All posts by Alex Black

New published peer reviewed research on Effects of Cognitive Acceleration

It was wonderful working with my fellow Authors Sarah Seleznyov, Stuart Twiss, Jeremy Hodgen and Mundher Adhami on this piece of research.

Cognitive Acceleration in Mathematics Education: further evidence of impact

If you are really serious about raising the standards of thinking and achievement in your school please get in touch.

Article link    Full text available


Do you want to play in The Game of Justice?

Climate change, Covid pandemic, Racial reckonings, Economic, Legal and other crises have brought discussions about Justice to the forefront of our public discourse.

Do you want to be one of three contestants to get involved and appear in one of the monthly episodes? Each episode will involve discussing the principles for some aspect of Justice. Each contestant will have brought 2 of their most important principles and 1 principle they strongly disagree with. The Game of Justice will be an hour or so via zoom and with permission of all involved published on youtube.

If you are interested and want to know more message or mail me.

Also for Theory of Knowledge teachers the unit lessons for Socially Constructing a concept of Justice help yourself to


End of decade thanks to Guest blogger and others

During the last four years of the now ending decade, Jaeann Tschiffely has added guest blogs. Many of them are about how her experiences of Let’s Think English and Maths training and application have enriched her teaching life. Thanks Jaeann you have inspried and challenged my thinking in many ways. Also, thanks to Michael Walsh @mikefnw75 and Sarah Seleznyov @sarahseleznyov who she still says are inspirations in her development.

Sarah blogs at

Michael blogs at

The Thinking Teacher Teaches Thinking

Every Lesson is a Vocabulary Lesson

Beyond the Engaging Conversation; Getting Kids to Think

PYP Exhibition and Symbolic Reasoning

“Can I draw?” Read Aloud and Dual Coding to Build Comprehension

Concept maps for IB Biology

Concept maps are a very useful tool for retrieval practice, metacognition and developing deeper connections and elaborate understanding in a subject domain.

A great set of tools can be found at

The software is free, works on many different systems, and can be stored in the cloud so they can be edited and embedded in web pages and exported in many different formats. Concept maps can be linked together to give many levels of detail.


Good understanding of theory can optimise practice

Last September, in Riga, I met several teacher trainers from the teacher training school of the University of Turku in the Rauma campus. We were working together on an Erasmus project called Assessment Companion for Thinking Skills (A.C.T.S). The three partners come from Latvia, Finland and the UK represented by members of the Let’s Think Forum.

The group from Rauma talked about their 3 key goals:

Making student thinking visible

Increasing the culture of question asking

and thus increasing student self-efficacy.

When they are talking about students they actually mean the student teachers they are training and also the school students they teach.

After several discussions, they invited me to come and run some lectures and workshops.

So in preparing for a visit, two experiences really nudged my thinking back to an idea that had been bubbling away under my conscious thinking.

One was a two hour discussion with Michael Shayer about how to deepen science teacher understanding of the pedagogy of cognitive acceleration (CASE). He talked about how teachers should basically undergo a practical and cognitive apprenticeship through their PGCE years and beyond. This would involve them applying the Curriculum Analysis Taxonomy and the 5 pillars of the existing CASE lessons to develop their own lessons to fit their curriculum.

Then a tweet by  @sarahseleznyov “Anyone know a reading about why peer triad lesson observations work?” Reminded me of a paper in Australian Journal of Teacher Education

by Nalan Akkuzu (2014). This applied the theories of Albert Bandura and Locke in the context of teacher education in very interesting ways.

Digging this out suddenly the idea of how Bandura on self-efficacy and the Vygotskian elements of the Let’s Think methodology are just what we need to explore.

I saw that Let’s Think lessons and teacher training sessions already used some of these variables.
The experience our group had in Zürich doing our LTE training of developing our own lesson “Feathers”, based on a short film stimulus, seemed to exemplify all of these experiences and certainly increased all of our self-efficacy. It allowed teachers an opportunity to vicariously experience others modify the way the lesson was delivered in a masterful way. Allowed a large number of conversations which persuaded us all of the importance of managing the cognitive conflicts and their resolutions in ways appropriate to the particular class and time the lesson was being used with.

Akkuzu quoting (Kukanauza de Mazeika, 2001; Wang & Wu, 2008) “Studies have shown that student teachers who receive verbal feedback at a high cognitive level exhibit professional growth through exploring the strengths and weaknesses of their own performance and developing deeper conceptual understanding of their classroom behaviors .”

This use of verbal/social persuasion is a key element of the social construction episodes of Let’s Think lessons where the teacher mediates using their understanding of the Vygotsky concept of Zone of Proximal Development. Here ZPD is understood as a set of characteristics about the readiness of the group in this particular context.

This is where a shared understanding of the theoretical principles of the pedagogy makes it visible in practice and leads to the successful use of experiences as feedback opportunities. A lesson built together by a group of teachers is both a product and a process amenable to the continued uses of the Bandura experiences that will further build efficacy.


Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W. H. Freeman.

Kukanauza de Mazeika, J. M. (2001). Effect of different types of feedback during microteaching sessions on preservice teachers. Doctoral Dissertation, New York University, New York.

Wang, S. & Wu, P. (2008). The role offeedback and self-efficacy on web-based learning: The social cognitive perspective. Computers and Education, 51, 1589-1598.

Using Curriculum Analysis Taxonomy in instructional design for schema development

Adey, P and Shayer M (1994) Really Raising Standards, Routledge, London discussed  the development and success of the often forgotten and misunderstood programme C.A.S.E. The work they did on the Curriculum Analysis Taxonomy allowed for the development of a series of lessons deeply anchored in domain specific vocabulary, experiences and concepts. The instructional design was in modern parlance to reduce extraneous cognitive load, map and match the intrinsic load and use strongly teacher led activities and discussions to make a range of germane loads available. The goal was to activate the emerging thinking schema needed for successful learning into more abstract objectives. Preparing the mind for new learning. This is why many studies have shown the long and far transfer effects.