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1. 4. Reflect on your first professional experience day –a-week visit. What mathematics did
you see, hear, read? Why do you think the classroom is set up the way it is for mathematics
learning? Support your ideas with literature.
During my first day-a-week visit at St. Michael’s Catholic School in Baulkham hills I was placed in
3 Blue, being a year 3 class. I was told by my supervising teacher that these students were scaled at
the lower end compared to the other three year 3 classes. 3 Blue participated in a mathematics
lesson during the afternoon session of the day. Students were asked to conduct their mental warm
up that they have been using over the last two weeks drawing on their prior knowledge of
multiplication. Students were encouraged to use the words, “multiplied by, equals, groups of” to
enhance their understanding for the main activity. Counters were provided as manipulatives in
support of students working out strategies which can be backed up by Robert Scott Liggett theory
that “The goals of any math instruction should be to focus on helping students understand concepts”
(Liggett,R. 2017). Students were then asked to create 3 number lines that included “rules” for
example a number line that went up by 2’s or went down by 8. Students were then to swap their
books and get their partner to complete their number lines by trying to work out the “rule”. This
lesson was created to meet outcome MA1-8NA and content point represent number patterns on
number lines and number charts. Therefore I thought this was a well throughout maths lesson that
engaged and challenged to students through multiplication and pattern thinking that specifically met
the required outcome.
2. Find or take a photograph that can be used as a stimulus for a maths learning experience in
measurement or space. Upload it and list 3 open ended questions you would pose to the
children. Support your ideas with literature
To create an engaging and interactive learning environment that supports students in their learning
of mathematics requires the use of open ended questions (Skalicky, Mitchell and Boucher, 2007).
1. How tall do you think you are? Estimate and record your answer
2. Perform the following with your learning partner:
– Measure the height of each other using a metre ruler and record your findings
– Compare it to your estimated height
– What is the difference?
3. Using your measurements, how many of you would measure up to the tallest man’s height?
The questions above aim to support “measure, record, compare and estimate lengths in metres,
centimetres and millimetres (MA2-9MG)” (NESA, 2018). The first question allows students to
estimate their height in either m, cm or mm, estimating is said to be an “enjoyable and very useful
part of mathematics” (Smart, 1982).
The second question provides the opportunity for students to work collaboratively, allowing for the
students to discuss and justify their answers with one and other as well as reflect. Hiebert, Fennema
and Carpenter specified “students who reflect on their work and communicate with others are in the
best position to build useful connections in mathematics” (Hiebert, Fennema & Carpenter 1996).
The third questions emphasizes “excellent teachers of mathematics arouse curiosity, challenge
students’ thinking and engage them actively in learning” (AAMT, 2006). Students will use their
skills of problem solving as well as thinking creatively to answer this question.
3. Imagine the Principal/Director asked you to prepare a document to present at a maths staff
meeting. The document is titled, ‘How to set up and manage mathematical learning
experiences”. Find literature that you can use to create a list of 10 items that would appear in
your document. Reference your material. Support your ideas with literature.
1. Create “interesting, functionally relevant classroom tasks which can enhance engagement in
learning” (Russell, Mackay & Jane, 2003)
2. Ensure that lessons cater to different levels/modes of student learning whilst remaining
engaging for all students. With strong reference to Gardner’s Multiple Intelligence
theory, teachers have the opportunity to educate through a variety of resources.
3. Be sure to ask good questions, both open-ended and some close-ended questions allowing for
students to think outside the square. As well as using precise and concise language to
avoid confusion (Integrating the theory of Bloom’s Taxonomy allows for students of
ALL levels to excel in their own learning)
4. Having a strong base of knowledge to draw from, including:
– How mathematics is learned
– Knowledge of the students
– What affects the students’ opportunities to learn mathematics
– How the learning of mathematics can be thoroughly enhanced (AAMT, 2006)
5. Create a supportive learning environment where students feel comfortable to have a discussion
through valuing all students’ input essentially making it an inclusive space
6. Providing students with a KWL chart aims to activate student prior knowledge (Know), provide
an opportunity for students to set their own learning targets (Want) and evaluate their overall
7. Ensure classroom layout is not in rows but instead in a circular arrangement. As a German
research has shown “that question-asking was more frequent when the children were seated
in the semicircular arrangement than in the row-and-column arrangement as well as leading
to equal opportunities for everyone in the class” (Marx, Fuhrer & Hartig, 1999)
8. Use of technology such as interactive whiteboards to allow for student interaction through
educational games and quizzes to enhance cognitive skills and tablet devices to assist in
9. Ensuring manipulatives are available in the classroom:
– By providing manipulatives, teachers have the opportunity to create more meaningful experience
for students (Stein and Bovalino, 2001)
– Engage students assisting them to stay focused (Florence, 2012) leading to enjoyment and being
actively involved in learning (Xie, Antle & Motamedi, 2008)
– Cater to individual learning styles such as kinesthetic and visual learners (Sundstorm, 2012)
– Research has shown that manipulatives are especially useful for students with an EAL/D
background, students who portray learning disabilities and low-achievers (Boggan, Harper
& Whitmire, 2010)
10. Promote the Think-Pair-Share strategy as it encourages students to think about a question and
then refine their understanding through discussion with a learning partner (Rankin, 2017).
The below process explains what students will gain from T-P-S
7. Imagine you had a budget of $300 to purchase manipulatives to assist the children you are
working with to understand patterns and algebraic thinking. View this catalogue and
select items that you will use and provide a way in which you will use them:
Manipulative’s are an important tool that should be used frequently in Mathematics. Using
manipulative in learning enhances understanding (Cook, 2012). The following items are some great
manipulative to use to help students understand patterns and algebra.
Whiteboard Hundred Boards Double Sided Kit – ($79.95) à ideal for visual learners.
Students can create number patterns and learn sequences. This is a great tool to practice
addition, subtraction and multiplication. Chinn states that whiteboards are very encouraging
to students as “the writing on the board can be wiped clean” (Chinn, 2016, p. 12).
Solid Pattern Mega Set (2160 pcs) – ($159.95) à Allow the students to play initially and
create various designs using the shapes. This manipulative is great for leaning about the
“principles of geometry, spatial planning and pattern design” (Hoffman & Glannon, 1993, p.
149). The open-ended of this task, allows students to think creatively and outside the box
with their patterns. Furthermore, students will learn about shapes through playing with
Bucket of Wooden Beads (2200 pcs) – ($49.95) à As there is enough pieces to go around,
this can be used within classroom demonstrations. Furthermore, patterns can be constructed.
This is a good tool to use with Early Stage 1 and Stage 1 students learning about pattern
sequences, e.g they can guess the next colour in the pattern.
Arithmetic String – Counting beads – Student 0-100 – ($9.95) à allows students to create
patterns and count effectively.
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