#pblmathed

PBL 4 – day 3, team- and self-assessment: today was a bit different because the presentations won’t happen until classes in April when everyone returns from a classroom practicum block. But the consolidation session and team- and self-assessment session occurred today.  We turned the peer- and team-assessment discussion into a self-assessment discussion, because it can often be easier to talk about one-self rather than another.

Being able to talk in a critical and improvement-focused manner with peers is often challenging and difficult. And this can also be the experience when trying to talk about oneself. Even if one has something to say, it is not always easy to start to speak. This is partly due to our (gentle, sometimes more intense) fear of being vulnerable, or showing a weakness and thinking we will be considered ‘less than’ for ever afterwards, and sometimes a lack of practice at risk-taking. All very human, natural, and normal feelings and thinking. 

One strategy might be to think of this scenario: in an interview, the interviewer will often ask for you to talk about a weakness. This is a very challenging question to answer and not feel you are leaving the interviewer thinking you are quite unfit for the position! But the “Mac sandwich” (from the McMaster Med School PBL process) of a) tell something positive about their contribution, b) provide constructive feedback on something to improve (this is the ‘weakness’ part), and c) provide a positive example of how they can use this feedback going forward (tell the interviewer how you have learned and implemented improvement with respect to your ‘weakness’) can be a conversational way to finesse the question, still be honest and forthright, and ultimately be able to talk.

PBL 4 – day 1, Everyone has some mathematics that excited them, that made them think, wow! That is cool! And that mathematics might have been the inspiration for continuing learning math, and maybe to become a secondary school math teacher. This is their chance to show us the math that got them, and still gets them excited, and then find a connection, a relevance to the expectations of the mathematics curriculum, and turn their mathematics into a rich learning task (RLT) (see Flewelling & Higginson’s 2002 A handbook on rich learning tasks).

There is also something different with this PBL task, can you see the difference? Yes, it is shorter, and, it also does not list Learning Goals. Perhaps making this task a bit more open-ended, and maybe appearing less like a ‘school/course’ learning activity. This is the fourth PBL cycle, and I am also wondering if the PBL protocol we have been using for that past three cycles and 13 meeting days has taken root in the preservice teachers’ thinking when facing a problem of practice… has it started to become a professional practice ‘habit’…

What math gets you excited! --> Rich Learning Tasks (RLTs).

PBL 3 – day 4, presentations, and self-assessment. The presentations were awesome! Five distinctly different approaches to course outlines, and all so very detailed from the perspective of student success first. Spiraling expectations, Backwards Design (UbD) approaches, summative tasks and exams, and coherency of a course from day 1 to day n, were the major learning points.

Self-assessment and peer-assessment: First, it can be very courageous to make yourself vulnerable with peers. But the benefit of a carefully structured approach to help navigate the action and the experience can be incredible for personal and professional growth. