Welcome to the EDMA262 Reflective Journal WikiEdit
A weekly reflective journal on the content of EDMA262
Mathematics education in Australia is falling behind national standards in comparison to countries around the world such as Singapore and Japan. As told by Dr. Yeap Ban Har (Maths - No Problem!, 2014), he explains that the Australian focuses mainly on the learning and memorising of procedures, but that can only take students so far. It is important that as a future educator, I make sure that students not only understand the procedure and how to use it, but understand why and how the procedure works. Memorisation and wrote teaching does not allow students to fully comprehend mathematics. Rather than making children memorise certain equations and formulas, it is important to teach, explain and create an understanding of all components involved for the how and why. This ensures that students will be able to use their own initiative and problem solving skills when faced with new and more complex problems, rather than trying to fall back on cookie-cutter formulas that they have memorised. In addition to this it is essential that students recognise and understand the difference between regular and mathematical English. There is a variety of ways questions can be worded in both the classroom and real world situations, therefore students being able to interpret these questions correctly is a vital component of teaching mathematics (Merilyn, 2012).
Mathematics: The Science of Patterns. Mathematical theories explain the relations between these patterns. These patterns include, measurement, time, space etc.
Numeracy: The basic ability to work with, understand and comprehend basic mathematical principles. Numeracy is the core basic mathematical skills that need to be learned and demonstrated to have a standard level of mathematical competency.
Hogan (2012) discusses the fact that the teaching of maths, as it is currently, does not give students a complete understanding of mathematical principles. Although most students have a decent numeracy level, the mathematical methods and procedures that are used in everyday life are often different to similar techniques that are taught in school mathematics. This means that the standard grasp of mathematical knowledge for Australian students does not allow them to fully utilize the skills and techniques they have learnt in school (Resnick, 1987). When teaching new mathematical principles, it is essential that these new ideas are shown in a variety of different contexts to give students an understanding of the various real life situations they may be used in. It may also be a helpful to present new contexts to the class and have them find what possible procedures or principles may be applied as a way to not only work on problem solving but also solidifying their current knowledge.
In our tutorials this week, we watched a child being assessed using the SENA test on their mathematical ability. The SENA test allows educators to assess the levels of mathematical knowledge, as well as their mathematical ability. This lets teachers plan lessons, catering to the levels of the students in their class.
When teaching a new mathematical concept, in this instance subtraction, it is important to take it step by step so that all components can be learnt individually before attempting the end goal. When teaching subtraction, students should understand and be competent with all previous components. The step by step for teaching subtraction includes:
- Can count forwards to 10
- Understands that counting forwards is travelling in an ascending
- Can identify higher and lower numbers on a number line
- Can count backwards from 10
- Understands that counting backwards is travelling in descending order
- Can Count forwards to 20
- Can count down from 20
- Can identify the number before a given number word
- Can subtract numbers from 0-10
These are the basic stepping stones for children beginning to learn to count forwards and backwards, eventually leading into learning how to subtract. It is very useful when teaching these concepts to young children to use concrete materials and resources, as well as using hand gestures to solidify their knowledge such as pointing towards the negative end of a number line whilst mentioning subtraction (Mildenhall, 2014). It is also important that as a future educator I understand that meaningful connections should be made to the mathematical concepts being taught. As (S. M. Linder, B. Powers-Costello, & D. A. Stegelin, 2011) suggests, incorporating learning experiences into real-life activities in the early years allows these connections to be made. These may include; estimating weight of objects or count building blocks from activities.
Week 4 Edit
In week 4 we explored the working mathematically proficiencies that are located within the syllabus. These include understanding, fluency, problem solving, reasoning and communication. These strands outline how the mathematics content should be taught, developed and explored. It is a guideline for us, as teachers, of the knowledge and ways of thinking that should be instilled into our students. I believe that these guidelines allow students to apply their knowledge they have learnt from the curriculum, as well as being able to prove, evaluate, analyse or explain mathematical principles they may encounter in real life situations.
Week 5 Edit
In week 5 we explored how mental computation and other estimation strategies are taught and learnt in the classroom. When learning of the multiple mental computational strategies for simple maths problems, it highlighted to me the fact that all children learn and think in different rates and ways. Designing lesson plans that scaffold and cater to each individual student allows for not only more engaging class activities, but also will increase student’s ability to learn (Bobis, 2006). When designing this lesson plans it is important to remember that students must be taught through a variety of different contexts to ensure they are getting a full grasp of the concepts rather than constantly regurgitating procedures they have previously been taught (Gervasoni, 2011). I will try to incorporate using a variety of every-day situations as well as concrete materials to give the broadest range of understanding I can to my students.
Week 6 Edit
I believe it is essential for each individual child to learn or create mental computation strategies that will assist with simple addition and subtraction. These strategies are shortcuts in thinking that allow students to use their own previous knowledge and methods to successfully reach a correct answer in a significantly shorter amount of time (Ruthven, 1998).
One strategy that was highlighted during our lecture to aid student’s mental computation for addition and subtracting is using paddle pop sticks to count, and bundling them together once they reach a group of 10 (Wong, 2017) - Shown in image below.
This strategy is effective for students because it allows them to understand that creating groups of 10 simplifies the counting into only two simple addition sums; the tens and then the ones. I believe that teaching students this strategy from an early stage is fundamental to being able to easily add or subtract more complex numbers in later years. When children are competent enough to use various mental strategies, I will ensure that I highlight that there is no right or wrong way of coming to an answer, and each child may find a method that works best for them. Similar to the activities we did in our tutorials this week, I will provide concrete materials for children to show how many ways a number can be presented. This allowed me and my peers to have a solid representation of some of the various mental shortcuts and strategies that can be utilised to simplify larger whole numbers. It is essential to provide repetition of these activities or problems that allow children to explore and understand these new mental strategies for them to be used efficiently throughout their whole lives (Greenes, Ginsburg, Balfanz, 2004).
