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Computational Thinking and Geometric Reasoning – Year Seven Mathematics

Schools are increasingly being asked to integrate digital literacy across the curriculum. In this article I will share how I have used the Python language to develop my students geometric reasoning.

Before you read any further, be warned this is coding with Python 101. If you are in a High Tech High with digital technologies well established across your curriculum, then this read will not be for you. But if you are in a traditional Australian high school, and are looking for a practical way to embed digital literacy across the curriculum, then the mathematics class may be just the place to start.

In the last few years I have immersed myself in the development of integrated STEM curriculum in my school. I am passionate that digital literacy should be embedded across the curriculum, just as numeracy and literacy are. It has however been a long time since my computer science units at university and I am trying to get my head around how to best make this a part of my normal teaching practice.

When Australian Education Ministers signed up to the Melbourne Declaration on Educational Goals for Young Australians in 2008, they recognised that schooling should support the development of skills in cross-disciplinary, critical and creative thinking, problem solving and digital technologies, which are essential in all 21st century occupations. Computational thinking, logical reasoning and algorithmic processes to solve problems naturally belong in the mathematics classroom, hence creating the ideal environment to begin the integration of digital literacy in a high school. In this article I will share how I have used some free online resources to develop a series of maths lessons to develop students computational thinking.

Year 10 Mathematics, Year 11 Applications and Methods students are required to solve trigonometric problems that involve directional language and bearings. It is my experience that these have always been difficult problems for students to solve. 

The example is taken from my year 10 test on non right angle trigonometry.

Stephen runs a distance of 10km in one direction, and then turns through an angle of 25⁰ and runs for another 6km. How far is Stephen from his starting point?

20171010_153051

While many of the students in my class could use the cosine rule, nearly all the students read the angle as interior. Students continually find directional language and bearings questions difficult and fail to draw appropriate diagrams from the instructions. As teachers we give them the follow on marks but really the deeper understandings of directional language has not been demonstrated.

The year seven mathematics curriculum requires students to develop their geometric reasoning using angles, transformations and rotations. It is with this year group that we began using computer programming with Python to develop a stronger foundation in students geometric reasoning.

Activity 1 – WHICH WAY?

Coding a computer requires the programmer to give a clear set of instructions. Our  year sevens were able to use computational thinking in their physical environment, by finding a variety of shapes on an obstacle course. With one student blind folded, students had to rely on the directions given by their partner. Using directional language of angles, rotations and bearings they moved around the basketball courts collecting their shapes.

This activity was taken from the Literacy and Numeracy Week resources. There is also a range of digital literacy resources available. Promoted across the country in September, you may want to use this as an opportunity to promote digital literacy and numeracy in your school.

Activity 2 – DESIGN A FLAG

The Python Turtle application is ideal for developing student understanding of directional language and geometric reasoning.Python is free to download and has a drawing module in it’s library called turtle that is part of the standard installation. To use it, you need only type: from turtle import *

FlagDesign a Flag is designed to give students their  first experience in programming, and has been specially developed by GROK learning for the HOUR of CODE . The HOUR of CODE is a global movement to get more students coding. In this activity students use Python’s turtle module to draw flags from around the world!

You can participate in the tutorial through GROK’s online platform, it is iPad friendly and the instructions are really easy to follow.  You can sign up for a free teacher account to access the full range of GROK learning resources. To use this application you do not need to have downloaded Python.

My HOUR of CODE activity had been chosen and I had linked it to the Year 7 Maths program. I had worked through some of the Python courses available on my free GROK teacher account. I was ready to integrate digital learning in my mathematics class…. well maybe not.

With 30 twelve year old students trying to access the internet and register an account, we didn’t get very far in our hour of code. Determined I  could get my year sevens coding in Python. I decided I would go offline and use Python idle directly.  Ask your I.T department to upload Python to your school computers.

Coding with Python is not suitable for iPads.

So I snipped the Hour of Code lesson into a Word document that I could hand out to students. I hope I don’t get myself in trouble for this admission but as the one hour lesson was written as a free resource, I think I am safe with this admission. In the document students were given explicit instructions how to open a new Python file and how to write code to draw particular flags. You will find the student copy in the resources at the end of this page.

Students worked in pairs on their programs and completed the task by designing their own flag. The year seven students loved designing their flags in Python and all students had a level of success in their journey. While not all students are going to go on to be computer programmers, all students can be given an opportunity to develop simple programs.  Mathematicians use computer programs to solve problems, a deeper understanding of mathematics can be attained by embracing the technology.

Coding doesn’t have to be a solo activity, let your students work in pairs

Will using Python turtle improve the geometric reasoning of these students in future years? Only time will tell, but I love the the self regulated nature of using turtle,  and the programming activity required them to think of exterior and rotational angles in a much more practical way.

