Mls014 Patchwork Assessment Assignment

NATIONAL INSTITUE OF EDUCATION NANYANG TECHNOLOGICAL UNIVERSITY

MANAGEMENT AND LEADERSHIP IN SCHOOLS |JANUARY 2009|

MLS014 Alternative Assessment for Project Based Learning

ALTERNATIVE ASSESSMENT DESIGN PATCHWORK ASSESSMENT IN MENSURATION

ACHARY GOPALAN SHIYAMALA COMMONWEALTH SECONDARY SCHOOL [email protected] 26 FEBRUARY 2009 TUTOR: DR KELVIN TAN

MLS014 Alternative Assessment for Project Based Learning Patchwork Assessment in Mensuration

PATCHWORK

ASSESSMENT

IN

MENSURATION RATIONALE Geometry in the Physical World The beauty of geometry is seen through many aspects of the physical world, such as nature and architecture. Many pupils learn mensuration simply through the application of formulae in problems and fail to see that it has great relevance to the real world and that the usefulness of mensuration is strongly related to the field of architecture. Assessment in Mensuration The Mathematics curriculum in Singapore is taught in a spiral approach: In Secondary One, pupils learn the volume and surface areas of prisms and in Secondary Two, pupils learn the volume and surface areas of pyramids, cones and spheres. Formative assessment has always been segmented by the various solids, that is, when pupils learn pyramids, assessment is solely on pyramids. However, in summative assessment, pupils are tested on a combination of the solids. This results in a lot of difficulties in pupils as they have always seen the various solids as separate. Patchwork Assessment The patchwork assessment I have designed seeks to address the two issues mentioned above. The objectives of this patchwork assessment are as follows: Pupils will be able to (a) appreciate the beauty of architecture through a ‘geometrical’ pair of

eyes, and

MLS014 Alternative Assessment for Project Based Learning Patchwork Assessment in Mensuration

(b)demonstrate

their

understanding

of

mensuration

through

interpretation and application, two of the Six Facets of Understanding (Wiggins and McTighe, 2006).

PATCHWORK ASSESSMENT N

Task

Rationale

o. 1

Maximising the Volume of a Pyramid Task 1 requires pupils to In this individual task, pupils are given a manipulate a piece of paper, piece of A4-size paper to form a square- a 2-D object, to form a based

pyramid

with

the

greatest pyramid, a 3-D object. To

possible volume. They are to calculate maximise the volume of the the surface area and volume of the pyramid, pyramid made based on formulae learnt.

pupils

have

to

make sound mathematical calculations before cutting

2

Making a Conical Party Hat

out the net of a pyramid. Task 2 requires pupils to

Pupils will form pairs and measure the work with a given set of circumference of their partner’s head. dimensions to make a cone. Each pupil is to make and decorate a This task is essential to the conical party hat, not exceeding 30 cm final

task

in height, made of paper for his partner. eventually

as have

pupils to

will make

Pupils are to give a peer assessment of geometrical solids with fixed the hats made for them based on a dimensions. Peer evaluation given set of rubrics, which include the fit is included for this task for and the artistic aspect of the hat. 3

pupils

to

appreciate

the

works of their peers. Alternatives to Using Formulae for Task 3 requires pupils to do Surface Area and Volume of Spheres some research and think of

MLS014 Alternative Assessment for Project Based Learning Patchwork Assessment in Mensuration

N

Task

Rationale

o. Pupils, in pairs, are to research, discuss methods that are out of the and come up with two different methods box to calculate the surface of calculating the surface area and area

and

volume of a ping-pong ball. Pupils are to sphere.

volume

This

task

of

a

allows

write a short report on the two methods pupils to understand that in and to calculate the surface area and the the volume of a given ping-pong ball.

real

world,

it

is

sometimes not possible to use

formula

as

some

dimensions are not easily 4

determined. Task 4 requires pupils to

Proposal of Model

Pupils are to search for pictures of appreciate

the

beauty

of

monuments or landmarks on the Internet architecture in the form of or books. In pairs, pupils are to share monuments and landmarks with the class their proposal of the in

the

world.

Pupils

will

model of a monument or landmark they observe that many beautiful have chosen to construct based on the monuments and landmarks following criteria: The model (a)

in the world are made of

must consists of at least one geometrical solids. The task pyramid, cone and sphere, but also requires pupils to make can

include

solids

learnt

in use of their learning to plan

Secondary One, (b)

the construction of a model.

can be made of paper or any Based

on

the

feedback

existing materials such as cans given by their peers, pupils or styrofoam, (c)

can make modifications to

must not be larger than a cube their plans. of 50 cm.

Peers

are

to

provide

feedback on the proposals.

constructive

MLS014 Alternative Assessment for Project Based Learning Patchwork Assessment in Mensuration

N

Task

Rationale

o. 5

Synthesis Task – Construction of The synthesis task requires Model

pupils to interpret and apply

Using Tasks 1 to 4, in pairs, pupils are to their

understanding

of

construct a model of a monument or mensuration in the form of landmark based on their proposal. The constructing a model. Pupils model is to be accompanied by a written have to make use of their report, stating clearly the rationale for learning from the previous choosing the particular monument or tasks to be able to complete landmark, and the total volume and the synthesis task. surface area of the model with clear calculations. Evaluation of Synthesis Task The model will be evaluated based on the following criteria: (a)

good

representation

of

monument or landmark chosen, (b)

compliance

to

dimensions

given, (c)

creative

use

of

variety

of

geometrical solids learnt, (d)

accurate calculation of the total volume and surface area of the model.

REFERENCES O’Daffer, P. G. & Clemens, S. R. (1992) Geometry: An Investigative Approach. Reading, Mass: Addison-Wesley Publishing Company.

MLS014 Alternative Assessment for Project Based Learning Patchwork Assessment in Mensuration

Tan, K.H.K. (Ed.) (2007) Alternative Assessment in Schools: A Qualitative Approach. Singapore: Pearson Education South East Asia. Tan, K.H.K. & Koh, K. (Eds.) (2008) Authentic Assessment in Schools. Singapore: Pearson Education South East Asia. Wiggins, G. P. & McTighe, J. (2006) Understanding by Design (Expanded 2nd Ed.). New Jersey: Pearson Education.

COMMENTS Comments by Tay Hui Yih The synthesis task is not an easy one; it is actually complex. The patchwork assessment helps to break down the synthesis task into smaller tasks and this helps to guide the students in managing the overall task. The synthesis task also allows the students to have a chance to be creative. Lastly, the task is an open-ended one and it caters to students of different ability groups.

Comments by Dayang Roslina Awang Haji Yahya Having the idea to allow the students to synthesis their knowledge and understanding on the mensuration of the three solids is very good. I find your strategy to let the students synthesising at the final task is logical and smart. I only have one question and one suggestion. My question is I noticed in Task 2, there is a peer evaluation by using the given sets of rubric, hence I am curious how the assessment for Task 1, Task 3, and Task 4 will be administered. Why is it only Task 2? Instruction for the activity is also not clear from the very beginning. Perhaps you should include in your instruction the required number of students in a group.