Numeracy is described as a working definition in Scott’s (2000) journal article, meaning a range of interpretations create change over a number of years and Scott believes this has always happened and will continue to do so. This is evident in relation to the timeline, as one can clearly see the differences over time.  Scott believes numeracy should be specifically catered to meet the needs of individuals and be built on three core focus points; confidence, content and context. Only by ensuring teaching is explicitly taught in appropriate contexts for individuals and allowing  explicit attention to the range of different needs of all students, Scott believes this is when we will see positive outcomes with relevant and high quality numeracy abilities for all levels of numeracy. The definitions relate to Scott’s article in their requirement for diversity, allowing room for difference in skill level and teaching based through contextual settings. 

The relationship between mathematics and numeracy is that mathematics is considered a study that deals with quantity, space, patterns, measurements and numbers. Numeracy involves having the ability to reason with numbers and other mathematical concepts. To deal with mathematical equations simply, individuals require numeracy to grasp these concepts. Furthermore, you need mathematics to understand numeracy, and you need numeracy to understand mathematics.  

Chloe :)

Paige’s description stresses the importance of a transdisciplinary approach to teaching science and mathematics for ecological sustainability, she talks a lot about students of today being the future problem solvers socially, culturally, politically and environmentally.  A transdisciplinary approach provides opportunities to improve numeracy levels not purely mathematical skills.

The important link between “school maths” and “real life maths” is developing the ability to use numeracy in day to day tasks. This can be developed by educators by relating the maths they are teaching in class to real-life situations. To help individuals gain whom are still struggling to grasps concepts, use the maths and teach it in a context that is targeted at a specific individual and their personal 
interests.  
- Emma 

If your group were to meet for the first time today (imagine week 1) and everyone in the group was to shake hands with everyone else, how many handshakes would there be?

 

1.       Describe to the people in your learning team how you solved this problem and share similarities and differences in your solution strategies.

 

5 people in my group:

1.       Dinar

2.       Rachel 

3.       Kerri 

4.       Emma 

5.       Chloe 

1 person x 4 shakes (5 people in the group), therefore 4 shakes x 5 people = 20 handshakes 

A shakes 4 peoples hands

B shakes 3 peoples hands

C shakes 2 peoples hands 

D shakes 1 persons hands 

E shakes 0 persons hands 

Total = 10

Therefore in a group of 5 people, there would be a total of 10 handshakes. 

 

 

2.       Record a variety of methods that make sense to you.

- Drawing a diagram and look at how many handshakes there would be 

 

3.       How did your experience with mathematics and problems solving at school impact on your attitudes/ abilities to problems solve this task? 

I always hated maths at school, especially in my junior and Primary school years. However, when I reached high school I started to understand it a little better, where I began to enjoy it more. I used to dread when my maths teacher gave us a problem-solving question, as I could never understand what it was asking. Although, with extra help in my primary years it helped me achieve a higher grade as I reached high school, and became a subject I could tolerate at school.
Chloe 

The narrator describes many mathematical skills involved in performing the given tasks.

Neither the scaffolders or fashion students are aware that they are using mathematical skills as they are completing a specific task that their training has been focused on.  They are simply “doing math’s with their hands.”

My view of being numerate is the ability to apply mathematical skills in context to solve any given problem, if the scaffolders and fashion students were confronted with a different problem could they solve it or do they simply know enough to perform their jobs successfully?

Workwise however, I believe they are numerate, but can they apply mathematical skills outside of this context?

 

Teachers need to be able to connect mathematics to the real world, based on the interest of the students, by making it engaging and celebrating student achievements at every stage of their learning journey.

 

All three numeracy frameworks talk about numeracy and applying mathematics to everyday life “confidently and for purposes that arise.” (Paige, K etal., 2008 Asia-Pacific Journal of Teacher Education), “Using mathematics ….  to meet general demands of life at home, in paid work, and for participation in community and civic life.” (Australian Association of Mathematics Teachers, 1997, p. 15).

Therefore, the numeracy levels of the scaffolders and fashion students are unknown due to not knowing the mathematical skills required outside of the examples shown.

_{This is my thoughts on this task, my actual answers are just over 200 words though, surely the questions are not included in the word count....}

 

Have a go at one or more of the problems below. They are all different!

It is useful to: 

A furniture maker has made 18 legs but can’t decide whether to make chairs, (with four legs) or stools, (with three legs). What possible arrangements can s/he make?

10:

1 chair, 4 stools     
with 2 legs remaining        
(1x4)+(4x3) = 4+12 = 16r2

2 chairs, 3 stools   
with 1 leg remaining          
(2x4)+(3x3) = 8+9 = 17r1

3 chairs, 2 stools                          (3x4)+(2x3) = 12+6 = 18

4 chairs                  
with 2 legs remaining         
4x4 = 16r2

1 stool, 3 chairs     
with 3 legs remaining        
(1x3)+(3x4) = 3+12 = 15r3

2 stools, 3 chairs                           (2x3)+(3x4) = 6+12 = 18

3 stools, 2 chairs   
with 1 leg remaining           (3x3)+(2x4) = 9+8 = 17r1

4 stools, 1 chair     
with 2 legs remaining         (4x3)+(1x4) = 12+4 = 16r2

5 stools                  
with 3 legs remaining        
5x3 = 15r3

6 stools                                            6x3 = 18

This problem can be approached using simple multiplication and addition, through trial and error.