Week 7 Edit
I believe that creating and teaching a good maths lesson relies on strong organisation of the educator. Ensuring a solid plan of what will be done, what will be achieved, how it will be achieved, and how long it will take is essential to maximising the effectiveness of a maths lesson.
As we have been constantly reminded of throughout our tutorials, asking open-ended questions that allow students to explore many different mathematical concepts through their own curiosity and initiative is much more effective than asking single answered questions. Throughout the unit, I have discovered that asking an open-ended question in itself does not automatically ensure that it will be successful in giving students the opportunity to explore and discover on their own accord. I will aim to create questions and tasks that allow students to explore their own curiosity of their world, whilst still achieving the required outcomes.
Week 8 Edit
As someone who is confident with their mathematical ability, converting units of measurement has always seemed to be one of the most difficult concept for myself, and others, to wrap their head around. Not only is there multiplication and division within the conversion, but students have to rely on prior knowledge of how many units are needed to be converted;
as well as the knowledge that the larger a unit is, the less of the units will be needed. The latter can be a difficult concept to grasp as the general idea is that the units are getting bigger so the number should be larger, when in reality it’s the exact opposite. For example, when 10 000m is converted to Km, most students would assume that the number would get bigger, but one kilometre contains 1000m so we divide by 1000 and end up with a smaller number. I have found that the use of manipulative objects, so far this semester, has increased my responsiveness to class tasks, so I have decided I will use manipulatives to give a visual representation of the different conversion of units. By consistently doing activities with manipulatives it gives children the opportunity to better understand this difficult concept in an engaging manner (Gaetano, 2014). This is similar to Drake’s (2014) approach at clearing up the common misconception of students measuring from the 1 rather than the edge of a ruler. By clearing up these misconceptions and clearly explaining the concept of measurement when it is taught, and reinforced throughout the early years, children have a broader understanding from the beginning.
Week 9 Edit
Relating to Marshall and Swan’s (2010) theory of manipulatives creating a much more responsive and engaging classroom environment, picture books similarly allow a mathematical concept to be introduced through a manner that provides a suitable and relatable context. Using the children’s book “Who Sank the Boat?” by Pamela Allen, we can introduce the mathematical concepts of volume and water displacement to children from an early age in fun and engaging manner. Children may have a grasp of perimeter and area, but once they get to volume is when things begin to be tricky. By creating activities that are able to be related to not only previous experiences, but also the focus book, children are able to broaden their conceptual understanding of volume (Macdonald & Lowrie, 2011).
Week 10 Edit
During the week 10 tutorial we were asked to select a clip from the children’s television show “Odd Squad”. Each clip featured a mathematical concept in a simple and engaging manner. This tutorial highlighted to me that using tv shows or video clips that show mathematical problems in “real life” scenarios, not only provides a stimulating and engaging experience to start the lesson, but also gives teachers an opportunity to use the video asinspiration for creating interesting and informative maths activities.
I have learnt that developing a proper understanding of measurement in children is vital to arming them with the knowledge to function optimally once they are older. Having the ability to design, estimate and measure are all key elements in the work force (Lehre., Jaslow & Curtis, 2003). For this reason, I think it is important to teach mathematics as much in the practical side as the theory side. Giving a physical representation of these situations allows the students to relate these activities to their surroundings. Piaget’s laws of conservation also stood out for me this week as an essential point of development to allow students to be fully prepared for their older years (Piaget, 1968). I believe that it is important to place an emphasis on these concepts for children to have a complete grasp of the nature and properties of units (Lehre t al).
Board of Studies NSW. (2012). NSW Syllabus for the Australian Curriculum. Sydney.
Available online at: http://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/content/
Gaetano, J. (2014). The effectiveness of using manipulatives to teach fractions.
Rowan University. New Jersey.
Greenes, C. Ginsburg, H. Balfanz, R. (2004). Big Math for Little Kids. Early Childhood research
Quarterly. 19(1). 159-166
Lehrer, R., Jaslow, L., & Curtis, C. (2003). Developing an understanding of
measurement in the elementary grades. In D. Clements & G. Bright (Eds.), Learning and teaching measurement (Vol. 1, pp. 100-121). Reston, VA: NCTM.Content
Lowrie, T. Macdonald, A. (2011). Developing measurement concepts within context:
Children’s representations of length. Maths Educational Research Journal. 23(1). 27-42.
Marshall, L & Swan, P. (2010). Revisiting mathematics manipulative materials: Paul Swan
and Linda Marshall revisit the use of manipulatives. They look at the different types
and the ways in which they are used by teachers. Australian Primary Mathematics
Ruthven, K. (1998). The Use of Mental, Written and Calculator Strategies of Numerical
Computation by Upper Primary Pupils within a ‘Calculator‐aware’ Number Curriculum. British Educational Research Journal. 24(1).
Piaget, J. (1968). Quantification, conservation, and nativism. Science, 162, 976-979.
Wong, M. (2017, Semester 1). Lecture 6: Approaches to teaching whole number, including
place value, the use of manipulatives and the inclusion of ICT [PowerPoint slides]. Retrieved from https://leo.acu.edu.au/course/view.php?id=22089§ion=13
Wong, M. (2017, Semester 1). Lecture 10: Teaching and learning in Measurement.
[PowerPoint slides] Retrieved from https://leo.acu.edu.au/course/view.php?id=22089§ion=17
Victorian Department of Education. 2001. Early Numeracy
Research Project Final Report. Victoria, Australia.