MathematicsLearningJournal Mathematics is the alphabet with which God has written the universe......Galileo
Week 1 Adventuring into Mathematics Learning Activity 1.1: If mathematics were a food..... I think it would be Mexican Layered Bean Dip, because no matter how much you dig, you never reach the bottom and it always gets mixed up.
Learning Activity 1.2: Donald in Mathmagic Land. Pre-Viewing Questions. Do you think mathematics can be fun? Explain your answer with an example. Yes I do feel that mathematics can be fun. You need the right type of teacher to keep things interesting and fun. In year 10 maths at school we were learning about probability, our maths teacher decided to give us hands on experience and took our class off to a Wednesday race meeting at Flemington Race Course. We learnt all about the odds and betting with probability being taught in a fun and exciting way.
How do you use mathematics in your everyday life? I use mathematics all the time. When I go for a coffee with friends, just counting out the money is maths. Shopping, mentally adding up items, deducting discounts, working out prices and which is better value. I use mathematics when I teach swimming. Working out the programs for the squads and how far they swim, time keeping, average times, fastest times etc. I am surrounded by Mathematics!!
Pythagoras was a mathematician in the time of the ancient Greeks. What do you know about the work of Pythagoras? I think Pythagoras had the first theory behind triangles. I also think he was a musician of some sort, maybe invented a musical instrument.
What other mathematicians can you name? If you can, say something about their work. Name some ways that mathematics is present in: Nature: Shapes of flowers, snowflakes Architecture: Pyramids, Castles, Sistine Chapel dome, buttresses on Notre Dame most ancient buildings, Skyscrapers, houses. Art: Paintings – working out sizes of objects in foreground compared to background. Sports: Field sizes, racquet and club sizes, ball sizes, statistics, scoring Games: jigsaw puzzles, Rubics cubes, monopoly, payday
Viewing and Post-Viewing Questions: What are some of the mathematical contributions made by Pythagoras?
Pythagoras’ Theorum: In right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Golden Rectangle Fractions Pentagrams Golden sections – mathematically reproduces itself indefinitely Magic spiral – repeats the proportions of the golden section into infinity
What is a Golden Rectangle? Why is it important in art and architecture? What do you see around you in your daily life that looks like a Golden Rectangle?
The Golden Rectangle is the mathematical law of beauty. It gives proportion to art and architecture. It is found in most ancient buildings like the Parthenon, Notre Dame Cathedral, most sculptures and Renaissance artworks.
In my daily life there are many Golden Rectangles. My house, garage door, dog kennel, pool, fence, buildings etc
What are some ways that mathematics is present in Nature?
Mathematical logic, pattern limitless. Everything is arranged according to number and mathematical shape. Pentagon – Starfish, sea star, petunia, frangipani, star jasmine, snow flakes, bee hives Golden Sections – Shells, snails, pine cones Golden Rectangles - trees
In the video you will see Donald experiencing a number of games that rely on geometry or other mathematics to be played well. Name these games and outline how mathematics is used in them. Outline at least two other games that you know that uses mathematics in some way.
Chess – calculated strategy. Moves are mathematical around squares. Baseball – diamond Football – rectangle Basketball – circle, spheres and rectangles Hopscotch – multiple squares 3 Cushion Billards – 2 squares joined to make rectangle, diamonds In all sports mathematics is required for time keeping and scoring. 2 others sports Swimming – rectangle, time keeping, working out distances and lap numbers, bio-mechanics Golf – club angles, distances,
The video spans thousands of years as it touches upon some mathematical achievements from ancient to modern times, but finishes in the mid – late 1990s (the video was made in 1959). Name some mathematical achievements that have occurred since the video was made (that is in the last 50 years).
Computers Calculators Cd’s and DVD’s Digital Television GPS
Learning Activity 1.3: A first glimpse into mathematics education Record Chart: A first glimpse into mathematics education
Learning Activity 1.4: A new gourmet restaurant Munching Mathematics Menu Atlantic Salmon on Crisp Nicoise Salad
A perfectly seared piece of Atlantic Salmon, resting on a bed of roasted potatoes, olives, spinach leaves, shallots and beans. All tossed in a light dill mayonnaise.
