PSYCHOMETRIC STUDIO

A Marvellous Info-Graphic From The US Data Quality Campaign

A marvellous info-graphic from the US Data Quality Campaign describing teachers and schools who use assessment data to target student learning. (I used this info-graphic a lot in my previous role at UNSW Global.)

Ms. Bullen's Data Rich Year:

http://dataqualitycampaign.org/resource/infographic-ms-bullens-data-rich-year/

Coupled with real-time assessment data and learning platforms we can assist teachers to track their student’s data along their individual learning pathway.

Real-Time Assessment Data

Another great video from Edutopia - This organisation is continuing its mission to highlight and document best practices in Education! 

Here is a video on how to use real-time assessment data. It shows: (1) how surveys are used to target student needs, (2) how pre-assessments are used to target teaching for students in a class, and (3) how a learning platform is introduced to track student grades and goals.

This effort individualises student learning goals, maximises student learning and teaching time, and allows for evidenced based instructional decision making. This "sets the student up" for greater mastery of skills and improvement in educational outcomes.

https://www.youtube.com/watch?v=ZB8LHwqRcaU&feature=iv&src_vid=8vDuGyToRoQ&annotation_id=channel%3A54f7f9c2-0000-2c69-961d-001a113ce40a

Great stuff! Four Stars.

Dr. Rick Stiggins A Manifesto For The Use Of “Assessment As Learning”.

Dr. Rick Stiggins in his blog has outlined a manifesto for the use of “assessment as learning”. His seven principles provide a challenge to all of us, as practitioners in the assessment field.

SOURCE: http://www.rickstiggins.com/2014/03/04/7-principles-of-student-centered-classroom-assessment/

Dr. Stiggins’ seven principles are:

Principle 1 - Assessments require clear thinking and effective communication.

Principle 2 - Classroom assessment is the key.

Principle 3 - Students are assessment users.

Principle 4 - Clear and appropriate targets are essential.

Principle 5 - High quality assessment is a must.

Principle 6 - Understand the personal implications.

Principle 7 - Assessment as teaching and learning. (Assessments and instruction can be one and the same, if and when we want them to be.)

Dr. Stiggins provides some outstanding quotes which mark out important signposts for the assessment as learning journey.

“Students are the most important users of assessment results. Students are consumers of assessment results – right from the time students arrive at school, they look at their teachers for evidence of success.”

“High quality assessment is essential in all assessment contacts. Sound assessments must satisfy five specific quality standards: 1) clear targets; 2) focused purpose; 3) proper method; 4) sound sampling; and 5) accurate assessment free of bias and distortion.”

“Assessment is an interpersonal activity. The principle has two important dimensions. The first has to do with the important reality of life in classrooms: Students are people and teachers are people, too, and sometimes we like each other and sometimes we don’t. Second, assessment is very complex in that it virtually always is accompanied by personal anecdotes and personal consequences.”

How To Use Assessment Data For Teachers

A great article summarising the uses of assessment data by teachers by Rebecca Alber at Edutopia.

See:

https://www.edutopia.org/blog/using-student-data-inform-teaching-rebecca-alber

The article highlights the importance of collecting multiple sources of data (e.g. assignments, class observations, student record file, classroom tests, formal tests) and use this information to tailor teaching and learning to the individual student. I call this triangulation of assessment data / results.

Here are some great quotes which capture the philosophy of the approach:

“From a child's cumulative files you can sometimes see a dramatic grade change somewhere along the road during their school journey. Perhaps prior to eighth grade, the child was an A student, then from there, D's and F's.”

“A disclaimer: just as one grade does not determine all that a student is or isn't, nor does one test score. Use standardized test data results along with other data (i.e. in-class assignments, observations) when making instructional decisions.”

“First, you can share the testing results with students individually and set some obtainable, realistic goals for them to work towards before the next test.”

“How about those ace students who didn't do so well on the standardized test? Possibly a nervous test-taker? Or it could simply be low motivation (since many students never hear hide nor hair about their standardized test results from previous years). Prior to the test, a brief pep talk or quick review of test strategies for lowering anxiety could be all that she or he needs.”

