EDUC4105

Reflection, week 14

Dynamic geometry software programs offer outstanding simplicity and wonderful results. While the graphics calculators are potable and available for any classroom, dynamic geometry offers superior function and results. I think it is a very useful scaffold for curve sketching and advanced and difficult curves. GBeing able to drag curves and watch the variables change seems invaluable in explaining relationships and the roles of different coefficients.

However, I think the intuition gained in hand drawing basic geometrical proofs such as dividing intervals into half etc are more possibly satisfying as a physical action, and hopefully will have physical (building, woodworking) applications.

Microsoft Excel is a program I have never enjoyed using. The bars nearly always need resizing, it is easy  to confuse word and number data, and the lack of “what you see is what you get” makes publishing the graphs and info a little bit of guesswork. I don’t have much experience with it, and can certainly see the benefits of its many functions, certainly its advanced numerical functions seem useful in trying to make sense of large amounts of data, and this cannot be ignored as a useful teaching tool.

Reflection, week 13

Webquests are a unique combination of both lesson planning and the lesson itself. A well-prepared Webquest should give such clear instructions it relieves students of verbal instruction and gives them a kind of working independence. If it is well scaffolded it should provided all the tolls and clues for the students to piece together the puzzle themselves, and in this way has good constructivist learning potential. The disadvantage is the potentially inflexible type of lesson plan. This inflexibility might result in restricting the abilities of the students, with a kind of fixed expectation. The chances of the students bringing in extra ideas or concepts can be limited by the inherent structure of the Webquests. As far as planning goes it offers a good opportunity to scaffold good group work for an individual class work by articulating each students role within each quest. It would take

Reflections, week 12

Graphics calculators seem to undo half of my high school learning with their ability to process algebra, solve quadratic equations and graph complex lines, all of which I studiously learnt to do by hand. Although some time is required to learn how to program them, I think mistakes in input are more easily noted, and the result it students should be in a stronger mathematical position. I think if learning to use the calculator was integrated into the entire high school learning, students would have a powerful tool which could aide in their understanding and give instant feedback to their understanding on the page. The pedagogical downfall that in an already very procedural state testing system that students will focus only on procedure and as with any and all technology it would be needed to integrate with other mediums and methods of understanding.
Programming the calculators is one aspect that has shows the calculators two sides. It could give students a deeper understanding of computers and programs and the maths they are doing, but they can just as easily turn into a confused and stalemated problem with lots of buttons to press in an exact and unforgiving order.

Graphics calculators

Reflection, week 11

Interactive whiteboards have many potential benefits for teaching. As far as visual learners go, they offer so much more than conventional whiteboards/blackboards, and so even simple features such as a highlighter seem to me to be a great advantage in keeping the learning visually engaging. The ability to both type and prepare board work mean that the teacher doesn’t need to have their back to the audience and can focus on helping students and give them a chance to walk around the room. One of its main advantages is that it is connected to the internet and can swiftly go form board to projector etc allowing easy transition between different media.

Integrating these benefits smoothly can be difficult, and I agree with the view that funding and developing new technologies is valuable but teachers also need training in how to use them effectively and creatively otherwise they could easily be very expensive and power dependant writing boards. Our inexperience with the boards has made some of our lessons very fiddly and impractical, but I don’t think it would be long until we were using them more effectively.

Reflections, week 10

A teacher’s e portfolio should give clear insight into the beliefs, methods and understanding of their teaching. I think a short personal background and a teaching philosophy give quick insight into a teacher and their practice, and so are important features. Lesson plans are probably the main feature of an e portfolio and should show some creativity and offer something new or alternative in either the teaching or examining processes. Even without many lessons, a variety of teaching strategies would also show the teachers knowledge and understanding of pedagogy. Although it is impossible for student teachers, some reflection, even on their prac teaching, or on their planning might demonstrate an ability to be life long learners. Finally the portfolio should navigate easily, be well organised and look nice to show the administration side of the profession off a little.

Social bookmarking has a great potential to minimise time wasted on the internet, and can hopefully give easier and more accurate methods of searching for teaching materials. With good tabbing, and clear descriptions, the potential is that teachers can find exactly what they need where they may have previously needed to compromise their ideas or content.

My ‘Volumes of revolution’ video

this volumes-of-revolution2

this was made in windows and I think is a windows media player format

this was made as a part of EDUC4106

Maths teaching websites

Educational Java Programs is a website containing some interactive ‘java applets’ that aim to scaffold the teaching of particular math topics. There isn’t much structure to the site, and there are only ten math applets, mostly geared to early high school or late primary teaching. This aside, the applets tackle integers, fractions, Pi, tessellations and Pythagoras theorem to name a few. The applets are very user friendly, visually well made and have lesson plans attached, making the site useful for these particular topics.
The Math forum is a fairly comprehensive site, covering a wide range of topics and abilities. It provides articles on teaching and also includes approaches to assessment. I have found this site to be most helpful in finding resources for more advanced and difficult topics, and I think it excels in this area. The in site search function was not very helpful and I was left better off just browsing the site for particular concepts, which often involved dead ends like subscription sites or courses. However most general topics are linked to both internet projects, software and classroom resources.

