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EDMA310/360 Mathematics: Learning and Teaching Mathematics 2, 2013 – Assignment 1 – Template 1 of 3

Rational Number Assessment

[Justine Le Griffon S00112649]

Australian Catholic University

Teacher report on your student’s Rational Number Knowledge and any

misconceptions (200 words)

Using a circle model, the student identified what fraction of the whole was one quarter, however

was unable to identify one sixth demonstrating a misconception about the relative size of a part to the

whole. Using set models, the student understood the whole to be a set of objects and the subsets of the

whole to make up fractional parts by referring to a collection of dots as comprising a single entity.

When presented with 18 dots of which 12 were shaded the student recognized that 12/18 dots were

shaded and used multiplication facts to identify another fraction being 4/6. He identified a value on a

number line less than one, however, when presented with a value more than one he neglected the value

of the numerator and instead pointed to the value of the denominator. When asked to locate 6/3 he

pointed to 3 and did not recognize that the fraction represented two wholes. Using a simple story

problem, the student could equally share three pizzas between five girls by partitioning each pizza into

five equal parts and distributing one piece of pizza at a time until equally shared demonstrating an

understanding about the fractional parts of a whole. He identified a decimal on a number line using the

counting on method. When comparing two decimals he chose the value containing more decimal places

as being larger demonstrating limited understanding of the place value system of decimals. When

multiplying and dividing values less than one by values more than one, the student demonstrated the

misconception that when multiplying values the result will increase and when dividing values the result

will decrease indicating a lack of understanding about decimals.

EDMA310/360 Mathematics: Learning and Teaching Mathematics 2, 2013 – Assignment 1 – Template 1 of 3

Critical evaluation of the usefulness of mathematics interviews for gaining

knowledge about students’ current mathematical knowledge that can be used to

plan future learning opportunities. Be sure to draw on relevant research literature

to support your evaluation. (200 words)

The use of a one-to-one mathematics interviews can greatly enhance and further teachers’

knowledge of how students think about mathematics fostering the ongoing improvement of both

mathematics instruction and student learning (Fennema and Frank, 1992). Interviews reveal valuable

information by probing students thinking to gauge what they know, a method that is not available when

teachers solely rely on written forms of assessment which can hide gaps in students understandings

(Burn, 2010, p.19). Clarke, Clarke and Roche (2011), state that interviews allow teachers to better

understand how students think and learn about mathematics by contributing to teacher knowledge and

expertise, particularly in relation to the teachers’ knowledge of students’ mathematical understanding

by giving a clear idea of what students are able to do (p.907). This assessment strategy provides

teachers with the awareness of common difficulties and misconceptions by probing mathematical

strengths and weaknesses as well as improving questioning techniques by providing a model for

classroom questioning (Clarke et al., 2011, p.910). Giving one-to-one attention and time enables ‘quiet

achievers’ to emerge by allowing such students to demonstrate their mathematic abilities and enabling

all students to communicate how they reason (Clarke et al., 2011, 906). Interviews also have a ‘high

ceiling’, if students have success they are provided with more and more challenging tasks well beyond

the usual curriculum focus (Clarke et al., 2011, 909). This provides teachers with an awareness of the

considerable range of the levels of mathematical understanding and diversity in a classroom and allows

teachers to quantify this and reflect on appropriate classroom experience for all students (Clarke et al.,

2011, p.911). Mathematical interviews provide teachers with a comfortable nature to gain insight into

student thinking and provide realistic expectations of what students know and can do in relation to their

thought process and problem solving strategies which is essential for guiding appropriate instructional

decisions (McDonough, Clarke and Clarke, 2002, p.223).

