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- 1. MathematicsLearningJournal
Mathematics is the alphabet with which God has written the universe......Galileo
- 2. 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.
- 3. Learning Activity 1.2: Donald in Mathmagic Land.
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
- 4. 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 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
- 5. 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.
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).
Cds and DVDs
- 6. Learning Activity 1.3: A first glimpse into mathematics educationRecord Chart: A first glimpse into mathematics education
- 7. Learning Activity 1.4: A new gourmet restaurantMunching 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!
- 8. 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 dont 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 students 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.
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