Will John Curtin College continue to develop activities that incorporate Python in their maths classes?  Most certainly…one of my year 8 students pointed out to me why does his math teacher use a Venn Diagram when he can just write a quick piece of code to sort the data? We have only just begun this journey with our year sevens, it is exciting to think where we may be five years from now. Watch this space as I share other applications of digital technologies in maths. I would also love to hear how other high schools are using Python across the curriculum.

Will we be ready when the primary school STEM gen get to High School? I hope so, it is a more difficult task for secondary teachers to start a cross-disciplinary approach but it can be done in the system we have.

Change occurs slowly, teacher by teacher, conversation by conversation.

“The world as we have created it is a process of our thinking. It cannot be changed without changing our thinking” Albert Einstein

 

Resources

obstacle-course_2017            Flags with Turtle DT Activity

Data Science – what does it look like in the classroom?

Data Scientist, the sexy new word for a statistician with programming skills?

Data scientists are highly sort after in industry and even though it may sound like some sort of a mystery science, data science is really just good old statistics with a touch of programming.  Most data scientists use some Python coding, however for students in the classroom, using an Excel spreadsheet is a sufficient enough introduction.  If you are an educator, especially a teacher of primary or secondary mathematics and your not quite sure what a data scientist is, I suggest you watch Data Science in 60 seconds.

So how do we get our students analysing big data in schools?

CENSUS AT SCHOOLS

The Government Statistics Departments of  Australia, Canada, New Zealand, United Kingdom and the United States all have there own version of Census at School. Census at School is a free resource that allows students to download other student’s data on an Excel spreadsheet. You can find links to each of these pages at the end of this article.  On the Australian site you can download a sample of up to 200, from the U.S site I was able to download a sample of 1000 students, 200 from each country. Samples of this size are   big data for students.

If you are a user of Google, Facebook, Apple or any one of these big companies then you are aware of how valuable a resource your data is. When you tick I agree to use that new app, website, search engine or server then your personal  information has been signed over to that company. By starting this blog I have agreed that my personal details  are owned by whatever platform you are reading this on.

BIG DATA IS GOLD

In Western  Australia the Kalgoorlie Gold Rush  transformed our Australian colony. Big data is here, ready to be analysed. We just need the people to  mine it

If we are to analysis and communicate statistics well, then we should be using technology.  I have found no possible reason for continuing to draw a pie chart by hand – its like long division, why?

From slide rule to calculator, it’s time for mathematics educators to accept that big data and technology are here to stay. Teaching children how to understand, sort, analyse and communicate data is much more important.

Why draw a pie chart by hand when an infographic is the most popular way to communicate statistics today?

So how does the Western Australian  Curriculum suggest we apply the statistical investigation process to real world tasks.

  1. Clarify the problem and pose one or more questions that can be answered with data                                                            

    The wonderful thing about working as a data scientist is that your skills are so transferable. Your students can choose a problem, a question that is relevant to them. Encourage collaboration between your learning areas by asking your science and humanities colleagues what content theme they are currently doing. The Australian Census at Schools website has a vast array of age appropriate ideas and resources that are lined up to learning areas across the Australian Curriculum.  I do suggest though that if you leave it open to students to choose a problem, look at it carefully to make sure that the question they choose is appropriate for your learning intentions. For example in the Yr 7 investigation I use I want students to recognise outliers and find the mean, mode, median and range. So I ensure there is a categorical and numerical data component to their question. 

  2.  Design and implement a plan to collect or obtain appropriate data                

    Students choose a sample that represents their problem. I tell my students “the bigger the better and repeated samples helps remove bias”. Working in a team or as a whole class,  each student can collect their own sample to analyse. The data sample is downloaded using  RANDOM SAMPLER on the Census at Schools website.  It is very easy to use and you just need to tick I agree that the data will be used for the sole purpose of teaching and learning.  If the students don’t tick the questions they want in their sample they end up with a very large spreadsheet of data. Personally I love that experience, but when students first see big data in this form it is overwhelming for them. This is when you refer them back to stage one – what is their problem and then delete any information that is not relevant to that. Saving the original, just in case there is a change.

  3. Select and apply appropriate graphical or numerical techniques to analyse the data 

    Now comes the the fun part –  lets start programming. I am going to assume as teachers you have all had some experience with spreadsheets using it as a tool for recording students results. Excel is a powerful application and is a great way to introduce programming language to students.  Get your students to first sort the data, they can find averages, measures of spread, counts using the predetermined functions for example =average(B1:B200) or =countif(A3:A1000,”yes”). I can guarantee that their first graph will be dodgy as students tend to just type insert chart without much thought to the variables they use. Your role as the teacher is to assist them in choosing appropriate graphical and numerical analysis for their data set. Youtube comes in handy if you need help using Excel.

