This is a continuation of last week’s blog giving the results of an application of the discourse structures in BtL to a Science GCSE exam paper:

**Variables**

The crucial idea tested in this exam is the concept of variables.

The work on abstract language in BtL culminates in teaching the concept of variables (from Book 2, chapters 14 and 22; FT, chapters 18 and 19).**Dependent variable:** Teachers’ Notes: *transfer of energy by heating*

Exam: *rate of cooling* (one kind of *transfer of energy*)

**Independent variable:** Teachers’ Notes: *surface area and volume*

Exam:

** Words (general/abstract) Object**

A. (A.PU1.2) **surface area ** beakers, water

B. Case Study 1 ** sizes*, diameter ** beakers, water

C. Case study 2 ** sizes*, surface area** (graph) paper cups, tea

D. Case study 3 ** volumes cm ^{3} ** beakers, water

E. Case study 4 **shape** surface area** (graph) flasks, water

**(Abstract words in bold ** Concrete words underlined)

**Words for independent variable in the exam paper:**

A, C and E give *surface area*, B gives *diameter*, D gives *volumes* (in cubic centimetres). These are precise mathematical terms (= can be measured).

In addition, B and C give* sizes* and E *shapes. *These are common words, ambiguous to a scientist. See Wikipedia below.

**Control variables**

The variables which play a part in the rate of cooling are: dimensions of container (volume, height, “shape”), volume of liquid, timing of measurements, standardization of measurements (hence question on resolution of instruments), ambient temperature? (They form what is called a *system* in BtL.)

In each of the case studies, one of these variables is chosen as the independent variable: in the exam question it is surface area, in Case Study 3 it is volume, in Case study D it is shape. The others are all control variables. Seeing the whole experiment as a system, as in BtL, must be a first step towards understanding what the scientist is doing.

The examinees are asked for only one control variable because to cover them all demands an understanding of many mathematical concepts. Hence the question is a mixture of scientific terms (and concepts) and common everyday ones.

**Provisional frameworks for experiments at school level**

This throws up one of the Science teacher’s difficulties: the knowledge necessary for real science is cumulative, but the student needs to have an idea of how science works before gaining all the mathematical understanding a scientist needs (e.g. for such concepts as *size *and *shape).* This is illustrated by the difficulty students have in learning to use the scientific (i.e. mathematical) word* mass* rather than the common word *weight*. It means sacrificing scientific precision to a mixture of common knowledge and science, which is confusing to everybody. What they can get in school is a provisional framework to be refined later. Would it be helpful to students to understand this?

*Size *and *shape* (Wikipedia)

The word **size** may refer to how big or small something is. In particular:

- Measurement, the process or the result of determining the magnitude of a quantity, such as length or mass, relative to a unit of measurement, such as a meter or a kilogram
- Dimensions, including length, width, height, diameter, perimeter, area, volume

**Shape**- From Wikipedia, the free encyclopedia
- This article is about describing the shape of an object. For common shapes, see list of geometric shapes. For other uses, see Shape (disambiguation).
- The
**shape**(Old English:*gesceap*,*created thing*) of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary – abstracting from location and orientation in space, size, and other properties such as colour, content, and material composition. - Mathematician and statistician David George Kendall writes:
^{[1]} - In this paper ‘shape’ is used in the vulgar sense, and means what one would normally expect it to mean. [...] We here define ‘shape’ informally as ‘all the geometrical information that remains when location, scale
^{[2]}and rotational effects are filtered out from an object.’ - Simple shapes can be described by basic geometry objects such as a set of two or more points, a line, a curve, a plane, a plane figure (e.g. square or circle), or a solid figure (e.g. cube or sphere). Most shapes occurring in the physical world are complex. Some, such as plant structures and coastlines, may be so arbitrary as to defy traditional mathematical description – in which case they may be analyzed by differential geometry, or as fractals.