Put Not Your Trust In Pyramids

Put not your trust in princes.

Psalm 146, KJV

Triangles and pyramids do to teachers what catnip does to cats.

Translation from Lolcat: ‘More triangles, please!’

Put just about any idea in the form of a three-sided polygon and watch teachers adopt it en masse as an article of faith. And, boy, have we as a profession unquestionably and uncritically adopted some stinkers.

What follows is a countdown, from least-worst to worst (in my estimation), of what I would collectively call . . . [PLAYS SINISTER ORGAN NOTES, ACTIVATES VOICE-ECHO] . . . PERFIDIOUS PYRAMIDS!

Number 4: Maslow’s Hierarchy of Needs

Why bring this one up? Firstly, Maslow never put his hierarchy in the form of a pyramid. This implies that all of a student’s ‘Deficiency Needs’ must be met before the ‘Being (growth) Needs’ can be addressed; Maslow was more nuanced in his original writings.

The analogy of psychological needs to vitamins was drawn by Maslow. Like vitamins, each of the needs is individually required, just as having much of one vitamin does not negate the need for other vitamins. All needs should independently contribute to subjective well being.

Tay and Diener 2011

Secondly, the methodology by which Maslow arrived at the characteristics of a ‘self-actualized’ person was by looking at the writings and biographies of a number of people (including Albert Einstein and Mother Theresa) whom he considered to be ‘self-actualized’: this is a qualitative and subjective approach that would seem highly open to personal bias and hard to characterise as ‘scientific’ (McLeod 2018).

Number 3: Bloom’s Taxonomy

As with Maslow, there is little to argue with the intent behind Bloom’s Taxonomy, which was an attempt to classify educational objectives without — repeat, without — arranging them into a formal hierarchy.

Bloom’s Taxonomy is often missapplied in education because the ‘higher’ levels are deemed more desirable than the ‘lower’ levels.

As Sugrue (2002) notes:

It was developed before we understood the cognitive processes involved in learning and performance. The categories or ‘levels’ of Bloom’s taxonomy … are not supported by any research on learning.

And, sadly,

the popular misinterpretation of the taxonomy has led to a multi-generational loss of learning opportunities. It is a triumph of philosophy over science, of populism over rigour, of politics over responsibility.

James Murphy, The False Dichotomy

Number 2: Formula Triangles

The main issue with formula triangles is that they are a replacement for algebra rather than a system or scaffold for supporting students in learning how to manipulate equations.

Koenig (2015) makes some trenchant criticisms of forumula triangles, as does Southall (2016) who argues that they are a form of ‘procedural’ teaching rather than the demonstrably more effective ‘conceptual’ teaching. Conceptual teaching encourages students to understand why a particular technique is used rather than applying it as a ‘magic’ formula. Borij, Radmehr and Font (2019) also have an interesting and nuanced discussion on these types of teaching (in the context of learning calculus).

Workable alternatives to formula triangles are the FIFA and EVERY systems.

But the winner for the educationally worst pyramid or triangle is . . . [DRUM ROLL]

NUMBER 1: The Learning Pyramid

To put it bluntly, there is no research to support the percentage retention rates claimed on any version of this pyramid.

Modern versions of the learning pyramid seem to be based on Edgar Dale’s ‘Cone of Experience’ first published in 1946 in his influential book Audio-Visual Teaching Techniques.

Dale’s Cone of Experience as presented in the 1954 edition (with ‘Television’ added from previous versions). From Lalley and Miller 2007

Dale’s main argument was to encourage

the use of audio-visual materials in teaching – materials that do not depend primarily upon reading to convey their meaning. It is based upon the principle that all teaching can be greatly improved by the use of such materials because they can help make the learning experience memorable…this central idea has, of course, certain limits. We do not mean that sensory materials must be introduced into every teaching situation. Nor do we suggest that teachers scrap all procedures that do not involve a variety of audio-visual methods

Dale 1954 quoted by Lalley and Miller 2007

The peculiarly neat percentage increments in retention rates on the learning pyramid are first found in Treichler (1967). As Letrud and Hernes (2018) note:

Treichler asserted that these numbers came from studies, but he did not say where they could be found. […] A set of learning modalities similar to those distributed by Treichler were at some point fused with a misreading of Edgar Dale’s Cone of experience as a hierarchy of learning modalities, and these early categories were supplemented and partly replaced with categories of presentation modalities like “audiovisual”, “demonstrations”, and “discussion groups”.

The final word is perhaps best left to Lalley and Miller:

The research reviewed here demonstrates that use of each of the methods identified by the pyramid resulted in retention, with none being consistently superior to the others and all being effective in certain contexts. A paramount concern, given conventional wisdom and the research cited, is the effectiveness and importance of reading and direct instruction, which in many ways are undermined by their positions on the pyramid. Reading is not only an effective teaching/learning method, it is also the main foundation for becoming a “life-long learner”


Borji, V., Radmehr, F., & Font, V. (2019). The impact of procedural and conceptual teaching on students’ mathematical performance over time. International Journal of Mathematical Education in Science and Technology, 1-23.