I have chosen this menu item as it is a complex example of many flavours coming together and working. This is how I see Mathematics. Each piece has to be just right to get the full effect. The Salmon is a piece of fish that needs to be cooked perfectly. It needs to be seared from the outside in, leaving just a fine band of pink in the middle. This helps the fish retain moisture and flavour. In mathematics, your primary education has to be similar to this. You need to have a good grounding. This grounding needs to give you the tools to further your knowledge later on (keeping your brain moist and retaining flavour). The Nicoise Salad however represents all the different aspects of Mathematics. If you leave one out, the flavour is different and may not work. I chose a dill mayonnaise to represent myself. I feel like a bit of a ‘dill’ when it comes to maths but would love to be all over it after this semester!
Learning Activity 1.5: Week 1 Assessment 1 preparation What are the learning outcomes for the unit? After completing this unit you will be able to:1. Identify, describe and apply effective teaching strategies for teaching mathematics.2. Analyse and critique strategies and resources for teaching mathematics in primary classrooms.3. Demonstrate knowledge of local curriculum documents connected to teaching mathematics.4. Show personal knowledge of mathematics suitable to a teacher of primary aged children. Unit learning outcome(s) for which this item provides evidence of learning 1. Identify, describe and apply effective teaching strategies for teaching mathematics.2. Analyse and critique strategies and resources for teaching mathematics in primary classrooms. Description/outline of what you have learned and how this learning demonstrates the learning outcomes you have specified above
The way mathematics has changed throughout the years, how we see mathematics, and the way it is all around us in our daily lives is the basis of my learning for this week. After joining our Mathsmates group, we had to answer the question ‘What is mathematics?’ I found that we all had very similar experiences with maths. ‘The overwhelming view of mathematics indicated one of very negative feelings towards a subject which most had very few, if any, positive memories of’ (Mathsmates, 2009). By completing both 1.1 and 1.4, we had a way to describe mathematics in a very different way. Food is something we all can relate to and being able to relate mathematics to it was a great way of identifying the areas that we don’t or do like. This is a very effective teaching strategy that I will use when I am teaching. This demonstrates outcome 1. Activity 1.2 has shown me the way mathematics has changed throughout the years. Not only our perception but also the way it is taught and the actual advances in mathematics. I also looked into my daily life and found mathematics everywhere. Activity 1.3 showed me my strengths and weaknesses in mathematics. I realised how little I really know and how much I need to learn. How this learning relates to your development as an effective primary mathematics teacher I feel that by recognising the way that mathematics and teaching methods have both changed throughout the years we can become more effective teachers. Once, teaching methods were content focused, we had to get through what was expected of us, today teaching needs to be ‘more learner centred’ (Booker et al., 2004). Effective teachers will build upon the student’s prior knowledge and not just teach what has to be achieved. This is a big change from when I was at school. By understanding the ways in which mathematics has changed over the years, I can see how different teaching methods are required. Mathematics is no longer the simple process of arithmetic (plus, minus etc), the term numeracy has been developed to encompass the old and the new. Booker describes numeracy as ‘a satisfactory description of the extended mathematical processes and understanding that are now required in everyday situations’ (Booker et al., 2004). To be an effective primary mathematics teacher I need to understand the nature of mathematics and how it is learnt.