  4. Interpret the results of this analysis and relate the interpretation to the original question

    So now the analysis is complete, what does the data say? Did it answer the original questions? Encourage your students to critique their analyses and conclusions. get them to identify any potential weaknesses in the analysis and make suggestions for  improvements. Over analysis is not always best, and it is OK to say there is no conclusion from the data they analysed.

  5. Communicate findings in a systematic and concise manner.

    Students write a report or display in a PPT to communicate their findings. They don’t include all of the raw data. I have had a little play on  www.canva.com and I really love how easy it is to create a really cool infographic. A little too easy as mathematicians know that 72% of statistics are made up on the spot.  So next year when I do this investigation again with my Year Sevens I am going to STEAM it up a little more by asking the Technology and Arts Media teachers if they can help create the Infographics.

I hope that you have found this article useful. As a secondary mathematics teacher,  I use this blog to share how my school has implemented STEAM education across the already existing curriculum. Unfortunately, due to funding cuts by previous Australian Government Administration the last Census at School survey was carried out in 2014 and the two administrators removed. If you feel that this resource could be useful and relevant to you implementing STEM Education practice in your school, could you please join me in lobbying the Australian Federal Government to reinstate the program.

  Resources

Census at School OZ

Census at School Can

Census at School NZ

Census at School UK

Census at School US

John Curtin College Statistics Investigation

Sustainability – A good place to start

Change doesn’t happen overnight, it always starts somewhere. A conversation, an idea …. a message in a bottle….

Lets reduce our plastic waste..

blue_bottles_web

Waste Wise launched it’s Message in a Plastic Bottle   program at John Curtin College of the Arts in 2015. The curriculum guide covers English, Maths, Science, Geography and Leadership. I was approached to trial the maths’ activities with my two year 7 classes by our  Waste Wise School co-ordinator and sustainability guru science teacher. With the introduction of Year 7’s into high school in WA in the same year , I was excited about trialing a program that was cross-curricular and authentic. STEM wasn’t the buzz word at this stage, but as educators we have always known that learning experiences are improved if they are transferable.

Year One2016

  • We trialed the lessons with two year 7 mathematics classes and some science classes. It was easy to follow, relevant, with very little preparation required by me. Big tick.
  • My students informed me they were also learning about water in their geography lessons. Another big tick –  its a part of the Yr 7 H.A.S.S program anyway
  • With the trial getting two two big ticks – we decided we would expand the program  to the other learning areas. Four teachers from the four learning areas attended a free workshop run by Waste Wise Schools. With time to collaborate, we decided to deliver the program in term one. This would used in English to support the students persuasive writing techniques, before the NAPLAN testing in term two.

Year Two – 2017 

  • Message in a Plastic Bottle is placed in the program for all year 7 Maths and Science classes. H.A.S.S and English trial the program.
  • It is noted by the English teacher trialing the program that the integrated approach has helped improve students’ persuasive writing, and many used it in their NAPLAN writing. Another big tick.

Year Three – 2018 

  • We are inviting Waste Wise Schools to visit our school to deliver a workshop to new year 7 teachers.
  • We plan to collect data to monitor what students have participated, yes, while it is in the program, we are a real school and there is always those teachers who run out of time because it wasn’t in the maths and science textbook.
  • We will have a closer look at the work produced by students in English and use this as the measure of success to encourage other staff to continue the program. This data can then be shared with schools like yours.

So in conclusion, these government initiatives and educational programs are free and they are happy to come out to your school to deliver professional learning.  This is a John Curtin College of the Arts example, of how we started to collaborate across the learning areas to bring STEAM learning practices into our school.

The world is producing too much waste. It is not sustainable, and it will not be fixed by some person in an ivory tower somewhere. Change happens through people. I have learned so much by participating in this program.  I didn’t really think to much about the amount of plastic I was using prior.

What did I learn? There is no difference between bottled water in Western Australia and the quality of our tap water. Often the 2000 times more expensive bottled water you buy is just tap water. The environmental impact and the amount of waste produced by bottles of water is mind blowing – I highly recommend you watch the video. Twenty – First Century Waterfall

Consider the message that will be sent via NAPLAN when 12 year old children start writing about plastic water bottles in this standardised test.

THINK GLOBALLY BY ACTING LOCALLY

Resources

Message in a Plastic bottle PDF File Resources  Years 7 – 10   Message_in_a_plastic_bottle_WEB

John Curtin College English Year 7 Persuasive Writing Booklet  miapb_persuasive_writing

Student Science Sample

My maths class

Hello World..