18/3 = 6 therefore it is possible to make at least 6 stools, the remaining legs can be used for chairs when there is at least 4 or more.

18/4 = 4 remainder 2, so at least 4 chairs can be made with the remaining legs used for stools when 3 or higher.

Using division, the maximum amount of chairs and stools can be calculated and then you can work backwards to find all possible arrangements.

There are eighteen animals in the paddock. Some are sheep and some are emus. If you count the legs you find that there are 50. How many sheep and how many emus in the paddock?

Sheep have 4 legs, emus have 2.

50/2 = 25 animals if all are emus, 50/4 = 12 ½ sheep

18x2 = 36     14 less legs than counted

18x4 = 72              22 more legs than needed

Trial and error:

20 emus = 40 legs, need 10 more legs NO

15 emus = 30 legs, need 20 more legs – 5 sheep = 20 animals

17 emus = 34 legs, need 16 more = 4 more sheep = 21 animals

14 emus = 28 legs, need 22 more = 5 ½ more sheep oops

Try with sheep first:

8 sheep = 32 legs, need 18 more = 9 emus = 17 animals

9 sheep =36 legs, need 14 more = 7 emus = 15 animals

10 sheep = 40 legs, need 10 more = 2 emus = 12 animals

7 sheep = 28, 11 emus =22 =
50 legs

This can be checked using an algebraic formula:

ax2 + bx4 =50        a = emus, b = sheep

(11x2) + (7x4) = 22 + 28 = 50

OMG! Wish I could make it simpler:

Try using counters, 50 and group them into fours and twos until the answer is reached.

Look at the date or choose someone’s birthday. For example, today is the 30^th July then our number is 30.

1.      Create an addition problem with today’s number as a solution;

6 + 6 =              3 + 3 + 6 =             1 + 2 + 3 + 4 + 2 =

2.      Create a subtraction problem with today’s number as a solution;

24 – 12 =           30 -10 -8 =            32 – 20 =                         

3.      Create a multiplication problem with today’s number as a solution;

3 x 4 =              2 x 6 =                            

4.      Create a division problem with today’s number as a solution;

24 / 2 =            144 / 12 =                        

5.      Use today’s number in an interesting equation; and 

a + 4 = 12          26 – a = 12             a x 3 = 12              108 / a = 9   

6.      Use BODMAS (or BEDMAS or BIDMAS) ie order of operations with today’s number as a solution.

6 + (3 x  2) =     
132 + 8 x 6 – (31 x 4) + 44 - 88 =

Note:  I always thought I knew BEDMAS, but I have just learnt it…..  I always did it in the correct order but have just learnt that the division & multiplication are done in order from left to right and addition & subtraction the same… 

As a group we came up with a range of different ways to solve the problem – but all came to the same conclusion, that in our group of 5 people, there would be 10 handshakes. The majority of the group used diagrams with arrows to solve the question, whilst others used or suggested tables, lists or acting it out. Multiplication and division was used in problem solving and different language used to explain the process we used. At school some of us enjoyed maths and had positive experiences with learning problem solving whilst others did not feel they were taught or did not grasp these skills. 
- Chloe, Dinar, Kerry, Rachel & Emma

 

This week we came to different conclusions, most us believe the scaffolders and fashion students are numerate. They can use the correct mathematical skills in their chosen profession with initiative and confidence without consciously knowing they are using these skills.  However, contrary to this one student suggests that they are not necessarily numerate but simply know their job, if faced with a different problem could they apply the correct mathematical skills to solve this in any given context.

We all acknowledge that teachers need to:

·         Change the misconception of mathematics to focus on problem   solving, not simply sums on paper

·         Allow students to use their own strategies for problem solving.

·         Introduce mathematics and problem solving at an early age.

·         Connect mathematics and problem solving to the real world and make it relevant to students.

·         Support students to feel comfortable and confident with using new mathematical skills for problem solving.

·         Celebrate student’s achievements at all stages.

Being numerate involves more than mathematical knowledge, initiative & confidence through trial and error with technological knowledge to support findings. 

All 3 frameworks suggest that to be numerate one must be able to apply mathematics to “meet general demands of life at home, in paid work, and for participation in community and civic life.”  (Australian Association of Mathematics Teachers, 1997, p. 15)

 

 

Our teams opinion differed, most us believe the scaffolders and fashion students are numerate. They can use the correct mathematical skills in their chosen profession with initiative and confidence without consciously knowing they are using these skills.  However, contrary to this one student suggests that they are not necessarily numerate but simply know their job, if faced with a different problem could they apply the correct mathematical skills to solve this in any given context.

Teachers need to:

·         Change the misconception to focus on problem solving, not simply sums on paper

·         Allow students to use their own strategies for problem solving.

·         Introduce mathematics and problem solving at an early age.

·         Connect to the real world to make meaning.

·         Support students to feel comfortable and confident with using new mathematical skills.

·         Celebrate student’s achievements at all stages.

Being numerate involves more than mathematical knowledge, initiative & confidence through trial and error with technological knowledge to support findings. 

All 3 frameworks suggest that to be numerate one must be able to apply mathematics to “meet general demands of life at home, in paid work, and for participation in community and civic life.”  (Australian Association of Mathematics Teachers, 1997, p. 15)

 

Scott (2000)

The children are introducing mathematical experimentation to understand key skills that they can use and build on in the future.  They have the confidence and positive attitudes to use their mathematical knowledge (content) in the correct context to get things done.