EDMA310/360 Mathematics: Learning and Teaching Mathematics 2, 2013 – Assignment 1 – Template 1 of 3

Critical evaluation of the usefulness of Open Tasks with Rubrics for gaining

knowledge about students’ current mathematical knowledge that can be used to

plan future learning opportunities. Be sure to draw on relevant research literature

to support your evaluation. (200 words)

The main purpose of a rubric is to capture the essence of student performance or development at

various levels (Humphry and Heldsinger, 2009, p.57). In an open task where students have multiple

interpretations and mathematical reasoning, a rubric serves as a way of formalising what a student

could successfully do with the relevant mathematical topic by identifying a level or quantity of

achievement (Humphry et al., 2009, p.57). Ideally, a rubric is designed and adapted by the assessor for

each assessment task so it continually evolves to match and assess the students varying levels of

understanding, as the creator can decide the performance at each level (Van de Walle, Karp, Bay-

Williams, 2010, p.80). Gough (2006) argues that rubrics can often be difficult to interpret and at its

simplest are just tabulated, weighted ways to collect and use learning outcomes to assess learning and

serve as a checklist for observable behaviours (p.8). McGathat and Darcy (2010) however contests that

when focusing on open tasks in mathematics teaching and learning, rubrics allow teachers to assess to

what degree students have applied or learned a specific task and how well the student has handled the

sub task by aligning what they can do alongside graded descriptions (p.2). Rubrics enable teachers to

plan for future learning opportunities by allowing them to look at the range of sub tasks all students are

struggling to learn, which students need extra attention and which part of a task needs further teaching

clarification and practice (Humphry et al., 2009). Rubrics allow teachers to analyse student ability so

that they can plan their future instruction and provide beneficial feedback to students that will lead to a

more conceptual understanding and higher quality work (McGathat et al., 2010, p.5).

EDMA310/360 Mathematics: Learning and Teaching Mathematics 2, 2013 – Assignment 1 – Template 1 of 3

References:

Burns, M. Snapshot of Student Misunderstandings. (2010). Educational Leadership. 67(2). 18-22.

Retrieved from http://web.ebscohost.com.ezproxy1.acu.edu.au/ehost/pdfviewer/pdfviewer

?sid=81d5a0 a0-19d6-42e6-a440- f6ec8dc4ae23%40sessionmgr4&vid=2&hid=21

Clarke, D., Clarke. B., & Roche. A. (2011). Building teachers’ expertise in understanding, assessing

and developing children’s mathematical thinking: the power of task-based, one-to-one

assessment interviews. The International Journal of Mathematics Education, 43(6-7). 901-

913. Doi: 1007/s11858-011-0345-2

Gough, J. (2006). Rubrics in assessment. Vinculum. 43(1). 8-13. Retrieved from

http://search.informit.com.au.ezproxy1.acu.edu.au/fullText;dn=149148;res=AEIPT

Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.),

Handbook of research on mathematics teaching and learning (pp. 147–164). Reston, VA:

National Council of Teachers of Mathematics.

Humphry, H., Heldsinger, H. (2009). Australian Council for Education Research. Do rubrics help

to inform and direct teaching practice? Retrieved from

http://research.acer.edu.au/cgi/viewcontent.cgi?article=1051&context=research_conference

McDonough, A., Clarke, B., & Clarke, D. M. (2002). Understanding, assessing and developing

children’s mathematical thinking: The power of a one-to-one interview for preservice teachers

in providing insights into appropriate pedagogical practices. The International Journal of

Educational Research, 37. 211–226. Retrieved from

http://www.sciencedirect.com/science/article/pii/S0883035502000617

McGathat, M., Darcy, P. (2010) Rubrics at Play. Mathematics Teaching in the Middle School, 9. 1-

9. Retrieved from http://eric.ed.gov/?id=EJ878921

Van de Walle, J. A., Karp, K. S., Bay-Williams, J. M (2010). Elementary and middle school

mathematics: Teaching Developmentally. (7th ed.). Boston: Pearson.

EDMA310/360 Mathematics: Learning and Teaching Mathematics 2, 2013 – Assignment 1 – Template 1 of 3