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!