Paige (2008)

The children are using a transdisciplinary approach combining different skills and knowledge to meet the functional dimension, sociocultural dimension and critical dimension.  The functional dimension is allowing them to use the correct skills for their needs at the time.

Goos (2007)

With positive dispositions children are building on their mathematical knowledge in context while using their current skills and available tools.  

·      Use open-ended questions.

·      Provide tasks that cater for the students abilities and ensure they are at suitable difficulty so that the students actually need to ‘problem solve.’

·      Plan tasks that that relate to real world contexts.

The examples showed the children participating in and developing numeracy skills through play.

Scott (2000)

 

In the examples the children have participated in numeracy tasks that relate to real world contexts (e.g. friends for lunch, we need more dirt). During each of the experiences the educators asked questions to extend the children’s learning and further develop numeracy skills. As the educators were interacting with the children during their experiences, I believe that this would assist in the children building their confidence.

-          Introduce mathematical language when talking in the classroom

-          Relating maths to the real world 

-          Creating activates that involve critical mathematic thinking, group work and problem solving. 

-          Ask open ended questions that allow students to think critically

-          Encourage ongoing exploration during mathematics 

The examples on Pg. 19 link to Paige (2008), where the four dimensions is used in everyday activities and tasks. Children use the functional dimension to engage with day to day tasks in a mathematical way, along with sociocultural dimension in determining how maths was used in the past. Children also used maths to make sense of their world, engaging in physical, political and spiritual environments in which we operate. 

ECE educators can encourage children by counting aloud and start conversations with them when they are engaging in play and relate it to mathematic skills in some way, such as discussing patterns, or getting them to estimate or predict as they play. 

Educators also have the opportunity to scaffold or extend students by asking meaningful questions that will develop problem solving skills by providing them with an open-ended question that requires thinking time and an opportunity to explore possible and different methods and solutions. 

ECE educators should also provide students with a range of different materials in their environment that both support and foster mathematical opportunities. 

The examples from the link showed children engaging with mathematical through play-based opportunities that educators were able to both observe, participate with and scaffold learning throughout. 

The examples also provided children with opportunities to connect the context to the real-world, and this is something that has come up a lot in our course content so far. The importance of children understanding the connections of mathematics to the real world and being able to use content in the correct context. 

 

Children are innately inquisitive, ECE’s can provide children with opportunities to use a variety of mathematical skills and build on their current kno wledge by:

·           Using open-ended questions 

·           Providing thought-provoking opportunities at challenging levels    to promote problem solving & build on their prior knowledge

·           Introducing and encouraging mathematical language & concepts 

o   More, less

o   cause and effect 

o   patterns 

o   estimation & prediction 

·           Relating maths to the real world 

·           Creating activates that involve critical mathematic thinking, group work and problem solving. 

·           Providing a variety of materials to encourage ongoing exploration 

·           Providing mathematically rich environments

·           Incorporating children’s interests

·           Recognisingthe mathematical skills used

 

Explore the examples of practice in the above link starting on p.19.
 Discuss these examples in relation to the numeracy frameworks we have explored so far.
 

The examples can be linked to all three frameworks however the one that stood out the most was Paige et al (2008).

Children use the functional dimension to engage with day to day tasks in a mathematical way within social situations through language, exploration, and participation. 

 

Five Queens

I believe that all 4 proficiency strands are being used by students to find the solution.

Understanding
Students need to understand exactly what needs to be done, as I know nothing about chess I had to read through the instructions a couple of times before I understood.  They need knowledge of horizontal, vertical and diagonal.

Fluency
Student need to think about possible ways to find the solution and if there is more than one mathematical equation that they can draw upon when doing so.

Problem-solving

This whole activity is a problem solving one, the answer is not obvious and students need to use their problem solving skills to find the solution.

Reasoning

Students need to think logically and analyse the problem before being able to come up with how they need to work and what skills are necessary in order to solve the problem.  

 How could you adapt it for younger or older students? What other contexts could be used? 

For younger students the grid could be made smaller 4x4 with 2 queens, this makes it a lot easier.  You could then increase the size as a way of scaffolding their understandings.

You could do it as an outside physical education game using squares of paper (easily moved) and people as queens.

 

 

Understanding-  To begin the game you have to know and understand what is going on. The students need to understand the mathematical knowledge that is required to complete the chess game. 

Fluency- Students need to choose strategies and procedures to follow. There will be trial and error, where students can reflect on what works and what doesn’t. 

Problem-solving- The whole activity is focused and based around the concept of problem solving. The students need to figure out where the queens need to go.

Reasoning- Children need to explain their reasons and thinking on how they reached a conclusion. This is shown in class discussions, where students had to think for themselves. 

-       A smaller and colorful grid enticing younger children to play the game. 

 

 

Students need to have an understanding of the directions horizontal, vertical and diagonal.

The students will need to decide on strategies to solve the problem.

The entire activity is based on problem solving. There is not just one single answer and the students will need to use their problem solving skills to work out where the queens need to be placed.

The students need to explain their thinking as to how they solved the problem.

 

The activity could be adapted for different age groups by changing the size of the grid and the amount of queens that need to be placed on the board.

 

The context could be changed to make it appeal more to younger students (e.g. trying to hide the chicken from the foxes). 

Understanding – Students need to have an understanding of what the game is and how the game works in order to play. Students also need to have the mathematical knowledge required for the skill level of the game. 

Fluency – Students need to develop and think of different methods and strategies, thus using a range of differing mathematical skills. This will be determined by their skill level and knowledge. 

