Pedagogical Content Knowledge: Weeks 5/6

And now onto weeks 5/6 for the PCK course I’m studying. Within two/three weeks we’ll be heading out into schools, so the content for this week is starting to become fairly central. i.e. what is the curriculum and how are you meant to plan teaching/learning around that curriculum.

Essential learnings for secondary middle phase

By the end we should be able to use the “essential learnings” (i.e. the Queensland curriculum) to plan.

After a bit of reading, brief summary of last week, onto an activity that seeks to aid in unpacking the essential learnings for our teaching areas.

I’m doing mathematics and ICT/IPT/IT. ICT is not an essential learning, at least not in terms of standalone subject teaching ICT. It is instead something embedded within all courses. There is support for a separate course in terms of borrowing from other KLAs. But it’s not real well defined, just yet. Especially for ICTs, those guidelines are “coming soon”.

WoW and K&U

Not World of Warcraft, but Ways of Working. It’s the combination of WoW and Knowledge and Understanding that is the focus of teaching, learning and assessment (apparently). However, individual components may be taught, the aim is to build up to the combination.

Intent is to use approaches to learning that are:

  • student-centred.
  • Active engagement.
  • Learning through investigation.

Unpacking Mathematics

So, the idea here is to use the Mathematics KLA to answer a range of questions aimed at “unpacking” the KLA. In the following I’ve used the questions being asked as a scaffold for my interpretations.

Learning and assessment

Am using this PDF as it gives an overview of the learning and assessment for the mathematics KLA across all the junctures. My main focus will be on the year 7 (what they should know) and 9 (what I’ll have to help them learn) junctures.

Looking for the key messages about what is taught and how it is taught

  • What is the nature of the KLA?
    To teach math!? Seriously, the aim appears to be to build on previous recognition of the connection between math and real life situations and expand the more abstract/mathematical applications. It does appear to have a focus on developing students who are able to manipulate/use/apply mathematics to a range of situations. To be able to see it in context. There is emphasis on collaboration and discussion. There does appear to be aspects of this that connect with the idea of quantitative literacy introduced in the literacy and numeracy course.
  • What are the implications for pedagogy?
    It has to be a lot more than read the book and do the exercises, which is what I remember of mathematics at high school. Which implies that pedagogy is going to require a fair bit more effort. i.e. I’m not confident that I currently could connect much of the content to real world contexts.
  • What does L&T look like in this class?
    Active, social, authentic…etc. But I retain just a touch of skepticism that insists that there should be appropriate levels of direct instruction as a scaffold/enabler.

Assessable elements

Using this document.

  • What are the assessable elements?
    I find it interesting that there is currently no discussion in this of weighting. Are all the assessable elements meant to be weighted equally? A decision for teachers/schools? I’ll copy the “rubric entry” for the A descriptor for each element

    • Knowledge and understanding.

      Comprehensive knowledge and understanding of concepts, facts and procedures

    • Thinking and reasoning.

      Insightful application of mathematical processes to generate solutions and check for reasonableness

    • Communicating

      Clear and accurate communication of ideas, explanations and findings using mathematical representations, language and technologies

    • Reflecting.

      Perceptive reflection on thinking and reasoning, the contribution of mathematics and learning

      Not sure this one is written grammatically correct.

  • How are they demonstrated in K&U and WoW?
    The first three are covered well in both. Though communication may not be quite as obvious, it seems to be there. Reflection is even less obvious in K&U. Both communicating/reflecting are more obvious in the WoW, with actual specific WoW related to the two. However, these tend to reflect activities that students should be doing with the K&U.
  • Are they auditable across both?
    I’m not even sure that make sense to be able to do.
  • What will assessment look like?
    An appropriate mix. Some individual tests/assignments focused on some core knowledge, but lots of authentic assessment to test the real world stuff, group work etc.

Knowledge and understanding

  • What are the conceptual headings for Year 9? What are the conceptual statements in each?
    • Number – Number properties and operations and a range of strategies can be applied when working with integers and rational numbers.
    • Algebra – Variables, algebraic expressions and equations, relationships and functions can be described, represented and interpreted.
    • Measurement – Units of measure, instruments, formulas and strategies can be used to estimate and calculate measurement and consider reasonable error.
    • Chance and data – Judgments can be based on theoretical or experimental probability. Data can be displayed in various ways and analysed to make inferences and generalisations.
    • Space – Geometric conventions can be used to describe, represent, construct and manipulate a range of complex geometric shapes. Mapping conventions can be used to represent location, distance and orientation in maps and plans.
  • how detailed are the concepts, facts and procedures for each conceptual statement?
    They seem to be descriptions of “classes”/collections of problems. e.g.

