Reflection 12 : A Glimpse of Lesson Study in Fuchun Primary School (23 Nov 2010)

The focus of tonight’s tutorial was on Lesson Study (LS) as a way of improving teaching and learning of mathematics. Dr Yeap illustrated the LS process through how Fuchun Primary carried out their lesson study.

LS is a teaching improvement process that originates in Japanese elementary schools. It is a professional development process designed to help teachers produce quality lesson plans and gain a better understanding of students learning. The process involves a group of teachers working collaboratively as a LS team, who will meet regularly to plan, design, implement, evaluate and refine lessons for a unit of work. To provide a focus and direction to this LS, the teachers select an overarching goal and related research question that they want to explore. This research question then served to guide the teachers in their LS in areas such as, how to foster and improve students’ thinking when they do mathematics. 

While working on LS, teachers work collaboratively to plan detailed lesson, which will be used by one of the teachers to teach in a real classroom with the rest as observers. LS provides teachers with an opportunity to observe a life teaching and learning lesson. It allows teachers to carefully examine students’ learning and understanding process by observing and discussing actual classroom practices.  The team will then come together to discuss their observations of the lesson. Quite often, the group will revise the lesson, and another teacher will implement the revised lesson in a second classroom. The rest of the teachers will take the role of observers and the group will come together again to discuss the observed instruction. Finally, the teachers will produce a report of what their study lessons have taught them, with respect to their research questions.

Dr Yeap emphasised that Lesson Study is a facilitation tool used in Professional Learning Communities and the three big ideas in a PLC are:

(a)    ensuring that students learn

(b)   building a culture of collaboration and

(c)    focusing on students’ learning outcomes.

The four critical questions that are the focal point in a PLC are :

1. What is it we expect students to learn?
2. How will we know when they have learned it?
3. How will we respond when they don’t learn?
4. How will we respond when they already know it?

One of the benefits of LS is that, it ‘forces’ teachers to examine their own practice in depth with regards to student learning and how they can engage their students effectively. In this way teachers are inspired to improve their pedagogical approaches continually as they are actively involved in the process of instructional change and curriculum development. This on-going teacher-led professional development focus on teachers taking the initiative to continuously seek and share learning and then act on what they learn. The goal of their actions is to enhance their effectiveness as professionals so that students benefit. 

Reflection 11 : Achieving Professional Growth (16 November 2010)

The focus of tonight’s tutorial is on professional development of teachers.

Professional development is, “the professional growth a teacher achieves as a result of gaining increased experience and examining his or her teaching systematically” ( Glatthorn, 1995, p.41). As teachers, we need to continually grow professionally in order to be in tune with what is happening around the world. Since the implementation of TLLM, there has been a significant increase in the level of support that teachers are receiving in their professional development. In the PERI’s Report, there is also an emphasis on investing in a quality teaching force with professional development as an on-going process for all teachers to ensure that they have not only the basic teaching skills, but also a good grasp of curriculum content as well as a sound mastery of a variety of pedagogies and assessment practices.

A good education system depends on high quality teachers who constantly seek to improve their practice. In view of this, MOE has introduced various schemes and new initiatives to support and enhance the quality of teachers. New initiatives such as Professional Development Packages, Masters and Doctoral Study Leave and Teachers’ Work Attachment have been well received by teachers. In MOE Work Plan Seminar 2009, Education Minister, Dr Ng Eng Hen stressed the importance of teachers seeing themselves as drivers of their own professionalism, setting up networks of professional learning communities (PLCs), coming together to share and exchange ideas on learning and teaching, engage in research, or simply meet up with colleagues who share common interests (MOE, 2009).

This quest for professional excellence is very much in line with the vision that DGE spoke about teachers wanting to Lead, Care and Inspire. In order for teachers to reach a higher level of professional competence and standing, PLCs was piloted in 50 schools in 2009 and by 2012, all schools will have a network of PLCs.      