Problem Solving – Students explore different methods and through trial and error will use problem solving skills and strategies. 

Reasoning – Students can express reasons for using particular strategies and understand the mathematical knowledge needed to do so. 

To simplify the game for younger children you could make the board smaller and with less queens. 

 

The year I STARTED UNIVERSITY, Margaret Thatcher died, at age 87. 2013

The year I HIGH SCHOOL, Barack Obama was reselected for his Second Term as US President.2012

 

The year I TRAVELLED ASIA, Donald Trump elected as the President of US.  2017

Dinar
I finished my high school the same year as Stephen King's novel, Cell, was published.

The year I moved to Australia, Julian Assange was arrested in London.

The year I had my first baby, Nelson Mandela passed away.

And these two are sequence of events that probably needs guessing which one happened first 😊
I was able to ride a bike.
I got my car license.

Attempt at putting Dinar's events in order: By Rachel

1. able to ride a bike

2. got car license

3. Finished high school: 2006?

4. Had first baby: 2013?

5. Moved to Australia: 2017?

In your learning teams, make a list of all the comparisons we use to describe the duration of an event or a cycle of events.

- Lunar
- Seasons
- Weather
- Months
- Days of the week
- Hours
- Minutes
- Time
- Significant events; birthdays, Christmas, easter, etc.
- Religious events
- Added by Dinar : Astrology positions and flowers or plants blooming seasons
- Years (added by Rachel)
- School holidays/school terms/semesters? (added by Rachel)

CYCLES  & EVENTS 
- Months
- Seasons
- Time
- Lunar

NOT CYCLES OF EVENTS 
- Birthdays

Now sort the units of comparison into two different groups, those that are based on natural events and those that are social or cultural constructions.

NATURAL EVENTS:
- Lunar
- Weather
- Seasons
SOCIAL OR CULTURAL EVENTS:
- Birthday
- Religious Occasions
- Time


Now compare your calendar to that of the Kaurna people. Record similarities and differences and discuss possible reasons for this.

- The Kaurna people's calendar has more events that are identified with natural events - things that will effect them, such as weather cycles, food etc. 
- Our calendar identifies many more social occasions.

For example, how ethically sourced are the 'cheapest' options? 

What constitutes "best" in this case?

Click here to access a range of other tasks. Complete at least 3 and upload your responses to the forum (individually or as a learning team). 

Again, when posting your responses, discuss the skills and strategies you employed. How are the chosen activities or problems a demonstration of numeracy? Link it to the frameworks and literature discussed so far.

Shall we split this one up this week? Work in pairs and someone on their own (I can do if need be) and then upload responses on here and then someone put them all together and post.

 See how you go…

Broke my foot

Started Uni for the first time

Got my drivers licence

Had 5 hour surgery after my 7^th ever netball game

Had my first child

Was $52.99

Now $47.99

You save $12 

 

But…

In another shop, it was also $52.99 but now has 12% off.

 

Product 2 is the better value when purchasing the product. 

How I worked it out…

$52.99 x 0.12 = $6.36

$52.99 - $6.36 = $46.63

Therefore, Product 1 has a total price of $47.99, where Product 2 total price is $46.63, which is lower. Thus product 2 is a better value. 

·      Started university 5

·      Met my Nan (my mums birth mother) for the first time 2

·      First family holiday to Queensland 1

·      Got my first job 3

(this is probably really easy to put in the correct order, but I had no idea what events to choose)

 
1.29120879% (rounded to 1.29%)

How I worked out the answer
23.5% ÷ 18.2% = 1.29120879% 

 

 

€2,580 

How I worked out the answer
14% of 3,000 

 

0.14 × 3,000 = 420

 

3,000 – 420 = 2,580 

The team members that used world events were quite easily put into the correct order due to current world event knowledge or with a little support from Google, for example:

·         In the year I started reception, the Olympic Games were held in Sydney.  (2000)

·         I finished high school the same year as Stephen King's novel, Cell, was published.  (2006)

·         The year I travelled Asia, Donald Trump elected as the President of US.  (2017)

 

Unless the dates were known, it was simply a matter of researching to find out.

 

However, team members that only listed life events were not all guessed correctly.  The task became a guessing game with expected times, due to cultural and common sense some events were put in the correct order.  For example, you would assume that one would learn how to ride a bike before getting a driver’s licence (although this is not 100% known).

To make it easier one could use photos of themselves or even use pictures of a common object that was ‘up to date’ at the time of an event, for example mobile phones, televisions, décor, furniture pictures or comment about their height or school year level/qualifications at the time.  Using things that automatically increase naturally over time.

 

$760 + $8.2308 + $8.3199 + $8.4100 

= 784.9607

= $784.96

(Whereas you had 784.967 making it $784.97)

 

(so it looks to be just a typing error?)

 

Suppose Cathy is able to make a repayment of $100 six months after the purchase and that this is her first repayment. What debt would she then have on her credit card? I got $710.74

 

Our difference in answers could just be because of the typing error in your last question?