    Lengths and angles that cannot be measured directly can be investigated using scale, similarity or trigonometry

  • What is the purpose of the examples?
    Mmm, this was stated in the presentation.They essentially offer clarification of what is intended.
  • What is it that you will be teaching as core concepts/facts/procedures?
    Mmmm, the stuff listed under K&U, especially pointed to by the bullet points for each conceptual statement. Am I missing something here?

Ways of working

THe comparison of WoW for the mathematics KLA

  • WoW are processes, generally complex reasoning. What are the implications of this for teaching and learning?
    A significant amount of teaching would have to focus on introducing, modelling, practising and reflecting upon these processes. i.e. how concepts are taught and introduced will need to explicitly draw on these WoW, the students need to see them in action and reflection upon them. They need to practice this. There will be overlap between these. The processes themselves are key ways of learning….
  • They can be used in their entirety or as subsets, what would be the difference for each of these?
    Overall, the complete WoW describe expectations of students at the end of the juncture. Subsets are more likely to be used in developing skills with these processes. e.g. “evaluate their own thinking and reasoning” includes 2/3 applications, only 1 might be covered at the start. Aspects of some WoW may be used as part of another. May wish to highlight these aspects.
  • If WoW are essential, what is the implication for grading students?
    The assessment has to provide students an opportunity to provide examples of the WoW. If you don’t have this evidence, you can grade them on the missing WoW.

K&U and WoW together

Learning, teaching, and assessment are required to focus on develop and deepen K&U through WoW. What are the implications for

  • Type of unit plan.
    Interesting, I don’t recall the concept of “unit plan” being explicitly covered in any of the courses. It’s been mentioned in passing, but…

    So let’s start with an annotated unit plan.

  • Method of assessment.
  • The pedagogy required.

Mmm, not sure I’m getting much out of this activity, not sure I could reasonably get much out of it. Much of the latter stuff gets even a little more opaque, or straight forward. e.g. what philosophy? Well it’s been explicitly stated in the slides – constructivism – though the essential learnings themselves don’t explicitly state this, it’s a fair interpretation.

Planning a nunit

Okay, so this should be interesting. Using an assessment alignment planner to plan a unit. This is the guts of it.

Mmm, gotten tired of terminology duplication for some and lack of standard definitions for others. Incredibly difficult to figure out exactly what is required from the question, how best to go about it, and how much authenticity it has with real practice.

Will have to ask and come back to this later. That’s disappointing.

2 thoughts on “Pedagogical Content Knowledge: Weeks 5/6

  1. Mmm, gotten tired of terminology duplication for some and lack of standard definitions for others. Incredibly difficult to figure out exactly what is required from the question, how best to go about it, and how much authenticity it has with real practice.

    I found that one of the most difficult things to get right was judging the appropriateness of the task with such vague criteria as “Comprehensive knowledge of concepts, facts and procedures”. Surely some of this stuff is relative as rudimentary knowledge of quaternions should be weighted more than complete understanding of fractions.

    When I ask other teachers how they deal with these issues, they usually reply with “It’s something that you just get a feel for”. Nice. What I would have liked (and still do) to kickstart the “feel” is many, many exemplars of standard units that demonstrate clear links to the curriculum. Even in prac you’ll probably only be exposed to a couple of courses that can be helpful in aligning your own designs, but I’m sure that throughout Queensland and (when ACARA kicks in) around Australia there are hundreds or thousands of exemplars to view if they were made available. There has been an attempt to make a repository on the QSA website, but the uploads seem to be rather sporadic (especially in IT).

    I know that each teacher’s units feel like their own babies and they aren’t willing to share, but surely if QSA / ACARA are heading this way they need to have a solid plan on how to bring new people into the “feel” of the level. Maybe the Uni course could help by making available multiple previous units that had been submitted for assessment.

    Part of my aim for developing the majority of content through moodle is that it will allow a fairly easy sharing method though the community hub. Hopefully there are other like-minded K-12 teachers out there that will share so that I can improve my units offered.

    1. I’m going to return to unit planning next week sometime. But I think there will be some commonality in experience.

      The sharing thing is interesting. I wonder if the next generation of teachers will make a difference. Not sure my fellow GDL&T students will make much. Many seem to be very reluctant to put material on their blogs. Others are more open.

      As for sharing plans, I’ve got a vague idea kicking around in my head for a more “connectivist” (very loosely used) for structuring and traversing the type of knowledge required to develop good teaching. With an obvious required output being a unit plan.

      I hope to share that idea once I get some time. But I also think the experience of developing a plan or two will help.

      Either way, I’m keen to figure out ways we can share plans.

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