PLC is another staff development team approach where teachers come together to work  collaboratively to focus on their learning rather than teaching until it becomes deeply embedded in the culture of the school. Through collaborative learning teachers are encouraged to collectively undertake activities and reflection that will enhance the curriculum and learning tasks for students in order to constantly improve students’ performance. The 3 guiding principles of PLC are:

1.      Ensuring that students learn

2.      A culture of collaboration

3.      A focus on results

Three crucial questions that drive the work of those within a professional learning community are:

• What do we want each student to learn?
• How will we know when each student has learned it?
• How will we respond when a student experiences difficulty in learning?

To consolidate our understanding of the three crucial questions and its application, we were asked to find the sum of all the interior angles in polygons of different shapes and sizes. In this activity, we learnt that in order for the open-ended approach to be effective the anchor-task, which is finding the interior angles of any n-sided polygons, must be rich enough for students to explore all possible ways  of giving a variety of responses. This would include both the anticipated and non-anticipated responses from the students too. Through class discussion and observation, the teacher would be able to gauge levels of mastery among students so that appropriate scaffolding for further teaching for understanding could be carried out. This ‘petalised’ lesson brought out the essence of what Learning More in TLLM is all about:

P -  When deciding on the most appropriate pedagogy, we need to take into consideration students’ readiness levels, their learning style and their existing knowledge. Readiness level refers to students’ “preparedness to work with a prescribed set of knowledge, understanding and skills” (Tomlinson & Edison, 2003). We then use the prior knowledge our students have as a starting point to guide us in our lesson planning. This will enable us to pitch our lessons appropriately so that students understand what we intent to teach them. As a result we will not make the lessons or tasks too easy or too difficult where students are either not challenged or may feel frustrated. It is important that we design appropriate tasks that will stretch our students’ thinking as well as to help them achieve deeper understanding.     

E – We can design meaningful Experience of Learning for our students by:

(a)   teaching for meaning and understanding of ‘big ideas’

In this task, students are to conclude that a polygon can be decomposed to form triangles and using their prior knowledge on angle properties of a triangle they will be able to find the interior angles in the polygon.

(b)   enabling them to learn by constructing knowledge

Students to induce that to find any n-sided polygons, they can get (n - 2) triangles and the sum of interior angles of n-sided polygon is (n - 2) x 180°.   

(c)    allowing time for them to reflect, explore and make connection

Students to be given time to test their assumptions such as, making use of specific angles (90°) and angles at a point (360°) to calculate the interior angles of any n-sided polygons. As they explore on the “What if” students reflect on their mathematical ideas and thinking. As they make refinement to this thinking they will develop greater depth of understanding of the subject. 

T –  Tone of learning is one that is conducive, productive and purposeful. This is made possible when the teacher used language to provide affirmation of the students’ effort. When students feel positive about themselves, their peers, their classmates and teachers, they are motivated and will stay on task. Students will view learning tasks as pleasant and stimulating, hence are effectively engaged.

A – In this particular activity, there is ample opportunity for the teacher to assess students’ learning. The teacher can conduct informal assessment through:

(a)   observing students learning behaviour

(b)   listening to students’ discussion with classmates

(c)    checking their verbal responses

(d)   the level of mastery

       

L – Learning content refers to what students learn. It comprises knowledge, skills and values. Learning content is meaningful and relevant when students have the opportunity to engage in authentic real-world learning and the content is relevant to them.    

S – Learning contents or tasks must be student-centred focusing on students’engagement. When successfully engaged, a student will demonstrate positive attitude as well as having the desire to enhance and increase his or her mastery and understanding of a subject.

Reflection 10 : Monitoring and Evaluating Progress with AfL (9 November 2010)

Our last two tutorials revolved around assessing student learning. Assessment procedures to gauge student learning should be as varied as the teaching strategies used to teach them. Although teachers used tests and evaluation, they should also use informal classroom observation, homework performance, project works, portfolios, journals, and even answers given during oral questioning that might assess a student’s prior knowledge. PERI’s Recommendation emphasised balancing knowledge with teaching of skills and values. Assessment for learning (AfL) has been defined as “the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go and how best to get there”(Marzano, Robert J)

Assesment must go beyond providing grades or scores about student learning. It has to provide rich descriptions of the current state of students’ achievement if it is to support improvement in their learning so that they can do better the next time. This requires teachers communicating with parents and students using qualitative and quantitative feedback supported by a comprehensive report to guide the learner’s action. To support learning, assessments must evolve from being isolated events that take place at certain time of the academic year to one that happens in an ongoing, interconnected series so that patterns in students learning will be revealed. Both students and teachers will be able to gauge not only the students’ current level of achievement, but also how much students’ capabilities have been improved. This serves as a powerful booster for students’ motivation and confidence too.     

