Category Archives: General

PYP Exhibition and Symbolic Reasoning

As an international school we offer the International Baccalaureate Primary Years Program. During grade 5 the students participate in “exhibition”, a time when they choose their own topic for inquiry, presentation and action. Our school has chosen to have the students present their Central Idea and Lines of Inquiry through the Arts. During this very hectic 6 week time the teachers still wanted to carve out time for the Let’s Think in English lessons. As it turns out this worked very well.
We chose to use Shaun Tan’s book The Red Tree and the Let’s Think Key Stage 2 lesson “Red”. The reasoning patterns emphasized for this lesson, Narrative Sequence with a strong dose of Symbolic Reasoning, were perfect for bridging to inquiry into a larger concept and then presentation through art.
After asking the students to put illustrations from the book in order, match them to the text they are intended to go with, and explain their choices, their attention is then drawn to the fact that there is at least one red leaf on every page. Students are given time to discover that the red leaf is a symbol and discuss what it symbolizes. They are then told that Shaun Tan has said the he was working on the idea of a book without a story and asked to explore the impact of sequencing on meaning.
Our students connected this author and illustrator’s choices very quickly to their own inquiry into a larger concept and effort to share their understanding of that concept through art. We then were able to create a bridging activity where they took the concept they were working on and created one symbol that could represent the concept. Students created symbols to represent concepts ranging from the quite concrete banana peel to symbolize food waste, to the more symbolic image of eyes representing self-consciousness.
Although the Let’s Think Lessons are stand alone and meant to be about teaching thinking and not subject matter, when you are teaching conceptually as we do in the PYP, there are ample opportunities for bridging and reinforcing the reasoning patterns.

Learn to Think curriculum

In researching programmes that are consistent with Let’s Think pedagogy and have a good evidence base, I was lucky enough to come across this gem.
Philip Adey and Weiping Hu (2011) worked together with other Chinese researchers to test the efficacy of a Learn to think programme.  Full text

Since then I have been in touch with Weiping Hu who organised how I could buy their grade 1 (UK Year 2) to grade 8 (UK Year 9) “Learn to think” curriculum materials.
I will get them translated from Chinese and trial some lessons with primary teachers in our school. I cannot wait to use them.

The curriculum uses the 5 pillars of Let’s Think pedagogy plus  an element called the Thinking ability structure model (TASM) based on Chongde Lin’s (2003) theory of intelligence

This is based upon the development of awareness of various factors e.g  self-regulation, purpose, materials, process, non-cognitive factors, and qualities and outcomes of thinking.

The model has three basic characteristics expressed as a 3 dimensional grid.

The X axis is thinking content, Y axis is thinking method, and Z axis is thinking quality. All of these factors depend on each other, facilitate each other, develop together, and form an integrated system.

Their research with Grade 1, 2 and 3 students in an ordinary provincial primary school showed significant gains for all students. These were especially  huge for, long and far transfer in grade 3  children’s assessments of Mathematics and Chinese.  The d numbers in Table 10. ( Cohen’s d is defined as the difference between means of treatment group and control group divided by a standard deviation for the data). Effect sizes of 0.4 upwards are considered educationally interesting according to John Hattie (2008). So the staggering 1.32 and 1.31 for Chinese and 1.29 for Mathematics 3 years later are effect  sizes so much larger than the original far and long transfer reported by Shayer and Adey (1994) in the early CASE trials.

Could it be that grade 3  (in particular)  and grade 5 to 7 are the ideal windows for Let’s Think style interventions to be really effective? Adey , Hu et. al.(2011 p.550) discuss this possibility.

“It took longer for LTT to improve Grade 1 and Grade 2 students’ academic achievement than it did for Grade 3 students (see Tables 8–10, Figure 4–6). The probable reason is that, on the one hand, the 3rd or 4th grade is the critical period of the development of students’ thinking ability, and the development of thinking ability can improve the academic achievement effectively, but there is a delayed effect; on the other hand, the LTT curriculum of Grade 1 and Grade 2 is more related to students’ daily life, whereas the Grade 3 curriculum is more related to subject knowledge. This result also indicates that the training of thinking method must be combined with subject knowledge in order to improve academic achievement more effectively.”

Adey, P., & Shayer, M. (1994). Really raising standards – cognitive intervention and academic achievement. London: Routledge.

Lin, CD, Hu, WP, Adey, P & Shen, JL 2003, ‘The influence of CASE on scientific creativity‘ RESEARCH IN SCIENCE EDUCATION, vol 33, no. 2, pp. 143 – 162., 10.1023/A:1025078600616

Hattie, John A. (2008). Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement.

