aeg5216 teaching mathematics 2 assignment 2: annotated collection of teaching ... · 2018-10-13 ·...

Melissa Belmont3884608

AEG5216 Teaching Mathematics 2

Assignment 2: Annotated collection of teaching resources and artefacts

1) Mathematics dictionary

Math Dictionary by Eula Ewing Monroe,

published 2006 by Scholastic Inc, New York.

This mathematics dictionary fits into all areas

of the years seven to ten mathematics

curriculum. It covers a wide array of

mathematical concepts, and includes examples

and illustrations.

This resource is useful for both students and

teachers. Students can use it as an

independent source of clarification and

information. Teachers can use it to gain ideas

about how to introduce new concepts, or to

find alternative explanations if students are

encountering difficulties in understanding. It

can also be used as a basis for developing

students' mathematics dictionaries in the

classroom.

Utilising a mathematics dictionary can also

help students to make the connection that

mathematics has its own language, that

concepts and vocabulary must be built on and

learned in order to gain fluency and ability, as

for any other language.

2) Western Treatment Plant (integrated curriculum) excursion


Melbourne Water, Western Treatment Plant:

http://www.melbournewater.com.au/content/sewerage/western_treatment_plant/western_trea

tment_plant.asp

An excursion to the Western Treatment Plant in Werribee as part of an integrated curriculum on

environmentalism or sustainability can be used to investigate many parts of the secondary

mathematics curriculum. Students undertake a guided tour of the plant, during which the

guide gives a detailed explanation of the workings of the plant and the waste water system in

Melbourne. Throughout this explanation a plethora of facts and specific figures are provided,

about diameter of storm water pipes and sewerage pipes, rate of flow of waste water, size of

treatment lagoons, rate of movement of water through treatment lagoons, proportion of

treated water used or disposed of, as well as much other information.

This information could be collected by students and used to complete an investigative project

on the mathematics behind the treatment plant and process, with additional information

available on the Melbourne Water website. This investigation could involve anything from area,

volume and capacity through to rates of change, and could factor into many aspects of the

curriculum. This could be used in a differentiated classroom as an enrichment task by varying

the complexity of the investigation required.

This is a way to provide real world context to mathematics, which as Goos, Stillman and Vale

(2007) point out is an excellent way to make mathematical connections for students. Students

would acquire concrete examples on which to hang critical concepts such as volume, making

the learning more relevant.


3) Pearson Mathematics 7 text book (Australian Curriculum)

Pearson Mathematics 7 Student Book by David Coffey et al (2011), published by Pearson Australia, Port Melbourne.

This text book has been designed

around the forthcoming Australian

curriculum, and is a purpose-

written book for year seven

mathematics. It has been

designed to be used in a textbook

based classroom, and covers all

essential aspects of the

curriculum.

As well as including the typical

worked examples and exercises

this text incorporates a good amount of real world contextualisation, which Goos, Stillman and

Vale (2007) note assists students in understanding the relevance of mathematics. The text

also includes a wide variety of mathematical games to scaffold understanding of the concepts

being taught.

A teacher not using a textbook based model of classroom learning could benefit from utilising

the games from this book which cover each aspect of the curriculum. It is commonly believed

that introducing an element of fun into mathematics by the use of games is a good way to

engage student interest and attention while still promoting mathematical learning.


4) Assessment tasks and rubrics for Year 7/8 maths

These are two assessment rubrics I designed for the end of topic (summative) assessment

tasks that were included in the year seven and eight mathematics planners for Baden Powell P-

9 College (Tarneit). The areas of curriculum covered were area, volume and capacity and

maps and networks, and the items included in the BELOW, AT and ABOVE levels were based on

the learning outcomes stated in the planner which were derived from the VELS.