 

13% ÷ 12 = 1.083% monthly interest rate

 

 

Month 1:

(1.083 ÷ 100) x 760 = 8.23 

760 + 8.23 = $768.23

 

Month 2:

(1.083 ÷ 100) x 768.23 = 8.32

768.23 + 8.32 = $776.55

 

Month 3:

(1.083 ÷ 100) x 776.55 = 8.41 

776.55 + 8.41 = $784.96

 

Cathy will have a debt of $784.96 after 3 months

 

 

Month 4:

(1.083 ÷ 100) x 784.96 = 8.50

784.96 + 8.50 = $793.46

 

Month 5:

(1.083 ÷ 100) x 793.46 = 8.59

793.46 + 8.59 = $802.05

 

Month 6:

(1.083 ÷ 100) x 802.05 = 8.69

802.05 + 8.69 = $810.74

 

$810.74 - $100 repayment =  $710.74 debt

 

13% / 12 months = 1.083% per month on total balance owing for that month…

 

The 1^st months interest is 1.08%, with no repayments made for each month, the interest rate basically doubles for the principle, 2^nd month 2.15%, 3^rd month 3.29%.  This interest rate applies for the balance owing each month starting at the original amount of $760.00.

 
The below is a table in word....

 | Month | Balance | Interest added | Percentage
| 1 | $768.23 | $8.23 | 1.08%
| 2 | $776.55 | $16.55 | 2.15%
| 3 | $784.97 | $24.97 | 3.29%
| 6 | $810.76 | $50.76 | 6.26%

 

 

$784.97

 

 

$710.76

 

 

This is because with debt, interest is added to a negative figure and with savings, it is added to a positive figure.

 

 

The debt will not decrease unless more than the added interest is paid, the more Cathy pays back each month (on top of the interest) the quicker the loan will decrease. 

 

 

Either wait until she has saved more money or endeavour to find a loan with an interest free period and try to pay it off within this interest free period.

 

•  When might you engage with this product/ service, for what?

•  What the best option is and justify your decision. 

•  What mathematics do you need to make this numeracy decision?

I'm just confusing myself though,,, would anyone like to have a look/play and give me your feedback......
I should have gone phone plans as they are less confusing....... : (

The make a critical statement by addressing statistics in a way everyone can understand, numeracy and critical thinking are not necessarily a requirement.  The topics are of interest to a wide range of ages regardless of education, social status, cultural and religious groups.  Overall it is very thought provoking.

It makes us think about the differences between us, breaking down the statistics to simplify how we and others live in the world and informing us of what is going on in the world around us.  Many of the statistics are very confronting and hard to relate to, however, this would vary from person to person.

It is very interesting, I do wonder how accurate it is though.  I did go into another world clock for comparison and they were slightly different, http://www.cosmosmith.com/population_clock.htm, population differed by around 25,000,000.

I thought it would be good to look at two stats that were similar:

Stat  | Growth/Yr  | Week  | Day  | Hr 
Road Injury Deaths  | 1,423,355  | 27,279  | 3,897  | 162 
Murders  | 1,388,069  | 26,602  | 3,800  | 158 

 

This to me is quite alarming, not just the actual number of deaths through road injuries and murders but the sheer numbers, breaking it down to a daily figure makes it even more alarming.  

In Australia, they announce the road toll in the media often.  However, murders are only mentioned in the news and there isn’t such an emphasis placed on the figures.

According to the Australian Bureau of Statistics, in 2016 227 murders were committed in Australia, and 619 road deaths.

This equates to:

 

 

They make a critical statement by addressing statistics in a way everyone can understand, numeracy and critical thinking are not necessarily a requirement.  The topics are of interest to a wide range of ages regardless of education, social status, cultural and religious groups.  Overall it is very thought provoking.

It makes us think about the differences between us, breaking down the statistics to simplify how we and others live in the world and informing us of what is going on in the world around us.  Many of the statistics are very confronting and hard to relate to, however, this would vary from person to person.
It also informs us to be critical in interpreting data around us. We might understand the meaning of those numbers provided in the video, even translate them into mathematical concepts such as percentage, average and probability. In addition to that, the most essential aspect is how we incorporate the knowledge with other areas such as culture, philosophy and justice, to sharpen our understanding and make meaning of the social world.

It is very interesting, I do wonder how accurate it is though.  I did go into another world clock for comparison and they were slightly different, http://www.cosmosmith.com/population_clock.htm, population differed by around 25,000,000.

I thought it would be good to look at two stats that were similar:

Stat  | Growth/Yr  | Week  | Day  | Hr 
Road Injury Deaths  | 1,423,355  | 27,279  | 3,897  | 162 
Murders  | 1,388,069  | 26,602  | 3,800  | 158 

 

This to me is quite alarming, not just the actual number of deaths through road injuries and murders but the sheer numbers, breaking it down to a daily figure makes it even more alarming.  

In Australia, they announce the road toll in the media often.  However, murders are only mentioned in the news and there isn’t such an emphasis placed on the figures.

According to the Australian Bureau of Statistics, in 2016 227 murders were committed in Australia, and 619 road deaths.

This equates to:

Focus: Road crash and Murder death rates 

It is predicted that 156,936 people will die today and 384, 701 will be born, therefore around the world there will be a gain of 227,765 people. The death rate is shared among a variety of reasons, this includes; Cardiovascular Disease, Cancer Deaths, Pneumonia Deaths, HIV/AIDS Deaths, Road Injury Deaths, Murders, Suicides, Malnutrition Deaths. However, the data being communicated in this instant is the amount of people that will die from road crash injuries and deaths, and people who are murdered. 

The data collected calculates the amount of people who have died since the beginning of the year, where it continues to rise. According to Cosmo Smiths world clock, it is expected that 1,423,355 people will die per/year from road crashes, and 1,388,069 people will die from murders. The entire world population is considered during this world clock. 

