«The teaching of measurement concepts is often sequenced from non-standard to standard units (see for example, Outhred & McPhail, 2000).Traditionally ...»
The Effects of Creating Rich Learning Environments for Children to
Jill Cheeseman Andrea McDonough
Monash University Australian Catholic University
Australian Catholic University
This paper reports on a design experiment regarding young children’s concepts of mass
measurement. 119 year one and two children were interviewed using a clinical interview both before and after the teaching period comprising five lessons that offered rich learning experiences regarding concepts of mass. The results of the interviews were that the majority of these Year 1 and 2 children moved from using non-standard units to using standard units and instruments for measuring mass.
The teaching of measurement concepts is often sequenced from non-standard to standard units (see for example, Outhred & McPhail, 2000).Traditionally children explored each attribute informally long before encountering standard units or standard tools for measuring (Clements & Battista, 1986). However, more recent studies have questioned whether this sequence is the best approach (Clements, 1999; Clements & Bright, 2003).
Studies of children’s development in concepts of length for example, found that using standard units better supported children’s development of measurement and that nonstandard units could interfere with this development (Boulton-Lewis, Wilss & Mutch, 1996). Similarly, withholding standard instruments such as rulers until the end of a teaching sequence has also been questioned (Nunes, Light & Mason, 1993). Nunes et al. found that using a ruler supported children’s reasoning about length and improved their performance “clearly profiting from the numerical representation available through the ruler” (p. 46).
McDonough and Sullivan (2011) found that although children moved through a sequence of comparing lengths, unit iteration and use of standard units over the first three years of school, there was a great diversity at each year level and suggested that children could be introduced to standard units of length in the second year of school.
Although the design experiment reported in this paper was concerned with children’s concepts of mass, the results of studies in other areas of measurement such as length are pertinent, particularly as studies regarding mass are scarce. Furthermore, it is important that research advice that children can and should move more quickly to the use of standard units and instruments in measurement of length be tested in context of mass measurement.
This study builds on earlier research (Clarke, Cheeseman, McDonough, & Clarke, 2003). In an earlier paper (Cheeseman, McDonough & Clarke, 2011) we argued that rich experiences involving measuring mass are needed, particularly at the Year 1 level where the data we reported from interviews with 479 students indicated that little progress appeared to have been made over a year. By rich mathematical learning experiences we mean those in which children are offered opportunities to engage in activities which have the potential to lead to conceptual understanding in mathematics, that challenge children to think, and foster the communication of mathematical reasoning.
The earlier paper also emphasised the importance of teachers assessing children’s understandings of mass measurement and structuring learning opportunities to build on and extend those understandings. Having made these recommendations we designed the present study to further investigate the learning impacts on young children of structured opportunities to learn about mass.
Methodology Design and Teaching Experiment The study can be considered design research (Cobb, Confrey, DiSessa, Lehrer & Schauble, 2003). A design experiment was described by Cobb et al. as “engineering particular forms of learning and systematically studying those forms of learning within the context defined by the means of supporting them” (2003, p. 9). This research involved a classroom experiment in which the research team collaborated with a teacher who was a member of the research team to take responsibility for instruction. The research intent was to assess children’s concepts of mass, “engineer” some rich experiences through one week of lessons and then re-assess the children’s understanding of mass.
We chose this methodology to examine the complexity of the classroom; including the tasks and problems the children were asked to solve, the discourse, the participation in the classroom and the materials with which the children were engaged. We acknowledge that design research is a highly interventionist methodology. In this case it drew on our prior research and gave the research team control over specified learning intentions. However, we acknowledge while the central matters are able to be controlled, many of the ancillary elements of classroom conditions cannot.
Content of the Lessons A unit of work on the topic of mass measurement was developed for Year 1 and 2 children. Five one-hour lessons were planned to replace the existing school planning in the area of mass. The lessons were designed to follow typical growth of children’s concepts of measurement identified in the literature (Outhred & McPhail, 2000). Accordingly the lessons began with comparing mass and moved toward quantifying mass using standard units of measure. The essential difference here was the more rapid move toward standard units. The lessons were designed to engage the children in rich experiences including real world applications, problem solving and play-based approaches (Baroody, 2009; Copley, 2006). The following discussion gives some insight into the nature of the tasks.
The first lesson, Party Bag Surprises, focused on comparing and ordering. The children worked in pairs, choosing and placing objects in opaque party bags to create three bags of different masses. The masses were created and ordered by hefting, that is, by holding a bag in each hand and comparing masses. For each set of three bags, another pair of children was challenged to work out the order of the masses by hefting (without being able to see what was inside each bag). Upon the children’s request, balance scales were made available for further comparison of mass. Much discussion occurred during this task. After using informal units of mass and balance scales in the second lesson, the third lesson of the sequence involved children measuring the mass of various envelopes and packages in a “Post Office”. The children used interlocking plastic cubic centimetres, each identified as having a mass of one gram. The cubes were available in sticks of ten that is, as ten gram weights, and as loose single cubes. The children chose a variety of parcels and using a balance scale and the cubes, measured the weight of each parcel and labelled it with the number and “g” for grams (see Figure 1). A discussion followed about surprises the children had regarding the weight of the parcels and issues such as height, shape or size relating to mass were explored. In the following lesson children were offered a range of experiences with objects including fruit and vegetables and packaged foods, and using a selection of scales including balance scales and digital and analogue kitchen scales. During the final lesson children made their own set of weights using playdoh, with the purpose of assisting them to develop mass benchmarks.