Week 2 School mathematics in today’s world Learning Activity 2.1: Preparing yourself for effective learning Useful Websites: http://www.aamt.edu.au/ - Australian Association of Mathematics Teachers (AAMT) http://www.merga.net.au/ -Mathematics Education Research Group of Australasia (MERGA) http://www.qamt.org/ - Queensland Association of Mathematics (QAMT) http://education.qld.gov.au/curriculum/area/literacy/docs/numeracy.pdf - Qld curriculum framework Mathematics http://www.qsa.qld.edu.au/downloads/learning/qcar_el_maths_yr3.pdf - Essential Learning Areas Mathematics Qld P - 3 http://www.qsa.qld.edu.au/downloads/learning/qcar_el_maths_yr5.pdf - Essential Learning Areas Mathematics Qld – 5 http://www.qsa.qld.edu.au/downloads/learning/qcar_el_maths_yr7.pdf - Essential Learning Areas Mathematics Qld – 7 http://www.qsa.qld.edu.au/learning/574.html - Qld Studies Authority
Maths Mates what is mathematics? Upon starting this week’s response, the consensus of our MathsMAtes group was that mathematics was just a set of numbers and simple addition, subtraction and multiplication equations that had no real purpose, a subject that required students to adhere to and understand a stale set of procedures and principles in order to gain any real knowledge in mathematics. However, since completing our weekly tasks we have realized that maths is more than just arithmetic and numbers with a bit of algebra, geometry and fractions thrown in; it is a subject that is “bound up and inseparable from the experiences we have in real life.' (Bottle, 2005). Maths is a valuable tool that allows us to be proficient in our daily lives, whether you are a skilled architect using geometry to measure the land you are using, or a house wife that is planning her monthly household budget, the skills obtained while learning maths allows you to accomplish such tasks with more confidence. Maths, although apparent in our daily lives, requires us to think in a certain way, it has its own language that “uses carefully defined terms and symbols” (Reys et al, 2009, pg 2). The language of mathematics develops a student’s ability to communicate their ideas and their understanding of maths. However, like with many new skills students must comprehend the “meaning of these words and [learn] when it’s appropriate to use them” (Reys et al, 2010, pg 3). Learning the language of maths assists students in deciphering the “order and internal consistency” (Reys et al, 2009, pg 2) of mathematics. This is to ensure that they understand the process of mathematical solutions and in order to do so, teachers need to guide their students in developing “their own understanding of mathematics” (Reys et al, 2010, pg 3). We as teachers need to instill in our students a way of thinking that allows them to view mathematics as more than just a blur of numbers and patterns, that it is a collection of concepts and procedures that all have an unyielding link between one another. Teaching students the relationships between subjects, like geometry and algebra, allows them develop a deeper understanding of how mathematical equations are solved. As well as showing students the relationship between different concepts in maths, teachers need to illustrate the relationship between maths and the role it plays in the day to day occurrences, and use these as examples so students are able to apply what they have learnt. As we have learnt, mathematics is a perplexing and often misunderstood subject, but if students grasp the ideas and concepts they will soon reach the conclusion that maths contains relevant information that requires students to use their experiences in their daily lives and apply it to the way in which they learn mathematics
Learning Activity 2.2: School mathematics in a changing world.
Additional Learning Log Entry: Things to do from what you have read (questions 1 and 2 on page 12) What are the three general goals mentioned in the introduction? Which do you think is the most important? Explain why. To help children make sense of specific mathematical content, including both procedures and concepts To help children learn how to apply mathematical ideas to solve problems To foster positive dispositions, such as persistence, flexibility, willingness to learn, and valuing mathematics I feel that the fostering of positive dispositions and giving children a willingness to learn are extremely important. If children are taught to have open minds and have the freedom to think and say what they think, all other aspects of learning flow from this. Children need to be taught that Mathematics is fun and it is important. I was never taught this a school. Mathematics to me was boring and we were never encouraged to think ‘outside the square’. Mathematics was rote learning and of you missed one aspect you seemed to just fall behind. There was no flexibility in teaching styles and we gave up fairly quickly. A teacher that encourages this fun and positive environment will give students a willingness to learn. Then complicated mathematical procedures and concepts will be accepted easier and problem solving strategies will develop. Students will also feel comfortable to question these procedures, concepts and strategies. Give an illustration (different to those in the chapter) of how mathematics is a study of patterns and relationships, a way of thinking, and art, and a language. Mathematics is a study of patterns – numbers relate to others, patterns in times tables ie 9x4=36, 9x5=45, 9x6=54, 9x7=63. Mathematics is a way of thinking – Mathematics is an art – Mathematics is a language – Has its own set of words describing different applications eg, algebra, geometry, square, fractions.