Dale, E. (1954). Audio-visual methods in teaching (2 ed.). New York: The Dryden Press.

Koenig, J. (2015). Why Are Formula Triangles Bad? Education In Chemistry, Royal Society of Chemistry.

Lalley, J., & Miller, R. (2007). The learning pyramid: Does it point teachers in the right direction. Education128(1), 16.

Letrud, K., & Hernes, S. (2018). Excavating the origins of the learning pyramid myths. Cogent Education5(1), 1518638.

McLeod, S. (2018). Maslow’s hierarchy of needs. Simply psychology1, 1-8.

Southall, E. (2016). The formula triangle and other problems with procedural teaching in mathematics. School Science Review97(360), 49-53.

Sugrue, B. Problems with Bloom’s Taxonomy. Presented at the International Society for Performance Improvement Conference 2002

Tay, L., & Diener, E. (2011). Needs and subjective well-being around the world. Journal of personality and social psychology101(2), 354.

Treichler, D. G. (1967). Are you missing the boat in training aids? Film and Audio-Visual Communication, 1(1), 14–16, 28–30,48.

Coe, Wilshaw and Ofsted

[T]he community suffers nothing very terrible if its cobblers are bad and become degenerate and pretentious; but if the Guardians of the laws and state, who alone have the opportunity to bring it good government and prosperity, become a mere sham, then clearly it is completely ruined.

— Plato. The Republic 421a (Penguin Classics) (Kindle Locations 2815-2817). Penguin Books Ltd. Kindle Edition.

I am not sure if I agree with Plato about cobblers and the community. As Benjamin Franklin once pointed out: “For want of a shoe…the kingdom was lost.”

However, I think his statement about the Guardians of the state stands. Equally so with the state-appointed guardians of education: Ofsted.

I think Professor Coe (http://www.bbc.co.uk/news/education-24079951) has done the education world a huge service by pointing out that the Ofsted king has no clothes. However, perhaps in the manner of scrupulous academics everywhere, Professor Coe might prefer a more nuanced “the king probably doesn’t have any clothes”.

Coe pointed out that there is no — repeat, no — valid research supporting the “Ofsted model” of classroom observation being either: (a) a reliable tool for assessing teaching quality or effectiveness when cross-referenced with other measures such as student learning gains; or (b) the observation-feedback process leading to an improvement in teaching quality. (See  http://www.youtube.com/watch?v=_-UyGwYHhGY for the section of his talk on classroom observations and http://t.co/AqY7Xqzknw for a link to his slides.)

I don’t know about anyone else but I am staggered by this. As a working teacher who is just about maintaining a precarious foothold on the treacherous scree of middle management, I always thought my seniors and betters had reams of evidence supporting the stuff they were asking us to do. And if they didn’t, well probably their seniors and betters did.

To hear a respected academic say that classroom observation might be “the next Brain Gym” was shocking.

And the Ofsted response? “Tosh and nonsense,” said Sir Michael Wilshaw.  “I don’t know of any headteacher who doesn’t believe that classroom observation isn’t anything other than a help. The fact that we are an inspectorate and we do make judgements has made a huge amount of difference.” According to the TES (13/9/13 p.8):

He said that new figures released this week, showing a 9 percentage point rise in the proportion of schools judged to be good or outstanding, proved that the watchdog’s tougher inspection regime had “galvanised the system”

This is, to my mind, a textbook example of the logical fallacy known as petito principii or “circular reasoning”. The form of this particular logical fallacy is as follows:

Logical Form:

     Claim X assumes X is true.

     Claim X is therefore, true.

Bennett, Bo (2012-02-21). Logically Fallacious: The Ultimate Collection of Over 300 Logical Fallacies (p. 82). eBookIt.com. Kindle Edition.

Let’s see what Wilshaw said again.

  • The inspectorate’s judgements make a huge amount of [presumably positive] difference.
  • Ofsted judgements show that more schools (9 percentage points!) are good or outstanding.

…therefore Ofsted judgements make a huge amount of positive difference.

Now please note that this does not necessarily mean that the conclusion (that Ofsted helps schools improve) is false, but merely that the argument put forward by the Chief Inspector to support that conclusion is fallacious. And it hopefully goes without saying that a fallacious argument is by definition invalid and must be dropped immediately.

The character Chief Brody in the film Jaws once remarked that they needed “a bigger boat”. The Chief Inspector needs a better argument. And in view of the large amount of taxpayers’ money going to support Ofsted, that new argument should be supplied sooner rather than later. As Professor Coe remarked (somewhat plaintively) in his excellent talk: “Just one would be nice.”

H’mm. More rigour, anyone?