´The neutrality of data – D’Ambrosio (1984, 1990, 1997), an ethno-mathematician describes mathematics as being neither good nor bad but nor is itself or its use neutral and this view certainly holds true for data;
The fact that the data is resourced worldwide; thus it is culturally unbiased. However, due to dynamic nature of much data it collects, the accuracy is questionable.  

The world clock allows you to see the times all over the world and make comparisons.  The statistical data is basically presenting a live picture of what is happening in the world, the filter options allow us to see total statistics in different time frames, year, week, day & hour.

 

The fact that the number of deaths due to road accidents and murders are broken down into a daily, and even hourly figure was quite alarming. This data therefore raised the question on what could be done to reduce these numbers?

 I think it would be interesting to add birth and death rate data specific to gender and age groups as well as causes of death, this would make it easier to identify and record ages of death rate as well as recording and identifying causes of death, such as infant mortality with potential causes such as S.I.D.S. 

·         the data’s effectiveness in communicating key ideas;
Facebook: Data is everywhere on Facebook, it can definitely communicate key ideas in many different formats.  However, the effectiveness would vary as what each person views is a personal choice.  

Facebook data can influence peoples choices and opinions, for example:

·         Shopping online.

·         Comparing products.

·         World views.

Email: Emails are directed on a personal basis and key ideas are often communicated effectively.  With the exception of spam where you can receive a lot of communication of no interest, it is up to the recipient what they choose to read and their personal perception of ‘key ideas’.

Weather apps: Depending on the particular weather app, some are simply communicating key ideas whereas others include a lot of extra information, some of which can be confusing.  Again it is up to the reader and what they are looking for as to its effectiveness.   

·         do you think any information is  lost in organising the data;
(chloe)
Facebook: Yes, data is lost through Facebook. Sometimes, there can be so much information to take in while scrolling through Facebook that much of the information is lost through the process. 

Email: Information through email isn’t lost when organising the data. Your emails are sent directly to you, where they are a form of communication and no information is lost. 

Weather apps: When a person wants to know what the weather is going to be like, they open up a weather website or app. The information in this piece of data isn’t lost, it is used by many to calculate weather updates and to prepare themselves. 

·         the accuracy of data you read and how number is used. (Rachel)
The data posted by anyone on Facebook can’t always be considered as accurate and the source of the information should always be checked. 

With many people owning a smart phone, weather apps are used everyday to check the weather conditions and prepare for the day. A weather apps data is a prediction and normally quite accurate, but could change. There could also be some slight differences between apps. The majority of the data from a weather app is in number form (e.g. the temperature forecast, percentage chance of rain, UV index, etc.).

Continuous Data

Information that can be measured on a continuum or scale. 

Examples of Continuous Data - Emma 

·         data that impacts on people’s everyday lives and they have control;
I answer this on power point format

·         data that impacts on people’s everyday lives and they have no control;

·         data that dictates specific actions – which actions?;
(Chloe)

This data provides actions to viewers stating you should not smoke. It provides a list of harmful effects on the human body that are very hard to ignore when reading the data. 

 

·         data that is misleading, explaining why it is misleading and how it can be misused, suggest a different way of presenting this data so it is no longer misleading.
(Chloe)

This piece of data is misleading as by looking at the graph you think that the Times is doubling the Daily Telegraphs sales, however by looking at the scale you can see that the Times is only winning by 10%. 

 

·   Can we relate these discussion to the Paige, Lloyd and Chartres (2008) framework? (Rachel)

Functional dimension: Data is used in everyday tasks. 

A weather app is a good example of this as the data provided is used to prepare for the upcoming weather conditions.

 

Sociocultural dimension: The way that data is used depends on cultural or social contexts.
When we look at the weather forecast is displayed in Australia’s temperature scale; degrees Celsius. In the US Farenheit is used to record the temperature, therefore a weather apps data would be different.

 

Most of the examples of data our group looked at involved the used of technology.

 

The weather app and the smoking health risks are good examples of this.

Post your summaries here (group or individual): You might like to consider a creative approach to your presentations. For example creating a collage of your data sets to illustrates the themes above - up to you! Please ensure your work addresses all of the task requirements. 

 

In your learning teams, access the Australian Curriculum: Mathematics, the Early Years Learning Framework and the Early Years Literacy and Numeracy Framework:

Firstly, each of you, read the overview pages/ general introduction and structure pages for each document; In particular, highlight what you consider to be the key elements of the curriculum/ learning frameworks. How are they the same? How are they different? I want you to think about the link between the general capabilities/ proficiencies in the AC and the Outcomes/ Numeracy Indicators in EYLF specifically here. 

Similarly, read through the overviews of the four proficiency strands and highlight what you consider to be aspects of thinking mathematicallyand aspects of mathematics content and conventions.

SECOND GROUP TASK (9.3)

Compare the PAT-M to your analysis of the PISA, TIMSS and NAPLAN samples: 

-          What is being assessed in these?

-          How is this different to the other “tests”?

-          How does this align with your discussion to date re: Numeracy V’s Mathematics?

1.     Summarise each document to give the main essence/overview. Highlight how important it is for you to have this overview.

Belonging, Being & Becoming:
The Early Years Framework highlights the importance of play in a child’s early years. It emphasises the importance of a child’s physical, cognitive and emotional development through a range of play based learning activities. 

Literacy & Numeracy Indicators:
The literacy and numeracy indicators aim at teachers or educators teaching at a preschool age. This document links with EYLF and aims at helping teachers plan, extend and assess their students work. 