Going Deeper Into The Pearson Product Moment Correlation - Thanks To W.M. 'Bill' O'Neil

I love checking statistical concepts in older text books. For me, these older books seem better able to explain the underlying concepts.

One such book is A guide to elementary statistics in psychology by the great W.M. 'Bill' O'Neil of Sydney University.

I consulted this work as I was developing my worksheets yesterday and I came upon this insight.

In relation to his working and derivation of the Pearson Product Moment Correlation, Bill O'Neil made this important insight clear to me -

"It may be seen from this equation that the product-moment correlation is the arithmetic mean of the product standard deviation measures of the instances."

An instance in Bill O'Neil's terminology is "Any case for which a frequency or a measure has been or could be obtained by observation." For example, a frequency count or a test score.

(This is an example of depthing your knowledge base. Not just staying on the surface level of some topic but going deeper and deeper. In this way we can say that we are always learning.)

Revision Exercise Worksheet Pearson Product Moment Correlation By Hand

I needed to undertake a quick revision of the concepts underpinning correlation for a new project. I have learnt that the best way to do this is to go through the calculations by hand in EXCEL. This revision process also allows you to depth your current understandings of the concept.

Attached are my worksheets for this revision exercise which compared the EXCEL statistical calculation (from the Analysis ToolPack) with common formulae for the Pearson Product Moment Correlation.

I used standard data for Drugs A and B. The formulae are added to the worksheets and the “hand calculations” using EXCEL are broken down into their separate steps to create the final result. For ease of checking, the EXCEL versions of the formulae are broken down into the Numerator and the Denominator.

Download Revision Exercise Worksheet Pearson Product Moment Correlation By Hand

Online references used:

http://psc.dss.ucdavis.edu/sommerb/sommerdemo/correlation/hand/pearson_hand.htm

http://onlinestatbook.com/2/describing_bivariate_data/calculation.html

http://davidmlane.com/hyperstat/A51911.html

What Is An Identity In Statistics?

What is an Identity in Statistics?

I read the term identity being used in a Stats review paper – “Their identities are plain” the authors said. Now that is an interesting term. But what does it mean exactly?

So I consulted Wolfram MathWorld. And found that:

“An identity function assigns every real number to the same real number. It is identical to the identity map."

"The identity function is trivially idempotent.”

SOURCE: http://mathworld.wolfram.com/IdentityFunction.html

Here is the picture which makes things even clearer.

 

OK. Now what does idempotent mean?

“A unary operation (or function) is idempotent if, whenever it is applied twice to any value, it gives the same result as if it were applied once; i.e., ƒ(ƒ(x)) ≡ ƒ(x). For example, the absolute value function, where abs(abs(x)) ≡ abs(x), is idempotent.”

SOURCE: https://en.wikipedia.org/wiki/Idempotence

OK. So now what does unary mean?

“In mathematics, a unary operation is an operation with only one operand, i.e. a single input. An example is the function f : A → A, where A is a set. The function f is a unary operation on A.”

SOURCE: https://en.wikipedia.org/wiki/Unary_operation

OK. Now I get it. Many thanks to Wolfram MathWorld and Wikipedia.

I now have a better idea what the term identity means in statistics!

A Useful Graphic Summarising The Paper By Marks (2016) In The Australian

Further to my blog post on the recent paper by Marks (2016) …

See http://nicholasmarosszeky.typepad.com/my-blog/2017/02/data-insight-marks-2016-prior-achievement-and-naplan-subscales.html

The Australian published an article by Amos Aikman which includes a useful graphic not included in the original paper (see below);

SOURCE: http://www.theaustralian.com.au/national-affairs/education/extra-school-funds-for-poor-a-waste-says-new-research/news-story/c83427eed3a88d8c84370d7933494dff

and a fantastic quote by Gary Marks which can be used as a summary of the paper about measuring SES, and to drive the exploration of the hypothesis in further research work:

“The ability to understand calculus, balance chemical reaction equations, comprehend and make inferences from unseen text or write readable essays is not ­because a student’s father works as a bank manager rather than a teller or because his or her mother has an arts degree rather than a TAFE qualification,”

Dr. Florez Petour Calling Out The Dynamic About International Tests Like PISA

Dr. Florez Petour in an article in the Oxford Magazine calls out the dynamic about international tests like PISA, and how they are used by Education Ministers to impact policy decisions and the behaviour of their Department.

