Assignment 1b: ICT provides a rich and flexible learner-centred environment in which students can experiment and take risks when developing new understanding.

ICT provides a rich and flexible learner-centred environment in which students can experiment and take risks when developing their understanding.


There are many software packages in the learning area of Mathematics which allow students to explore Mathematics concepts.


During my placement, I observed a teacher using Geogebra to explain the relationships between angles and circles to a year 9 class, for example, “The measure of an inscribed angle of a circle is half of the measure of its intercepted arc”. The software package allows students to visualize, experience and explore moving the angle within a circle. Students can test the theory and explore the limits. It is much better than having a teacher draw diagram after diagram to prove their point. This software allows students to see that the theory works in practice, and it is easy for students to check different cases by themselves and actively reconstructing the knowledge.


Using Geogebra to demonstrate the inscribed angle theorem is shown in this Youtube video:

 http://www.youtube.com/watch?v=DNwwrOnkqDA


The Geogebra website (http://www.geogebra.org/cms/en) has a lot of material for students and teachers to look at. Many of the theories and concepts of mathematics can be explained and explored with this application. Physics is another subject area where teachers could use Geogebra, to explain different ideas such as reflection and motion.


There are other programs that allows student to explore. In my Year 7 class, students have been working on Algebra. They are learning to understand rules and how to write them. The teachers in my placement had put together a list of activities that students can do on the FUSE website.


An example FUSE page - attribute trains


These activities allows students to use trial and error, and to work at their own pace. If students did not get the rule at the first attempt, they can try again. With visual prompting, students are able to try different things to find one that works.


The Learning resource ID on FUSE are ZPPGQ7, 9UEJA5 , 59L99F, BJU6UV, NNY4JA and many more. On each of these interactive pages, students are not only able to explore, they are able to practice and check their answers immediately.  Students will know whether their choice is correct without waiting for the teacher to come and check. They are able to try again if it is not correct.

These are just a few of the things that I have seen. ICT allows students to take charge of their learning. They are able to check their own work to make sure they understand. Students are able to work more independently. If students are anxious about making mistake, they can work by themselves and not worry about their friends finding out about mistake. This encourages students, especially students with low confidence to be braver with their learning. The resource that available on line mean that students are able to explore a lot more by themselves. And they can explore a lot wider and deeper in a shorter period of time.

ICT week & Career Expo

On Wednesday 27th, July, I went to the ICT week and career expo with a few of my fellow students.  It was a very interesting experience.  Due to our commitment at uni, we missed the opening address.

However, we went to a session on Developing Software for Mobile Devices by Rajesh Vasa, Swinburne University.  Most of the participant are high school students.  There are at least 3 different high school students.  Rajesh Focus on the Design of the software.  It is interesting to hear him said that only 20% of the development is focus on writing the program.  Most of the time need to spend on analysis and design.

I also talked to a lovely lady from VITTA.  She showed me the new government website for teacher and students called FUSE.  It contain lots of information for teachers and students.  Great resource to keep in our bag!!!!

Assignment 3 Unit Plan

 “Which Plumber to use”

Introduction:

Students will analysed which plumber they want to employ to do a job for them.  They will represent the cost in linear graph.  Compare two different plumbers cost.  Product a report of which one will be better to use in different size job.  Students will use Geogebra to compare the graph.

Duration:  5 lessons (50 minutes lessons)

Assessment:

Student will demonstrate elements of Level 6 standard in Mathematics and Information and Communications Technology.

Students will be assessed on:

            Understand difference between pronumeral and variable

            Understanding the meaning of gradient and constant in y = mx + c.

            Understand function notation.  Eg f(x) and g(x)

            Able to express the cost of the plumbers in Linear equation form.

Graphic representation of the cost

Understand scaling

Represent graph using Geogebra

Label the graph clearly.

Present information in a report format

VELS – Victorian Essential Learning Standards

Domain	Dimension	Element of standard
Mathematics	Structure	They recognise and explain the roles of the relevant constants in the relationships f(x) = ax + c, with reference to gradient and y axis intercept, f(x) = a(x + b)2 + c and f(x) = cax. They solve equations of the form f(x) = k, where k is a real constant (for example, x(x + 5) = 100) and simultaneous linear equations in two variables (for example, {2x – 3y = – 4 and 5x + 6y = 27} using algebraic, numerical (systematic guess, check and refine or bisection) and graphical methods.
	Working Mathematically	Students choose, use and develop mathematical models and procedures to investigate and solve problems set in a wide range of practical, theoretical and historical contexts (for example, exact and approximate measurement formulas for the volumes of various three dimensional objects such as truncated pyramids). They generalise from one situation to another, and investigate it further by changing the initial constraints or other boundary conditions. They judge the reasonableness of their results based on the context under consideration.  They select and use technology in various combinations to assist in mathematical inquiry, to manipulate and represent data, to analyse functions and carry out symbolic manipulation. They use geometry software or graphics calculators to create geometric objects and transform them, taking into account invariance under transformation
ICT	Focus	Students explore the distinction between legal and illegal uses of ICT and create information products that comply with ICT intellectual property law. This particularly relates to copyright.
	visualising thinking	Students use a range of ICT tools and data types to visualise their thinking strategies when solving problems and developing new understanding. They use visualising thinking tools and apply ICT techniques to support causal reasoning and to model and describe the dynamic relationship between variable and constant data values to test hypotheses. Students are efficient and effective in their use of appropriate ICT tools and editing techniques for assisting in visualising thinking. When solving problems, students discriminate between such tools and strategies based on their suitability for problem solving in new situations.
	Creating	Students apply a range of techniques, equipment and procedures that minimise the cost, effort and time of processing ICT solutions and maximise the accuracy, clarity and completeness of the information.