PBS Teacherline is a professional development site for educators. This is a correspondence education site where you pay per course, with most courses averaging 30 hours. Its courses cover everything from teaching strategies and approaches to particular subjects such as ‘Fostering Cooperative learning, discussion, and critical thinking in elementary Math’. This site seems to imply that it might help American based educators maintain some sort of state level professional development, so Australian teachers would need to be keen learners to pay for these courses as professional development is not quite so prevalent in our system, or more to the point, the value of these courses might be hard to judge.

Talk in the classroom

Clare Lee’s 3rd chapter offers insight into effective classroom practices for using talk in the classroom. The strongest focus in this chapter seems to be on the teacher’s ability to scaffold learning without mediating every conversation and without rephrasing or rewriting students expressions of mathematical concepts. Lee gives good clear examples of the benefits of holding back, and really shows the importance of building students usage up progressively. The analogy to speaking French for the first time in France is one I related to well and gives me an enthusiasm to help break down any shy or tentative usage in students by creating a similar classroom atmosphere that Lee aspires to.

Frank Tapson tackles the roots of defining mathematical terms in his article The Language of Mathematics. Without Elucid’s definitions of lines and points it would be difficult to use these terms to define shapes. In the classroom then it becomes important to look a little into the meanings of words to avoid confusion for students. Tapson poses the situation of drawing a variety of quadrilaterals but using only a square, and the test and marking difficulties a teacher might face without exploring such meanings. He concludes with an excellent flow chart for quadrilaterals.

Webquest review

I found an interesting project ‘Landscape Design’ on the Webquest site which looked to be a creative look at area, hopefully applicable to some 7-10 lessons in the NSW math syllabus.

Landscape Design

Strengths:

• Well suited to group work as specific tasks can be assigned to the students
• It involves some higher-order thinking through the creating and designing aspects of the quest
• Well presented with interesting pictures and worksheets
• All the resources were computer based and even the worksheets could be typed in ‘word’
• Involves possible uses of the web, ‘powerpoint’ and ‘word’
• Involves perimeter, area some volume and costing into a single project
• Has simple potential for adaption to the NSW syllabus

Weaknesess:

• Needs extra direction and clarity for group work roles
• It could be done by a single single student, although this would be difficult
• Mostly low order procedures with no real analysis and few real decisions
• Not actually published on the web
• Some links (marking Rubric etc) didn’t work
• 1st floor area calculation doesn’t link in well, distracts and confuses garden porject
• Lacks necessary direction for where exactly the land should go (inclusive of the house or next to?)

landscapedesignwebquest.doc

Language Pitfalls and the advantages of good Language.

Continuing an analysis of language in the maths classroom, Clark and Ramirez (Language Pitfalls and Pathways to Mathematics) make some simple points about the potential confusion in the classroom. Some of their points have been covered in previous articles such as teaching more explicitly for ESL students. I liked their focus on symbols and the inherent meaning implied by many symbols and the need to explain the specialised context and appropriate meaning. As we teach maths such as Coordinate Geometry, deeper meanings are implied on algebraic letters in certain combinations such as using the point (x,y) and the point (p,q). These are general points which end up having consistent roles in proofs or worked examples. I can see the potential for misunderstanding or attaching too much meaning to some symbols. This article illustrates both the power and importance of classroom discourse in aiding a clearer understanding.

Jamison’s Learning the Language of Mathematics is an article that doesn’t focus on the pitfalls and difficulties but rather explains the many benefits of explicit language in a maths classroom. In teaching logic and concepts in maths, Jamison argues that students need to express an understanding in correct, clear and concise manner. Too often he sees that students are left to learn this expression themselves or by ‘osmosis’. I think this is why people in general see some people as good at maths and other are not, while the solution is perhaps giving everyone a deeper understanding of how to express and interpret maths. Jamison’s focus on good definitions is a very practical analysis, and something as a student teacher I  can see the need for. On my first prac I found it very hard to write a definition of ‘area’ and my teacher pointed out that the word ’space’ may not be so good in an area defininition as space really implies three dimensions. ‘Surface’ was suggested as a better word, and the process helped my understand how clear and correct explanations were so important. Jamison is passionate that maths language should always involve complete grammatical sentences and shows that with clear foundational teaching you allow students to gain a deeper understanding of maths.

transitive relation