The rubrics were designed in order to facilitate marking of the students' work, and to ensure

that all teachers in the team were marking consistently. A copy of the rubric was also given to


the students with the assessment task in order to help them understand what was expected of

them. There was evidence that some of the students studied the rubric closely, and attempted

to incorporate all of the elements required for the AT standard, if not the ABOVE, with varying

degrees of success. The tasks were performed under test conditions.

Giving students clear and concise assessment rubrics is a good way of managing expectations;

a well designed rubric can aid in grasping the requirements of a task. Ideally the rubric should

be developed concurrently with the task; understanding the abilities that need to be

demonstrated can assist in designing a comprehensive assessment.

5) Assessment tools for common misunderstandings

Department of Education and Early Childhood Development, Mathematics Domain P-10.

Common Misunderstandings – Level 5: Proportional Reasoning

http://www.education.vic.gov.au/studentlearning/teachingresources/maths/common/commissl

vl5.htm

Identifying and correcting misconceptions can be a vital component to a student's long-term

understanding and enjoyment of mathematics. The Mathematics Domain on the DEECD

website has a range of tools that can be used to assess such misconceptions at each level.

The Level 5 tools deal with proportional reasoning, and cover a large part of the curriculum at

year seven and eight. Fractions, ratios, percentages, rates and proportions are all covered.


Where a teacher identifies a potential deficiency in a class or particular student, these tasks

can be used to assess the student's understanding. This assessment can then form the basis

for further work in that area, if required. The website includes an advice rubric for each task,

and suggestions for correcting the misconception.

Having observed misconceptions at work in a combined year seven and eight classroom I can

clearly see the value in these activities. The resources provide excellent strategies for

identifying issues, and could be used to good effect particularly at the beginning of the year

and of each new topic embarked upon. A clear understanding of a student's abilities and

reasoning about these topics ensures the teacher can tailor the unit or classes to scaffold that

student's learning.

6) Rethinking Mathematics – Real world contexts for mathematical learning

Rethinking Mathematics - Teaching Social Justice by the Numbers edited by Eric Gutstein and

Bob Peterson (2006), published by Rethinking Schools, Milwaukee.

Although the content and focus of this book are based

in the United States of America, in my opinion, this is

the pinnacle in real world contextualisation and

integrated curriculum. The editors and authors of this

book provide anecdotes and examples of how social

justice issues have been used to teach a variety of

mathematical concepts, and by doing so have engaged

students in the mathematics on much deeper levels.

The examples in the book cover many aspects of the

mathematical curriculum, including but certainly not

limited to algebra,statistics, representation of data,

understanding large numbers and maps. This

mathematical knowledge is embedded in investigations

and analysis of real social justice or community

relevant issues.

This approach is an excellent way to build a more

inclusive and equitable classroom, given either careful

or negotiated selection of topics to be explored. It also

fosters a problem-solving attitude toward

mathematics, aiming at building on students' higher

level mathematical thinking.


7) Maths Talent Quest Project – The Great Pyramid of Lego

This Maths Talent Quest project involved the students performing an investigation of the Great

Pyramid at Giza, and calculating how many Lego blocks would be required to construct it. This

was a year seven project, and fits within the VELS regarding volume of solid objects.

This project demonstrated the students' ability to research maths concepts (the formula for the

volume of a pyramid) and relevant data (the measurements relating to the pyramid).

This project, or some related investigative project, could be used to encourage problem-solving

and cooperative learning skills. Given the wide variety of Lego block styles and the varying

levels of accuracy implicit in the investigation it would be possible for groups within the same

class to end up with different solutions. Discussion of these differences could be used to

facilitate higher level mathematical thought.


These kind of real world based problem-solving activities could be used to engage unfocused

students by careful selection of topics, or (regulated) choice of topics, geared towards their

interests.

8) Maths Talent Quest Project – Raft Mathematics

This Maths Talent Quest project was completed by a year eight student. It involved the

construction of a scale model of a raft that the student possessed, and included an

investigation of the sailing speeds of the two rafts to check for comparability.