While not agreeing with all the statements the author has made, the article does providing much political cultural insight and food for thought. This is healthy. I especially like the description of the dynamics of policy legitimisation - including externalisation, scandalisation, and the use of audit culture.

Here are some direct quotes:

“Authors like Gillies (2008) and Gür et al. (2012) have highlighted how media, and especially the press, have acquired an important role as governance tools in contexts where neo-liberal ideologies in education are predominant. They become the means for governments to demonstrate that they “are doing it right” or to justify predesigned and unproven reforms on the basis of spurious causal relationships. And numbers derived from assessment systems provide a very efficient way of legitimising policy decisions.”

“One general strategy is externalisation; that is the appeal to an external model or parameter when a local policy is being contested or has a controversial nature (Steiner-Khamsi, 2004). The reference to an external party is used as a means to legitimise the policy and take the responsibility away from the local government, e.g. the use of PISA parameters as a reference to the ‘world class education’ that we are all supposed to aspire to. A second strategy is scandalisation (Steiner-Khamsi, 2003), which refers to the use of assessment results and league tables to generate a feeling of public scandal after which the intended reform will be perceived as a necessity.”

“At local levels accountability systems in relation to assessment data are used as a governance tool. Managerial principles in education, in the context of neo-liberal ideas, require the installation of an audit culture (Suspitsnya, 2010: p572), where systems are developed in order to monitor quality and effectiveness of the “service” provided to “consumers” of education. Through these mechanisms the State can keep its power despite the increased autonomy of schools and their supposedly devolved power by governing from a distance (Ozga et al., 2009).”

The article goes on to give examples of “PISA Shock”, to describe the tyranny of the experts in this area, and the role of the OECD in the marketisation of education.

The article is worth a read. See attached:

Download Florez Petour 2013 The misuses and abuses of assessment data

Top Quotes From William P. Fisher, Jr

William P. Fisher, Jr. is not just an internationally recognised master of Rasch Measurement, he has also made significant research contributions highlighting the importance of developing measurement standards, networks, and traceability in the human sciences.

Here are some top quotes for a recent article about measurement standards:

“Metrological standards that effectively and efficiently facilitate the creation of markets are a part of the rules, roles, and relationships produced by skilled actors in institutions interested in making economic transactions possible. Though the details of both the technical and social networks involved in achieving universal agreement based in metrological standards are well described, practical guidelines for their implementation are still in development.”

“Thus, though it is widely said that ‘we manage what we measure’ measurement is unfortunately often not well understood. Assigning numbers to observations as ratings or costs is often deemed sufficient even when superior, relevant, and accessible scientific methods of instrument calibration and standards development are left unnoticed and unexplored.”

“We need to understand quantitative measurement as having (1) a highly technical scientific, experimental, and laboratory component in which constant amount unit amounts are mapped on number lines, and (2) a network of metrological connections traced between every instrument and the relevant reference standard defining the universally uniform unit of measurement. When the variables of the human sciences are effectively quantified in these terms, then psychological, social, and environmental quality of life will be made available for humanity’s self-empowerment and self-knowledge in ways never before imagined.”

“Crosby (Crosby 1997, p. X) shows that the unity of mathematics with measurement in a quantitative model of the natural world explains why, between 1250 and 1600, Europeans “were able to organize large collections of people and capital and to exploit physical reality for useful knowledge and for power more efficiently than any other people of the time.” It can be reasonably expected that the similar unification of mathematics and measurement in a quantitative model of the psychosocial world also will enable new magnitudes of efficiency and effectiveness to be achieved in caring human relations.”

SOURCE: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2083975

NB: See the original article for the citations used in these quotes.