Schoolteacher trainees’ difficulties about the concepts of attribute and measurement

Abstract

BAttribute^and Bmeasurement^are two fundamental concepts in mathematics and physics. Teaching these concepts is essential even in elementary school, but numerous studies have pointed out pupils' difficulties with them. These studies emphasized that pupils must learn about attributes before being taught how to measure these attributes, which can be done through activities involving comparing and sorting. In France, as in numerous Englishspeaking countries, official teaching instructions for the elementary-school years (Grades 1 to 5) recommend this approach. We consider that to be able to teach attributes, teachers themselves must master and differentiate the concepts of attribute and measurement. Indeed, these concepts are part of any teacher's subject matter knowledge, especially of what Ball called Bspecialized content knowledge^, which is needed to effectively teach both attributes and measurement. In this study, we analyze the level of mastery of these concepts among French teacher trainees. Our findings suggest that future teachers do not clearly differentiate these concepts, and that the concept of attribute is the less well understood. We highlight that an erroneous understanding of attribute is extremely prevalent: almost half of our participants think of attribute as a vague, imprecise notion. Finally, we discuss the possible causes of this misconception and its implications for teaching.

Measurement in Primary School Mathematics and Science Textbooks

“…Those authors stressed the importance of establishing measurement consistency and the respective margin of error and analysing possible sources of error in measurements. All the foregoing is discussed in a paper by Passelaigue and Munier [13], who reviewed measurement in the science and mathematics curriculum and the contributions made by research on teaching those two disciplines. Spanish Royal Decree 126/2014 includes the measurement of object mass, volume and density in the primary education natural sciences curriculum.…”

“…The need for tasks geared to perceiving and comparing attributes and using nonstandard units prior to introducing standard measurement, along with activities fostering the use of tools, has been stressed both in research and curricular proposals [13]. Differences have nonetheless been identified with respect to the ages deemed most suitable for introducing those ideas.…”

“…That should be followed in a subsequent stage by instruction in the use of everyday measuring instruments and the introduction of the metric system, which is a goal of both mathematics and science education. In addition, since an estimate of object dimensions often suffices and estimation helps understand measuring processes and can prevent erroneous instrument readings, it should also be taught to even the youngest children [10,13]. Conversely, indirect measurement, relationships between units of measure and operations involving measurements is taught beginning in the fourth year of primary in mathematics classroom, whilst the margin of error associated with measuring instruments is a conceit that should only be addressed in secondary education in both mathematics and science classroom [14,15].…”

Exploring MLD in mathematics education: Ten years of research

“…-the article focused on teachers' knowledge or difficulties (e.g. Passelaigue & Munier, 2015. "Difficulties" appeared in the title: Schoolteacher trainees' difficulties about the concepts of attribute and measurement); -the author(s) used the word 'difficulty', 'difficult' or 'inclusion' in their everyday meaning (e.g.…”

Lesson study with didactical engineering for student teachers in Brazil

“…Connecting mathematical and physical knowledge, Passelaigue and Munier (2015) state: “the simplest way to measure something is to make a direct comparison with a measurement. This method requires choosing the measurement standard [a unit, authors’ addition] that is used for attributes of the same type as the object being measured.…”