This kind of project can be used in the classroom to explore concepts of ratio, proportion and

scale; these occur throughout the curriculum in the lower secondary years, and the

complexity of the task could be modified to cater for the specific year level being targeted. It

could be a guided class exercise, or could be used as an investigative project in order to

develop students' problem-solving and cooperative learning abilities. Such an investigation

could be used as an enrichment task for a differentiated class – different levels of complexity

required of different students.

The task could be widened to incorporate investigation of mathematical concepts such as the

golden ratio or similar, depending on the choice of topic. This kind of project could easily be

linked to an integrated curriculum – this could deepen understanding of the topic in other

subject areas, and provide real world contextualisation for the mathematical principles being

utilised, thereby deepening students' understanding and engagement.


9) Technology in Maths - Equity and Technology – A Case Study by Colleen Vale

There are several examples in this article about the equitable use of technology in

mathematics classrooms, however I found one example in particular compelling. The teacher

used a projector, laptop and a spreadsheet with formulae, and ran a guided investigation with

the class to explore the concept of π. An understanding of π as a constant is a vital foundation

for many parts of the curriculum, especially those regarding area and volume; also, if

students can understand π and that it is a constant, they will be much better placed to

understand other mathematical and scientific constants they are likely to encounter in later

studies.

The teacher had students measuring diameter and circumference of various circles and

entering the measurements into the spreadsheet – a formula would then calculate the ratio

(π). I can definitely see the value in this investigation as I was asked several times during my

teaching rounds what π is and what it means. The students I taught would have very much

benefited from this hands-on approach. Not only would this approach provide a solid

understanding of the concept, but it would also highlight the importance of accuracy in

measurement (as inaccurate figures would give less accurate values representing π), it could

be used to review ratios and finally it gives students an insight into how they can use

technology and maths to look at real world problems and puzzles.

10) Technology in Maths – mathsgames.com

http://www.mathsgames.com/


Games in mathematics can be used in a variety of scenarios for a range of reasons. It was

evident during my placement that students can be quite motivated to finish up work and

perform well if promised the reward of playing maths based games online. The games

themselves can also be a teaching tool, and reinforce mathematical learning.

MathsGames.com has a range of directed games that cover different aspects of the curriculum,

from fractions to shapes to algebra. Each game is different, and many have ability levels to

cater for different year levels or differentiated learning.

Students having trouble with a specific area of mathematics might be able to gain

understanding through playing games, and observing a student interact with a game may

provide the teacher with insight as to where the students' difficulties lie.


References

Coffey, D, Strasser, D, Aus, B, Dimitriadis, G, Harnwell, J, Smith, T... Nolan, J 2011, Pearson

Mathematics 7 Student Book, Pearson Australia, Port Melbourne

Department of Education and Early Childhood Development 2009, Mathematics Domain P-10:

Common Misunderstandings – Level 5: Proportional Reasoning, viewed 10 October 2011,

http://www.education.vic.gov.au/studentlearning/teachingresources/maths/common/commissl

vl5.htm

Ewing Monroe, E 2006, Math Dictionary, Scholastic Inc, New York

Goos, M, Stillman, G & Vale, C 2007, Teaching Secondary School Mathematics: Research and

practice for the 21st century, Allen & Unwin, Crows Nest

Gutstein, E & Peterson, B (Eds.) 2006, Rethinking Mathematics - Teaching Social Justice by the

Numbers, Rethinking Schools, Milwaukee

MathsGames.com 2011, viewed 10 October 2011, http://www.mathsgames.com

Melbourne Water 2011, Western Treatment Plant, viewed 10 October 2011,

http://www.melbournewater.com.au/content/sewerage/western_treatment_plant/western_trea

tment_plant.asp

Vale, C 2006, 'Equity and Technology: A Case Study', pp. 512-518, on Mathematics Education

Research Group of Australasia Incorporated, viewed 10 October 2011,

http://www.merga.net.au/documents/RP592006.pdf

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