Australian Curriculum: Mathematics:
This document/s highlights key learning outcomes in each year level in all mathematical strands. Educators must be familiar and have the Australian Curriculum in order to plan, teach the curriculum outcomes, observe their students learning, and assess children’s learning and their development in mathematics. 

2.     What are the core aspects of thinking mathematically and aspects of conventions and skills evident throughout these sections?

Sorry guys, I have no idea what this question is asking ??? 

3.     What are the overlaps that you picked out and how does this compare with your reading (double journal entry) of Zevenbergen? 

Both the Early Years Framework and the Australian Curriculum compare as similar to Zevenbergen’s definition of numeracy. They all state the importance of learning environments that promote problem solving and that nurture imagination and eagerness. By supporting these factors, it assists in developing positive disposition towards mathematics and numeracy.  
Zevenbergen (2005, p. 4) highlights the importance of numeracy in developing mathematical skills that are used to solve every day situations. In relation to the literacy and numeracy indicator, it similarly shows aspects of children’s learning during everyday experiences, and how educators can prompt and expand children’s mathematical concepts 

 

1.       What is being assessed in these?
Number and Algebra, Statistics and Probability, Measurement and Geometry 

2.       How is this different to the other “tests”?
It seems to be aimed at younger students as the text is larger and more spaced out, which is also accompanied by cartoon figures. The questions are short. There are no real-life situations, which is what the PISA test focuses on. 

3.     How does this align with your discussion? (Numeracy v Mathematics)
I believe that this test requires a balance of both mathematical and numeracy knowledge, however, I would say there is more of a focus on Mathematics compared to Numeracy. 

 

 

 

The EYLF aims to give children an opportunity to extend and enrich their learning in primarily play-based situations. The EYLF recognised the importance of communication and language, including in numeracy when providing opportunities for children to develop their skills in this area.

The Literacy and Numeracy Indicators are used for teachers and ECE workers to inform their planning, teaching and to monitor the development of children’s literacy and numeracy. The indicators connect with the EYLF and the information recorded helps support the transition into school. The indicators allow teachers to recognise and describe, plan, monitor and identify children’s numeracy (and literacy) understandings and learning. It also allows opportunities for educators to share and report and reflect to improve upon their pedagogies. 

The ACARA document provides an overview of what expected of each individual year level. The proficiency strands being; understanding, fluency, problem-solving and reasoning and are seen as a fundamental part mathematics across all content strands. Teachers need to be familiar with the document in order to plan for effective teaching that reaches each of the proficiency strands. 

 

 

 

Understanding 

 

Fluency 

 

Problem-solving 

 

Reasoning 

 

The Framework provides broad direction for ECE educators to facilitate children’s learning. These expectations are communicated through the following five Learning Outcomes: 

 

-       Children have a strong sense of identity 

-       Children are connected with and contribute to their world 

-       Children have a strong sense of wellbeing 

-       Children are confident and involved learners 

-       Children are effective communicators 

 

The Early Years Learning Framework and the Australian Curriculum provide a foundation upon which students can actively engage with the learning in their environments. The EYLF is an integral part in transitioning into the Australian Curriculum, providing the foundations of learning for children. The EYLF, ACARA and the Numeracy and Literacy Indicator all support the intention of providing learning environments and content that is engaging and ensures children are prepared for the real world, thus connecting the content of what is learned to the real-world. Aligning with Zevenbergen’s article, highlighting the importance of allowing children an opportunity to learn in environments that are supportive and nurturing and provide opportunities for children to learn a range of different problem-solving skills and strategies. Like the EYLF and the ACARA document, Zevenbergen also highlighted the importance of creating an environment that fosters a positive attitude towards mathematics. 

 

 

What is being assessed in these?
PAT-M assesses; Geometry & Measurement, Number & Algebra and Statistics & Probability.
How is this different to the other “tests”?
The content of what is being assessed is more closely in line with the Australian Curriculum.
How does this align with your discussion to date re: Numeracy V’s Mathematics?
The PAT-M test measures both numeracy and mathematical abilities. I think it uses examples of real-life situations as well as mathematical concepts.

Number & Algebra, Geometry & Measurement and Statistics & Probability.

The questions are quite short compared to the others and isn’t divided into sections. It relates closer to the Australian Curriculum.

I feel that the PAT-M test assesses both Numeracy and Mathematics knowledge and skills. 

In your learning teams, access the Australian Curriculum: Mathematics, the Early Years Learning Framework and the Early Years Literacy and Numeracy Framework:

Firstly, each of you, read the overview pages/ general introduction and structure pages for each document; highlight what you consider to be the key elements of the curriculum/ learning frameworks. How are they the same? How are they different? I want you to think about the link between the general capabilities/ proficiencies in the AC and the Outcomes/ Numeracy Indicators in EYLF specifically here. 

Similarly, read through the overviews of the four proficiency strands and highlight what you consider to be aspects of thinking mathematically and aspects of mathematics content and conventions.

ACARA’s aim is to provide teachers with the proficiency strands to provide students with fundamental numeracy skills for the future.  Including essential skills and knowledge of numbers, measurement, geometry, statistics and probability.  It outlines the need for numeracy skills in a range of disciplines developing mathematical understanding, fluency, reasoning and problem-solving skills in familiar and unfamiliar situations.  

The 4 proficiency strands:

Understanding – introduces children to connections, numbers and calculations.

Fluency – involves counting in sequence, patterns, comparison, language of chance and duration of time. 