Hu, W., Adey, P., Jia, X., Liu, J., Zhang, L., Li, J., Dong, X., (2011)  Effects of a “Learn to Think” intervention programme on primary school students: Effects of “Learn to Think” intervention programme. British Journal of Educational Psychology 81, 531–557. doi:10.1348/2044-8279.002007

Learning to Learn. Learning to Teach.

What makes us grow as Teachers?

The training our group of teachers have received from Michael Walsh of the Let’s Think Forum has been the catalyst for many foundational thoughts and discussions. Mediating the thinking of children has challenged us to mediate our own learning. Subtle changes in what we have seen as the way thinking about the text and immediately related ideas to the text . Also reasoning outside and beyond has been so clearly revealed. Observing other teachers, including Michael, has allowed for a deepening of what team teaching can be. Almost a way to observe yourself is made available. Of course this is only metacognition.

In thinking about the essential role for teacher mediation I found the concept of lifelong learning or as the Lisbon treaty of the EU  calls it “Learning to Learn” totally relevant to my own professional development.
Learning to learn is defined by  Hautamaki et al. “The ability and willingness to adapt to novel tasks, activating one’s commitment to thinking and the perspective of hope by means of maintaining one’s cognitive and affective self-regulation in and of learning action” (Hautamäki et al., 2002, p. 39).

When a moment arrives in a thinking lesson to challenge students to make their reasoning more specific and clear, an opportunity to learn arises. This is how very different minds share the willingness to respond to each other with shared respect. Mediation is more than an isolated technical act. I feel we are all pulled into the need to respond adaptively to the new ways of thinking that are emerging.  In these moments we commit to share a perspective of hope.  The challenge these opportunities presents is a microcosm of a wider commitment. This is also a partaking in the deeply emotional and moral undertaking that lifelong learning is. During some of the observations  feelings arose that made me suddenly realise  that when a thinking lesson is in full flow it is a thing of beauty.

Hautamäki, J., Arinen, P., Eronen, S., Hautamäki, A., Kupianien, S., Lindblom, B., Niemivirta, M., Pakaslahti, L., Rantanen, P. and Scheinin, P. (2002) Assessing Learning-to-Learn: A Framework. Helsinki: Centre for Educational Assessment, Helsinki University / National Board of Education.

Analogies and anomalies as opportunities for mediation

A short film “The hole” is the stimulus for a thinking lesson we have recently used. The reasoning patterns Intention and consequences are the target of the class discussions  launched by this stimulus. In a recent lesson a  grade 5 student put forward the analogy “If the photocopy machine had printed the class mathematics test, what would you do?” As a TOK teacher I jumped in with questions that explored this analogy and in what ways it was the same as the message in the film and how it may be crucially different. I was also tempted to explore more general features of reasoning by analogy with the students. This rich learning moment made me think very hard about the differences and commonalities between direct instruction and mediation. I now have several unanswered questions.

How far should we push  students with questions about their reasoning towards our own understanding of the forms of reasoning ? Should we just take the reasoning patterns students express in as the starting point? How much do we add to these forming notions? Do we stop mediating when we directly and explicitly point out reasoning patterns? Can we successfully move between direct instruction and mediator of thinking?

Beyond the Engaging Conversation; Getting Kids to Think

As teachers we thrive on that really great conversation with a class of students.  It doesn’t matter whether they are 6 or 16 it is fun to see them passionate about a story you’ve read together, a sudden discovery they’ve made in science, or a connection they’ve made in math. It is so rewarding to see them excited when they have learned something new.  It can be a comfortable place for us to sit and bask in the good feeling.  It is also pleasant for the students.  They are engaged, but have we really stretched their thinking. I don’t think the Zone of Proximal Development is a familiar or comfortable place, but rather new and awkward.

Those really great discussions should be a starting point not an end; a crack in their simplistic understanding that needs a teacher to exploit and move toward greater complexity. When they are already engaged, we can use that to ask them to do the next hard thing, to think.  We must mediate;  ask them why, ask them to provide evidence, ask them to explain their thinking, and ask them to take a step back from that really engaging text and look at Reasoning Patterns.  

Michael Walsh, our tutor from Let’s Think in English, has provided us with 5 reasoning patterns to explore with children in discussion of literature:  Classification, Frames of Reference, Symbolic Representation, Intention and Consequences and Narrative Sequencing.  This will not happen organically, but must be planned for and opportunities exploited, by intentioned mediation.

Feuerstein et al.(2006) make it clear that the “mediating agent (the teacher) is guided by intention”  “The central feature which makes an interaction mediational is the mediator has an intention to transcend the immediate needs or concerns of the recipient of mediation by going beyond the here and now, in space and time.”

The interesting thing is, that when I have tried this with students it doesn’t diminish their engagement, instead they transfer that enthusiasm from the interesting story to the new cognitively demanding challenge.  They are actually engaged by the challenge, by pushing through the new and awkward, by engaging with that new way of thinking until it becomes less awkward and becomes their own.