In this tutorial, we had the opportunity to use a variety of tools to assist us in carrying out a performance task - finding the height of the pillar on level one. Through collaborative team work, most of us were able to arrive at an answer. Why did Dr Yeap give us such a task?  He used an authentic task to illustrate what performance assessment is about. We learnt that performance assessment, also known as alternative or authentic assessment, is a form of testing that requires students to perform a task rather than select an answer from a ready-made list of multiple choice questions. Tasks used in performance-based assessment include essays, oral presentations, open-ended problems, hands-on problems, real-world simulations and other authentic tasks.        

Dr Yeap observed us at “work” and he occasionally would ask some questions to set us thinking. He took the role of a coach, facilitating our learning. Through this we were also being assessed - checking on how we developed our approaches to the task and  demonstrated what we know. It was followed by reflection on our learning process. I liked the approach Dr Yeap adopted, that is, getting us to reflect on :

(a)    I could have thought of these methods myself

(b)   These methods make sense to me

(c)    These methods do not make sense to me    

We discussed about six methods which all of us felt make sense, and watched a video. Through these we have a better understanding of performance assessment which is not about testing strategies. It actually involves students in the construction of various types of products and as they get involved, they develop the process of problem-solving too.Thus, making learning meaningful. In fact performance assessment measures what students can do with what they know, rather than how much they know. Through performing the task, students get to demonstrate how effectively they can put concepts, skills and information together to a real-world problem.

It is important that students understand how and why they are being assessed too. In this aspect, teachers need to share the learning goals with students to make assessment criteria more transparent. When academic expectations and criteria for assessment are clearly spelt out, it “facilitates learning process as the feedback given is explicit and specific for the learner to take action to improve his learning” (Wiggins, 1998). When teachers have clear expectations of how their students will be assessed, they too will provide consistent feedback to students and monitor their progress along the way. One way of providing clear descriptions of assessment criteria and standards for students’ work is through the use of scoring rubric (Wiggins & McTighe, 2005). When students are aware of the assessment criteria, they will be able to keep track of their own progress.

The class was shown an example of a rubric that has three levels of mastery. There is technically no limit to the number of criteria that can be included in a rubric. However, Dr Yeap stated that he found having three levels are sufficient. The type of rubric used is dependent on the purpose of the assessment and its evaluation. In conclusion, rubrics not only can be designed to formulate standards for levels of accomplishment and used to guide and improve performance it can be used to make these standards clear and explicit to students.                   

Reflection 9 : Area of 5? Is it possible? (26 October 2010)

In this tutorial, we were being “assessed” through a simple activity, Area of Five. Our task was to create quadrilaterals with an area of 5 squares. Is it possible? Yes, it could be done! We were given geoboards, rubber bands and ‘geo-dots’ papers. We manipulated using rubber bands, experimented with and tested out our assumptions. Initially some of us were ‘boxed’ in by our interpretation of quadrilaterals as the usual regular 4-sided figures. When the idea of decomposing a square into 2 triangles is being shared, we begin to see the possibilities of abstractions such as, ‘half of a square’ and ‘take away from the whole’. Probing questions were asked to scaffold the used of subtraction strategy to find other possible ways of making quadrilaterals with area of 5 squares. Soon we began to use the idea of triangles to come up with more ‘sophiscated’ quadrilaterals.