Figure 1. Children weighing envelopes and packages using Centicubes.
Pre and Post Interview Data Task-based interviews were used to assess children’s learning before and after the teaching phase of the study. Each child was interviewed twice (see Cheeseman, McDonough & Clarke, 2011) by teachers trained in the use of the protocol. Children proceeded as long as they continued to have success with tasks. Written records were made of each child’s responses for later examination and analysis. Subsequently codes were assigned to the responses to specify the growth point demonstrated by each child.
Coding Analysis Codes were assigned independently by at least two of the authors according to the framework growth point demonstrated by success on the interview tasks. The tasks were designed to assess the milestones in young children’s thinking about the measurement of mass as defined in the framework of growth points developed in the Early Numeracy Research Project (ENRP, Clarke, Cheeseman, Gervasoni, Gronn, Horne, McDonough et al., 2002), shown Table 1. The pre-and post-interview data were analysed using SPSS.
Table 1 Mass Measurement Framework (Clarke et al., 2002)
0. Not apparent No apparent awareness of the attribute of mass and its descriptive language.
1. Awareness of the attribute of mass and use of descriptive language Awareness of the attribute of mass and its descriptive language.
2. Comparing, ordering, & matching with the attribute of mass Compares, orders, & matches objects by mass.
3. Quantifying mass accurately, using units and attending to measurement principles.
Uses uniform units appropriately, assigning number and unit to the measure.
4. Choosing and using standard units for estimating and measuring mass, with accuracy Uses standard units for estimating and measuring mass, with accuracy.
5. Applying knowledge, skills and concepts of mass Can solve a range of problems involving key concepts of mass.
Teacher-researcher Role of the Authors The role of the authors was that of active participant-observers in each classroom. The third author, who is a practising primary school teacher, taught lessons during the teaching experiment.
Observational Data In addition to the quantitative data, observational data were gathered by all authors to provide further insights into young children’s thinking about mass measurement. Notes, photographs and audiotapes were used to document actions, comments and thoughts of children during the lessons.
Examining the data from the original study alongside the present data reveals an interesting distribution of patterns. Table 3 shows the distribution of interview results expressed as percentages. The two sets of results with the most similar patterns are those of the Year 1 students who had been part of the teaching experiment and the Year 2 original students. So it can be seen that after an intensive week of teaching and learning about mass, the Year 1 students had a similar profile of thinking as did Year 2 students from the original (ENRP) study.
A summary of the change in growth point code from the first to the second interview is shown in Table 4. The first and most startling result to examine is the negative growth by one student. This was a student who achieved growth point 5 at the first interview and when he measured 135grams of rice and was asked, “How many more grams of rice would you need to have one kilogram?” he initially answered 965g but quickly self-corrected to 865g.
At the second interview 8 weeks later he was asked the same question as the interview protocol called for students to begin the interview one step before their first error. He calculated the answer as 965g but on the second occasion he did not self-correct.
On reflection the authors believe that having the correct answer to this question as a “gatekeeper” for a growth point code of 5 Applying knowledge, skills and concepts of mass was too stringent a requirement. The reason being the skills required to answer the question were more about the mental computation (1000 – 135) than about measurement knowledge.
One third of the cohort of students remained at the same growth point of the mass framework after one week of teaching and learning. This is hardly surprising as a growth point in the major research project from which the framework originated; the Early Numeracy Research Project (Clarke et al., 2002) found that a growth point typically took a student about a year to achieve. The growth points were designed to be major milestones in children’s mathematical thinking.
Approximately one third (38%) of the students had developed their thinking about mass by one growth point after a week of enriching experiences. And 28% of the students made impressive learning gains of 2, 3 or 4 growth points. The mean was 1.1 growth point gain.
Table 4 Difference between 2nd and 1st Interview Results Change in growth point from Interview 1 to Interview Frequency 2 (in growth points) (n=119) Percent
-1 1 1 To illustrate the growth possible from the first to the second interview, we can examine the case of Andrew, a Year 1 boy. In the first interview, Andrew could heft to compare the mass of items and was able to use the language of heavier and lighter. However, Andrew seemed uncertain about using balance scales and was unable to explain how the scales showed items were heavier or lighter. During the first lesson of the teaching week, Party Bag Surprises (described previously) it was noted that Andrew worked enthusiastically with his partner to discover the difference in mass of two very similar bags. This pair asked to use digital scales so they could “get a number” that would show which was heavier. During the fourth lesson, Andrew was observed persisting for some time to find the mass of one potato using balance scales and a set of mixed weights. After many minutes absorbed in this task, Andrew was able to proudly say that the potato had a mass of 275 grams. In the second interview, it was clear that Andrew had made remarkable growth over the course of the teaching week. He was able to use the balance scales to measure with informal units and could also accurately weigh objects on the balance using standard weights giving the answer in numbers and grams. Andrew demonstrated that he was beginning to understand how to use kitchen scales and could explain how the scale worked. Perhaps of most note was that Andrew, a quiet unassuming student, became one of the most enthusiastic and eager participants during the teaching week.