EDC243 Children as Mathematic Learners
.docx
keyboard_arrow_up
School
Curtin University *
*We aren’t endorsed by this school
Course
243
Subject
English
Date
Jan 9, 2024
Type
docx
Pages
10
Uploaded by ElderDangerJay30
EDC243 Children as Mathematic Learners
Assessment 1: Report
Curtin University
Introduction This report will analyse and discuss the results of a Place Value Assessment Interview (PVAI) conducted with a Year 5 student (Toni). This report will describe the aspects of place value this student is experiencing difficulties with and look to suggest a series of appropriate teaching activities that could be used to assist this student. This report will then discuss the planning of future interventions for the student to continue past her present stage while building on her previous skills, knowledge and understanding.
Place value (PV) is the basis of our number system, it is the system in which the position of a digit in a number determines its value. Place value understanding develops from a variety of experiences, such as mental computation and counting, usually in base tens to begin with (Reys et al., 2020). The four properties of PV as discussed by Ross (2002) are Additive property; where
the quantity that represents the whole numeral is the sum of the values represented by the individual digits, Positional property; where quantities that represent the individual digits are determined by the positions that they hold in the whole numeral, Base-ten property; in which the values of the positions increase in powers of ten from right to left, and Multiplicative property; where the value of an individual numeral is found by multiplying the value of the digit by the value assigned to its position (Ross, 2002, p. 419). There are set stages of development for PV that align with the First Steps in Mathematics (FSiM) key understandings (KUs) (DoEWA, 2013), these stages help educators to understand a student's progress and mathematical development. To further assess a student's progress through these stages, diagnostic interviews such as a PVAI (Place Value Assessment Interview) are conducted, in which the stages of development structure a sequence of mathematic skills students should be able to achieve unassisted at various points academically. These interviews then help teachers identify misconceptions or spots of difficulty students may be experiencing, so they can then create learning interventions and corrections to ensure students are aligned to the average level of skill for their age group.
Diagnostic interviews are a tool that is underpinned by a constructivist approach to learning, in which the student is asked to actively construct or make their own knowledge based off their own experiences and understandings of the materials taught to them (Elliott et al., 2000, p. 256). Tools such as a PVAI, use Vygotsky’s theory of the Zone of Proximal Development (ZPD) to identify gaps in a student’s knowledge and play on Vygotsky's concept that when a student is in the zone of proximal development for a particular task, providing the appropriate assistance will give the student enough of a boost to achieve the task (Vygotsky, 1978, p. 86). To assist the student through the ZPD teachers are asked to focus on three main components as explored for Toni in this report; the presence of a teacher or someone who has a higher level of skills than the learner, social interactions with a skilled tutor that allow the student to practice and observe their skills (such as a PVAI), and the use of scaffolding or supportive activities to support the student
through the ZPD as explored in this report in the intervention, contingency and future learning sections.
Analysis of the Diagnostic Interview
Through the PVAI conducted, it is clear Toni has several misconceptions and difficulties where correction is required. The following section will identify which questions from this interview she has issues.
Questions 4 and 6 highlighted Toni’s issues with FSiM (DoEWA, 2013) KU2, with failing to be able to correctly look at groups and quantification and has been unable to correctly represent numbers with the material (icy pole sticks) as well as KU6 where she has been unable to correctly use partitioning of numbers by place value. In terms of place value development, here it
is clear Toni sits at stage 2, with a slight development into stage 3, but is not ready to progress (DoEWA, 2013). Here it is identified that Toni is currently at a year 2 level, as she meets the Australian curriculum content descriptor ACMNA031, recognise and represent multiplication as repeated addition, groups, and arrays (ACARA, 2017), which is well below the appropriate skill level for a year 5 student. In question 10, it is shown that Toni is unable to successfully model FSiM KU8, failing to compare and order the numbers themselves. This is particularly clear in the second part of the question where Toni states she is unable to attempt ordering the numbers on a line as the second line starts at ‘39’ and not ‘0’. Here Toni demonstrates she is below a year 2 level in her place value development as she is unable to meet ACMNA027 by failing to order numbers to at least 1000 (ACARA, 2017)
Question 12 is also a problem area for Toni, with her failing to correctly partition three-digit numbers, and therefore is unable to meet FSiM KU6, looking at flexible partitioning by place value. This places Toni at a stage 3 for her place value development and year 3 level according to the ACARA (2017) content descriptors, as she currently is unable to meet year 4 level ACMNA073, applying place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACARA, 2017). It can be identified that Toni is at a year 2 level, as she is able to identify ACMNA028 as she has use partitioning to
group 1000 in hundreds, tens, and ones to facilitate more efficient counting, and split the three-
digit number into its base-ten properties. Question 13 demonstrates Toni’s inability to use multiplicative properties within place value. Here she has demonstrated in her answer that she is an additive thinker (Reys et al., 2020). She has failed to meet KU4 and KU5 of FSiM, and has shown a misconception with the term ‘times bigger’ and having interpreted that as addition and not a multiplication phrasing. Toni has been unbale to meet stage 5 of her place value development as her misconceptions around additive versus multiplicative properties requires correction. Due to this misconception, this means Toni’s
skill level is at a year 2, aligning with ACMNA031 (ACARA, 2017).
Through the answering of questions 14 and 15, it is identified that Toni has achieved up to level 2 of the FSiM development stages aligning with FSiM KU2 in being able to write the 'ten group' as the basis for building numbers beyond single digits and is working on progressing to level three. It is clear Toni is an additive thinker (Reys et al., 2020) and she has not yet mastered the skill of being able to use horizontal patterns to recognise the ‘second group’ of numbers in a 100-
10-1 pattern. In this question we can see that Toni is unable to meet the requirements of reading and writing four-digit numbers and therefore does not meet ACMNA052, recognising, modelling, and ordering numbers to at least 10,000, which is a year 3 level skill, and fails to successfully master FSiM KU4, with being unable to recognise the pattern in which number are said and KU5, with being able to write numbers correctly. Intervention and Contingencies To correct Toni’s inability to successfully model question 10 and KU8, failing to compare and order the numbers themselves, the following task can be used to scaffold and correct her misconception that place value in a line and ordering numbers is not dependent on the entire sequence from 0 – maximum number being there, for example, where she states she is unable to attempt ordering the numbers on a line as the second line starts at ‘39’ and not ‘0’. An intervention activity to correct this would be the ‘three in a line’ game (see Figure 1), as it looks at number ordering and place value This activity could be amended slightly so the line did not start with ‘0’ to assist Toni with being able to successfully identify where on a line the number
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help