Where is the assessment? As we discussed and experimented with all the different possibilities, we were being assessed. Through our solutions, it could be seen how we process our thinking and whatever prior knowledge we had about quadrilaterals. The strategies that came out naturally from us which were evident in our solutions indicated our knowledge and competence. In order to stretch the learning, scaffolding would then be required to ‘teach’ higher level thinking, thus developing and sharpening students’ meta-cognition. The practice and drill exercise using mental calculation strategies showed how on-going assessment could be used to diagnose and improve students’ learning. Through this and the word problem activities, we could see that mathematics is no longer about computational skills but testing students’ thinking skills as well. Newman’s error analysis procedures gave six reasons as to why a student could not do word problems:

(a)  Reading - a child who could not read a word or symbol

(b)  Comprehension - a child who can read but cannot comprehend the problem

(c)  Knowledge of heuristics/strategies - 

(d)  Transformation - a child who can understand what is read but unable to identify the operation to solve the problem

(e)  Computation difficulty - a child who can identify an appropriate operation but do not know the procedure to carry out the operation accurately

(f)   Use computation for a solution

In the spirit of ‘teach less, learn more’ we need to redefine how workbook exercises are to be ‘dished out’ in class. In other words, we have to provide engaging and meaningful learning experiences so as to help us gauge our students’ understanding, identify their strengths and weaknesses. This allows us to support our students in their learning and help them to become better learners.

How does assessment engaged students then? According to Black and William assessment refers “to all activities, undertaken by teachers and their students in assessing themselves, that provide information to be used as feedback to modify teaching and learning activities.” Through the ‘Area of Five’ we saw how learning could be assessed informally to help students learnt meaningfully. As teachers observed students’ learning behaviours, they would be able to make informed moment-to-moment decisions in the execution of their lessons to maximise learning in the classroom. As they gather and interpret these information, teachers would be able to ask themselves whether their students have learnt or how well they have learnt; whether they have provided input to support students in their learning. In assessment, validity and reliability is an important consideration that teachers need to know. When making assessment, it is important to use as many evaluative measures to ensure that reliability and validity are not compromised.

On-going assessment allows teachers to determine the gaps in students’ learning and bridging those gaps with further instruction or guidance. In the course enabling them to make changes and refinement to their teaching or reinforce concepts taught when they find students are not keeping up with their lessons.  

Assessment is an integral part of the learning process. It should be used diagnostically in relation to the student and is part of teaching! Students are engaged in their learning when they are motivated to learn, demonstrate positive attitudes and show a desire to increase their understanding and mastery of what they learn.  

Reflection 8 : Where is the more when we teach less? ( 19 October 2010 )

This evening’s tutorial focus on the experience of learning:

(a)    Learning by inquiry

(b)   Learning by interacting

(c)    Learning by doing

(d)   Learning in and of the real world

(e)    Learning by reflecting

One of the factors that influence how a child learn is the experience arising from the task assigned by the teacher. In order for students to learn more, they must have the opportunity to engage in learning activities that allow them to distil whatever ideas they have into a big idea. Teaching knowledge is insufficient. Knowledge is only gained and applied when it is meaningful. The ‘tile, structure and circle problems’ allow us to explore with concrete materials, looking for possible patterns to help us start the problem-solving process. As we discuss and talk we formulate strategies that can be used to test our assumption. In the process, we also rely on our logical reasoning to support that thinking, synthesise information that eventually led to the generalisation stage.

The development and improvement of thinking must be systematically approached so that we help our students to develop their meta-cognitive ability. We cannot assume that students can reason, inquire and form concepts without having been taught the necessary thinking skills. We need to plan learning activities that embody the learning of concepts, stretch our students’ thinking so that they acquire a deep understanding of what they learnt. At the same time motivate them to find solutions that can affect their attitudes and beliefs; making sense of what they are learning so as to transfer that learning into a new context; and reflect on what works and what needs improving.

Initially, we may need to scaffold students’ attempts at meta-cognition by modelling the strategies and making their thinking visible. However, students must be given time to explore underlying concepts and to make general connections to other information they possess. They need to be able to reflect upon their learning, persist in their thinking deeply to identify pattern across different contexts, and to arrive at their own conceptual understanding.         

The teachers play a critical role. We have become facilitator of learning rather than the source of information to whom the students look for affirmation Students acquire a deep understanding when we focus on teaching for meaning and understanding of ‘big ideas’ rather than focus on facts and procedures. As teachers we must enable our students to learn actively by constructing knowledge and expanding that experience of learning.      