Problem solving – applying their skills and knowledge through modelling, sorting, counting and using literacy skills to discuss, find, compare and investigate solutions.

Reasoning – by using, current knowledge, understanding, fluency, problem solving children can make sense of and show comparisons, calculations and explain processes.

Each of the 4 proficiency strands encourage children to think mathematically across various content and contexts.  They should be included simultaneously across the curriculum, allowing students to gain an understanding of the importance of numeracy and what it means in their individual world.

Are to be used by preschool teachers to support planning and learning, to monitor and inform/discuss children’s development with parents and families, aligning with ACARA, this information also assists in and supports school transition.  It highlights the importance of positive learning environments, literacy and numeracy knowledge and skills as a foundation for future learning.

The 4 indicators:

The child and the Early Years Learning Framework – at the centre of the chart identifies children’s individualities and current knowledge.

Learning processes – acknowledge and support a child’s individual knowledge and learning processes, in numeracy these include noticing, sorting, patterning, wondering, communicating, reasoning, generalising, visualising and comparing.

Indicators – there are four indicators for both literacy and numeracy.  Numeracy indicators centre around the concepts of exploration, measurement, analysis and understanding of children’s worlds.

Key elements – there are key elements for each indicator providing measurable aspects for each.  They can be used by teachers to ensure the indicators are being met.  

Working in partnership with parents and families supports children’s learning and allows teachers to target specific outcomes for each student according to their current knowledge and dispositions.  It aims to ensure all children are ready for transition to school with the necessary foundations for learning.

The indicators allow teachers to acknowledge and measure and encourage numerical understanding and mathematical thinking skills.

The EYLF acknowledges the early years as an important learning and developmental stage in a child’s life.  Centred around relevant and meaningful play based learning it aims to enrich and extend children’s learning across the language and literacy, numeracy, social and emotional and ethical and cultural skills.

Children begin to understand key numeracy concepts through counting, organising, investigating, exploring, generalising and comparing using trial and error and current knowledge when problem solving.  Given the opportunity to ask questions, and respond to open ended questions they engage in critical thinking by modelling, demonstrating, speculating, explaining and sharing through social play based experiences.

Educators can use intentional teaching strategies by keeping children’s current knowledge, abilities, interests and overall learning in mind.  This enables teachers to provide positive learning experiences for children, and scaffold on their learning.  Children use mathematical thinking when problem solving through play in numerous ways from spatial awareness to counting and sorting while sharing.

Given relevant and meaningful opportunities to problem solve in positive learning environments is highlighted in each document, including Zevenbergen.  Each of the documents can be linked for continuity of teaching and reporting on children’s current knowledge and achievements throughout each stage of their learning journey. 

Early Years Learning Framework:

The Early Years Learning Framework (EYLF) highlights the importance of play in a child’s physical, cognitive, social and emotional development.

 

Literacy and Numeracy Indicators:

The Literacy and Numeracy Indicators links to the EYLF and are used to inform the planning, teaching and monitoring a child’s development of literacy and numeracy in a preschool setting, which will help support the transition to school. 

 

Australian Curriculum: Mathematics:

The Australian Curriculum: Mathematics provides the learning outcomes of what is expected for each year level. Teachers must understand and use the curriculum when planning and conducting lessons and observing and assessing students’ development.

 

 
I didn't understand this question either.

The Early Years Learning Framework and the Australian Curriculum aligns with the Zevenbergen reading as they all highlight the importance of creating supportive and nurturing learning environments that allow children to develop problem solving skills and a positive disposition for mathematics.

PAT - M

What is being assessed in these?

The Progressive Achievement Tests in Mathematics purely assesses year 1 -10 student’s mathematical skills and understanding in:

There are a series of PAT tests for other areas of the curriculum.  Results support teachers by indicating individual student’s skills and abilities from test to test for future teaching.

How is this different to the other “tests”?

The Pat-M test is all multiple choice answers and includes formulas as well as some numeracy type testing.

How does this align with your discussion to date re: Numeracy V’s Mathematics?

I believe this test is more mathematically focused, it relies more on knowledge in comparison to a deep understanding of numeracy.

The site is primarily about the assessment for common misunderstandings and provides tools for teachers to facilitate assessment along with advice about what the results indicate about that student’s understanding. It also provides some information of key addressed in each level of Mathematics in middle school. The tool emphasizes on its benefits to identify students who are under-achieving and in need of extra attention. The ideas of what mathematics skills are missing on each level will assist teachers in extending the focus of attention from the individual who needs support on their further learning. The tool can also be categorized as a formative type of assessment where it can be conducted on random days and on any type of circumstances, not in a formal test environment; thus, students are more likely to be relaxed and reflect their maximum capacity during the assessment.

The website doesn’t give information of how it is conducted in detail, only a brief background and cases as examples. It doesn’t relate its position to the ACARA’s framework and seems to be limited only the scope for Victoria state wide.

(There was actually 6 levels listed but I only did levels 1-3 as it would've taken up more than a page)

 

Assessment for Common Misunderstandings highlights the importance knowing and understanding student’s current knowledge to scaffold on their learning.

It provides tools in the form of diagnostic assessments for each Level of the Victorian Essential Learning Standards (VELS).  

The assessments support teachers with the information of individual student knowledge to support their learning.  Each tool assesses key ideas which are important to further learning.  

It addresses many misconceptions in numeracy and allows teachers to pinpoint if and where students are lacking in knowledge as well as their individual learning strategies.