How exciting, my own BLOG page , WOW didn’t in a million years expect the journey of life to bring me here, but that is the wonderful thing about life and mathematics. When faced with a problem, a mathematician uses algorithmic thinking and logical steps to find a solution. My problem is that I am a passionate secondary mathematics teacher in a College of the Arts  – yes think FAME… So I hear you say, how is that a problem?

Well in a way it’s not. I have an amazing group of creative students I work with every day. Students are selected to this government school because of their gifts and talents in the Arts. It is also a traditional school, with traditional buildings and traditional industrialised educational silos – i.e Maths, Science, English, Phys Ed, Technologies etc. Students are well tested, you should just see the entry selection process,  and curriculum content and tertiary entrance exams  drive them to succeed.

So that’s the school I work at and as you can imagine in an Arts College the appreciation of the STEM subjects  is often lacking in the students. Our STEM teachers have had to work extra hard to develop an appreciation of STEM in our students. As a whole school we have worked side by side with our specialist arts and humanities to develop curriculum experiences that break down the barrier that exists between the educational silos. Giving authentic learning experiences to our students.

Have we spent a lot of money on STEM – NO! Do we have passionate and amazing educators in our school YES!  So the purpose of my BLOG is to share with you how my school’s STEAM team, get the job done. How we provide real learning experiences that prepare our students for the future that awaits.  In doing this I hope that you can find ideas that you can use in your classroom to develop the creative and critical thinking skills of your students.

So if you think the A doesn’t belong in STEAM then this is not the BLOG for you. But if you are interested in finding out more about how a College of the Arts won the Governor of WA STEM Award award in 2015 and 2016 then you have come to the right page.  I will use this page to share some of the programs we have used or developed in our school and also any other STEAM related projects that catch my eyes.

Beware also, my personal views and values will drive the way that I write.  I am not an academic, and  I have been a secondary school mathematics educator since 2000. I chose education first and mathematics was my chosen specialist area. Today I am passionate about mathematics but this was not the case when I was a student. I was just good at it – I think it was because we were not allowed to talk. As a mathematics educator I now found the beauty of mathematics in the world around me and I love to share that with my students. Engaging gifted students in their schooling and recognising that they potentially can be our most at risk students drives me.

My major was mathematics and I have a minor in Computer Science, but I have never taught computing. With the introduction of the Digital Technologies curriculum though in Western Australia I have re-discovered just how much I enjoy programming and Python is my language of choice. My mission is to give all of our Year 7 students a little bit of Python in maths. I hate complicated stuff and flashing light and whistles. I don’t do robots but I appreciate the Computational Thinking that makes them works. I want my students to see that coding is a way for them to be creative and solve problems. Digital literacy is just another core competency for all children. It sits alongside numeracy and literacy.

I wont baffle you with big words, I don’t understand most of them myself. I am on the committee for the  Maths Association of Western Australia assisting them to develop and maintain their student activities.  I continue to evaluate resources and opportunities that I think improve learning experiences for students. Free is always best, and I don’t believe we need to re-write the wheel just because we now have the acronym STEM.

I have been driven to start this BLOG because I have just attended the inaugral WA STEM Conference . This conference was organised by three of the WA Proffessional teaching Associations  STAWA, MAWA, ECAWA and Scitech during the school holidays.  The 300 attendees were passionate educators who gave up their school holidays to attend. I heard these teachers ask:

  1. How do we implement this great educational pedagogy in the traditional schooling system that we have? In particular to high schools, how do we begin breaking down the silos that we call departments/learning areas.
  2. How do we measure that it is actually adding to the educational outcomes of our students?
  3. How do we share this overload of information to our school colleagues and the many educators who still have their head in the sand thinking it is a fad that will pass?

So this is what drives me and inspired by my colleagues website page Jody Crothers I thought I can help other teachers withSTEM implementation. I have seen first hand what can be achieved in a traditional high school that values the natural curiosity and creativity of it’s students. I have learned so much in the past five years – and each year  just gets getting better and better. My school started small, a handful of teachers think tanking some ways to improve STEM education in our school. With the support of our management we now have more and more  staff coming on board the STEAM train every day. It has never been mandated to us, it all started from the ground up, teacher driven and there is a renewed enthusiasm across the school.

Robots and A.I  are on the news most nights and talk of job losses are scaring many – including me.  Not knowing the end solution to a problem can cause a bit of anxiety for many – a bit like maths anxiety. But by collaborating and nurturing the natural curiosity in our youth, developing their STEM capabilities I believe their is amazing opportunities for the future of the world.  I want my children and the children I teach to be confident to create,  not just consume.