Reflection 7 : Making Connections ( 12 October 2010 )

My essential take aways from Dr Yeap's tutorial :
What teachers teach is not as important as how teachers teach. 

Teachers have to be sensitive to the differences in students’ readiness to learn and they should plan activities according to students' readiness rather than assume that all students are the same. Teachers who understand how their students learn new things will choose learning activities that allow students to learn most effectively. Practice and drill can be an interesting and fun learning process when it is turned into a game. In‘Salute’, students practice multiplication facts in a fun and non-threatening ways. As the game is played, there is a lot of peer interactions, coaching and self-assessment taking place without students being aware of it. The learning environment is emotionally safe as it is non-evaluative which encourages students to take relevant risks intellectually and in the process found themselves engaged. When students feel positive about themselves and their peers they become motivated and stay on-task.

Students who are actively engaged in interactive activities will be stimulated to seek information that lead them  to problem-solve both independently and collaboratively, such as, ‘Take 1 Take 2’ and ‘O_N_E – 1’ games. These games ‘hook’ students by captivating their attention, challenge their thinking and help them to make sense of learning. The use of questions engage students by challenging their viewpoints and assumptions; provoking and stretching their thinking to a higher level; first by making a conjecture and then proceed to test it out. This is evident in the way Dr Yeap posed questions to help us arrive at the conclusion that the concept of multiples is applied in the game, and in the process helping us to see the relevance and meaning of the game as a learning activity to engage students.    

Most importantly, the daily classroom learning experiences must provide moments of enjoyment for students. Students must views mathematics as a subject of enjoyment and excitement which will provide them with the opportunity for creative work and moment of enlightenment. When ideas are discovered and insights gained, students are spurred to pursue mathematics beyond the classroom.

This is the essence of the PETALS Framework where each dimension addresses a different aspect of learning and teaching, which when put together, will greatly enhance learning.   

Reflection 6 : Exponential Growth

I am glad that my team has completed the assignment and submitted it yesterday. Throughout the e-learning weeks, I have learnt to explore many e-learning platforms and their uses. It was tough at first but I manage to pick up some skills. I am still learning. I can now go online and chat with Bo Bo and Joe. It was fun and exciting learning how to toggle from one platform to the next. My sms skills has improved tremendously too! I am very glad to have such patient, caring and wonderful team-mates. Joe and Bo Bo help me with a lot of all these IT stuff. They are ever ready to help and are very encouraging.

Through our numerous face to face meetings, we not only discuss the how, the what and the why of the e-package, we have fun too. It was stressful for all of us as we have to juggle between work and study. We had to rush from work to our meeting place, present our search and ensure that we were well prepared so that we could answer thought-provoking questions posed by the team. We had to clarify aspects of our findings when members foud it hard to understand the rationales of our proposal. This really depleted our brain juice but nonetheless the "grueling" was an effective way to keep us focus on the key ideas we intend to put forth in our e-package.

We have actually started a professional learning community without reaslisng it! We worked collaboratively on our e-package - we researched, discussed and shared our learning. There was collective team work in the way we shared responsibilities for our leanring. We engaged in conversation on ways of improving our learning, working towards a common goal - the production of our e-package. In the course of our discussion, we actively sough for answers and solutions, learnt to be open to new ideas, like using cmap or mindmap to summarise our learning. Besides working collaboratively as a team, we also  encouraged experimentation as an opportunity to learn, such as using google document and pbworks, etc. As our e-package gradually took its form, we reflected on the action that were taken and evaluated its effectiveness so as to keep improving it. 
           
This learning journey has taught me a valuable lesson, that is, together we learn more than if we were on our own. I can see the power of group diversity and appreciate its dynamics. This experience has reinforced my belief - team learning is a powerful learning platform that teachers need to ride on to promote  professional development so as to grow professionally. Team learning builds upon personal mastery and shared vision. This involves creating a snapshot of what is important to both individuals and the school community. Although individuals are responsible for their own actions, feelings and opinions, it is the common good of the community that guides decision making. As teachers’ capacity increases and they develop a feeling of success, they will better understand that when they ally their strengths and skills they are able to reach goals they could not reach on their own.

My learning has increased exponentially!