion that mathematics should be taught in a way that mirrors the nature of the discipline (Lampert 1990), instead of practising concepts and skills in isolation. How can teachers design lessons that create opportunities for students to make conjectures and engage in constructive argument about problems in order to discover important mathematical concepts? What are the attitudes and processes that we need to develop in our students to help them understand the essence of what it means to do mathematics?

Designing the Learning Environment
There is no doubt that accuracy is important in mathematics. However, teachers have to communicate to students that understanding concepts and communicating mathematical ideas are more important than just getting the right answers. Promoting mathematical discourse is a strategy to develop students’ understanding and communication skills in mathematics.
Let us start by examining the kind of structures that need to be in place to facilitate discourse in a math class.

1. Setting expectation for learning – The first step in transforming a traditional classroom to one that promotes discourse is to set the right expectation for learning. Students need to understand that their role in the classroom is not just listening to the teacher and waiting for answers. In the new learning environment, they will be exposed to open-ended tasks and they would need to play a more active role to complete the task. The teacher will assume the role of a facilitator in these activities, who will scaffold and point them to the right direction but not necessary show them the correct answers all the time.
2. Establish classroom relationship – There will also be a shift in relationship between students. Learning will become more social and ideas will be exchanged freely. Their peers will no longer be just someone who sits beside them, they will be their learning partner and collaborator to build each other’s knowledge. The relationship between the student and teacher will also be changing. The teachers will not be the only source of information. Instead, they will direct students to various resources to uncover the key learning points of each topic.
3. Establish rules and management system – Teachers have feedback that conducting collaborative learning activities can be quite chaotic; students are noisy and teachers are not in control. The key to good classroom management is to establish clear rules on the dos and don’ts when students are engaged in learning activities. It is also important to put in place a system to manage conflicts that may arise during interaction among students.

Teacher as facilitator
It is a misconception that in this new learning environment, teachers just present the problem and wait for things to happen. Do you think students will be able to discuss, solve the problem and present the solution automatically? Learning does not happen by chance, it happens by design.
In order to achieve participation and conceptual understanding, teachers have to design lessons that provide opportunities for students to:

1. articulate their understanding,
2. engage in peer-critique and
3. build knowledge collaboratively

To make students thinking visible during discussion and promote engagement, teachers could consider two aspects of teacher discourse: cognitive discourse and motivational discourse. (Stein, 2007)
Cognitive discourse refers to things that teacher says to promote conceptual understanding of mathematics by making their thinking visible. The objectives of teacher discourse are to

1. help students make connection,
2. help them learn from mistakes and
3. stress individual accountability

Motivational discourse refers to things that teacher says to promote students’ engagement and addresses the affective domain. Students need an affective support structure in the classroom that makes it a safe environment that allows them to learn through mistakes and take risks.
The objectives of supportive motivational discourse are to:

1. Promote learning

1. Focus on the process of learning
2. Challenging students
3. Viewing errors as constructive
4. Supporting persistence

• Promote positive emotions

1. Using enthusiasm
2. Using humour
3. Reducing anxiety
4. Addressing emotional needs

• Foster peer collaboration 

1. Building collaboration
2. Emphasizing joint goals/shared responsibilities

Discourse Assessment
Teachers need time to develop competency in using mathematics discourse to advance learning in class. To help track the progress as a class goes through this transformation, Hufferd-Ackles, Fuson, and Sherin (2004) created a framework to describe and evaluate the level of mathematics discourse in the classroom. (Refer to table below)

Components	To compare   lessons from Term 1 to Term 4 based on analysis of lesson observation videos
Questioning	Was there a shift from the teacher as the main questioner to students & teacher as questioners?
Explaining mathematical/ science thinking	Did students increasingly explain & articulate their ideas?
Source of mathematical/ science ideas	Was there a shift from the teacher as the source of all math/science ideas to students’ ideas also influencing the direction of the lessons?
Responsibility for learning	Did students increasingly take responsibility for learning and evaluation of others and self?

Adapted from Hufferd-Ackles, Fuson & Sherin (2004)

Four components are examined – questioning, explanation of mathematical thinking, source of mathematical ideas, and responsibility for learning. Teachers can use this framework to assess the discourse level of the whole class. It can also help them identify individual students who are not actively participating in the discussion so that additional scaffold and support can be provided to encourage this group of learners to be more active in class.
Conclusion
Promoting mathematical discourse in the classroom can help to strengthen students’ processes in mathematical reasoning and their skills in communicating mathematical ideas. As students learn to make and test hypothesis, question, and agree and disagree about problems, they are learning the essence of what it means to do mathematics. As teachers, we need to re-examine our practice and re-think how we can use mathematical discourse to better engage our learners.

References

1	Hufferd-Ackles, K., K. Fuson, and M. Sherin. "Describing Levels and Components of a Math-Talk Learning Community". Journal for Research in Mathmatics Education 35 (March 2004) : 81-116
2	Lampert, M. "When the Problem is not the question and the solution is not the answer: Mathematical Knowing and Teaching." American Education Journal 27 (Spring 1990):29-63
3	Stien, C. "Let's Talk, Promoting mathematical discourse in the classroom."Journal: Mathematics Teacher. Issue: November 2007, Volume 101 , No.4