I said in my last post that my mantra question while teaching is “What is my student really learning from the choice I make?”  If I want them to learn to think deeply and complexly I must make the decision that will push us both out of our comfort zone and into that unfamiliar and awkward ZPD.


Feuerstein, al. (2006) Creating and Enhancing Cognitive Modifiability: The Feuerstein Instrumental Enrichment Program

The Thinking Teacher Teaches Thinking

As teachers we make literally hundreds of decisions every day. From the mundane “Can I go to the bathroom?” to the more complex “What do I need to teach next and how?” And even the mundane count when you think of it from the child’s point of view. They learn much about themselves from our decisions.
Something is always being learned whether we want it to be or not. Frank Smith in The Book of learning and Forgetting says, “The problem in school is not that many students aren’t learning but what they are learning – They learn to be non-readers or that they are non-spellers or that they can’t do math.” It was only when I moved to Switzerland that I realized that at some point in my life I had learned that learning a second language is hard. This is something that the Swiss don’t learn and I can never forget, even though I wasn’t asked to memorize it.
When we don’t let students struggle and fail before they succeed, they learn that we don’t believe they are capable and they certainly don’t learn how to learn. When we give too much praise at the wrong time they learn not to think, but to find the “right answer”, and sometimes they learn not to trust or value our opinion because they know they did not give their best. They learn to be compliant rather than creative when we do not trust them to learn.
Early in my career my principal, Norm Sam, gave me The Book of Learning and Forgetting by Frank Smith. This book caused me to reflect and come up with a question that I ask myself continuously as I make those hundreds of decisions every day, “What will my student really be learning from this choice or that?” Not what I am teaching or what do I think I am teaching, but what is he really learning from me?
As thinking teachers what are the question you ask that guide your decision making?

Relational reasoning

Michael Walsh, our Let’s Think in English tutor from King’s College London sent us an article to read in preparation for our next training. Relational thinking and relational reasoning: harnessing the power of patterning  by  Patricia A Alexander
The article explores the foundational, measureable, variable and teachable nature of relational reasoning. This is my visual attempt to make sense of it and link it to my understanding of Let’s Think methodology.

Thinking about Finland and testing times.

The world needs young people as its future citizens to be good thinkers more than ever. These concerns led me to look at some International comparisons. As part of out Lets Think research project we wanted to find out the cognitive development level of all our grade 5 and 6 students. We used a test based on the  original interviews of Jean Piaget. These were developed by Philip Adey and Michael Shayer at Kings College London.  It is  a group interactive test called Volume and Heaviness. There is a huge literature showing the spread of development from concrete to formal reasoning using such testing instruments. Formal reasoning is necessary to think about complex problems where many variables are interacting. Like say….. immigration!!.

In evaluating our results I came across Examples of data that show how thinking levels declined in the UK between 1976 and 2003. Also the distribution of thinking levels in representative US schools was measured in 2011.

Highlights are:

That the average 11 year old in the UK  in  thinking level down to that of a 8 or 9 year old over 27 years.

The second study (2011) shows 15 per cent of US school graduates were capable of formal abstract thought .

Whereas 19 percent of Finnish 14 year olds had already reached this level. This would seem to account for their outstanding performance in PISA tests.

Is the common factor that US and UK school systems have been dominated by , standardised testing, competition and accountability through league tables? Or is it like the joke about the high rates of teenage pregnancy in the UK and US  being caused by the common factor of speaking English. Do the Math!!


Every Lesson is a Vocabulary Lesson

I have come to realize that every lesson we teach is a vocabulary lesson. When students struggle with the meaning of key words or command terms in a task, it can derail the key objective in a lesson or result in an inappropriate assessment of the students’ knowledge. This was made evident again in two recent lessons, one English Literature and the other math.
In a math lesson where the main objective was double digit multiplication, the problem given to develop the students understanding was one of area. It soon became apparent that many students were confusing perimeter and area despite having worked with the concepts the previous day. Had the students been given time to construct a definition for area together and differentiate area from perimeter, they would have had the necessary tools to keep their table group from getting lost in the vocabulary.
In the English lesson the students were asked what they could infer or deduce about the characters, from the text. Before the reading began the students were given a few minutes together in table groups to talk about the words infer and deduce, and how they differ from the word know. The groups then shared their ideas and as a class came to an understanding of the two key command terms. It took less than five minutes for the class to come to a socially constructed common understanding that gave them what they needed to keep their group working on the real task of the lesson.
As a teacher it is easy to assume that students have a common understanding of the vocabulary they have been taught and that they understand the task they are asked to do. Often when you begin to analyze errors and find where students go wrong, you will find vocabulary is at the root. Giving the students time to socially construct the meaning of words and play around with them, even after an initial understanding, will broaden their ability to use language and participate in the content.