           

Teaching and assessment activities:

Lesson	Activities	Teacher explanation	Student outcome	VELS
1	Give a formula y = 3x + 2, draw up a table such as x Y 1 2 3 Plot each graph on Geogebra. Create a line of best fit. Can you read from graph what happen when x = 7?	Introduce Geogebra.  Explain to student they can access it via internet.  It is open source software. After activities, teacher explain the meaning of variables.	Understand difference between pronumeral and variable Able to express the cost of the plumbers in Linear equation form. Create graph to visiulised thinking.	Maths: Structure ICT: visualising thinking, Copyright issue.
2	Instead of plotting each point, student use notation f(x) = 3x + 2.  We see the graph the same as last lesson.	Explain the standard notation in Mathematics.	Understanding the meaning of gradient and constant in y = mx + c. Understand function notation.  Eg f(x) and g(x) Create graph to visiulised thinking. Student able to manage their files.	Maths: Structure ICT: visualising thinking. Creating
	Students enter g(x) = 2x + 3.  What can we see?	Teacher lead discussion on the function of m and c in the standard forms.
	Students need to save their work to be used again next lesson,
3	Students able to retrieve the file they saved from last lesson.		Students able to retrieve files from last lesson. Student understand the relation of zooming and scaling.	Maths: Working mathematically ICT: visualising thinking. Creating
	Students explore the graphic view options.  Students need to find answer to the following questions: 1.      What happen when the ratio in x-axis and y-axis changes? 2.      How can we zoon in to the intersection? 3.      What happen to the ratio when we change the minimum and maximum of x-axis without changing y-axis? 4.      What happen when we remove the number on the axes? 5.      What happen if we change the minimum and maximum of x-axis to 3 and 10?  Is there still intersection of the graph?  If so, will it be on the right hand side or the left?	Teacher lead class discussion to ensure students have sound understand scaling and zooming.
4,5	Student will be given the problem solving task. “You need a plumber to do a job.  When you rang John and Chris, you got two different quote.  John charge $150 for a call out fees and $80 for each hour.  Chris charge $100 for a call out fees and $100 for each hour.  When will John charge less then Chris?  And when will Chris charge less then John? At which point in time, they will cost the same?” Student present project in A3 size paper.  Include a print out of their graph.  Student could choose to present it in powerpoint format and submit electronically.		Able to express the cost of the plumbers in Linear equation form. Able to produce graphically presentation of the cost. Able to analysed and give answer. Present graph in the appropriate scale, ie, display the intersection of two graphs. Label graph clearly.	Maths: Structure, Working mathematically ICT: visualising thinking. Creating

Reference:

“Mitchelmore, M., & Cavanagh, M. (2000).  Students' difficulties in operating a graphic calculator.  Mathematics Educational Research Journal, 12(30), 254 – 268.”

Summary on Students' diffidulties in operating a graphic calculator

“Mitchelmore, M., & Cavanagh, M. (2000).  Students' difficulties in operating a graphic calculator.  Mathematics Educational Research Journal, 12(30), 254 – 268.”

In this paper, the authors looked at the different students faces when operation a graphic calculator.  He summarised into a few area. (In this blog, I will focus the technology side of the difficulties.)


1.  Scale.  In particular when the x-axis and the y-axis were not scaled equally.  And often students confuse the difference between scale and zoom function.  In Geogebra, the scale are number on the axes.  But in some graphic calculator, they are not as clear.

2.  Accuracy and Approximation.  Students assume that they can trace the graph and find the accurate number.  But sometimes (in the example shown by the authors), the number they are looking might not be rational or nice (such as whole number).


3.Representation by pixels. Students understand the jagged representation of graph being the approximation.  However, Students' focus on reading the graph rather then using other means to find the intersection could be a problem.


In summary, students would benefit from teaching guide their attention to the there area that was mention before.

Assignment 3 Update

“Mitchelmore, M., & Cavanagh, M. (2000).  Students' difficulties in operating a graphic calculator.  Mathematics Educational Research Journal, 12(30), 254 – 268.”

From reading this article, I really would like to plan a unit of work on for students to learn to use technology to enhance their learning of Mathematics.  Since students are not required to purchase a graphic calculator in year 7 - 10, I decided to introduce them to Geogebra, which is a free software that is available to use on many platforms.

In a overview, I am thinking of fitting it into the visualizing thinking and creating.  Student will start their work from series of questions that require them to explore the graphic representation of functions, the different representation of unit of the set of axis and their relationship.  Toward the end of the unit, students will create graphic representation of a real life situation and make analysis on the different graph.  

Because I am not teaching student to use standard software such as Word, Power Points and Excel, do you think it still part of ICT?

Useful link

Here are some of the useful link I found over the Internet.  Some might be useful, some might not.

The next two links are to some resource for teacher.  Unfortunately, you need to pay to join the membership.  However, if you are interested in the courses, you can still attend without being a member.  It might just cost a little more.

ICT in Education Victoria

Australia council for computers in Education



ABC Tech Stream is a very interesting site.  They raise different issue with technology in classroom.  Could be useful for students to have a look for social issue in Yr 11.  Unfortunately, they don't run this anymore.  But the article there are very interesting.  



Chris Betcher’s blog:  He is a IT teacher for many years.  There are different teaching issue.  I found him interesting character.  Not a good place to look for supporting article for what you need.  But as a good to know referenced.

Next placement

I am very excited about my next place.  The school I will be going next have the laptop program.  I believe all student have a laptop and year 7 have iPad either this year or next year.  I am looking forward to find out more.  Love to see how it is use for the year 7 to 10.