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
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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/
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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.
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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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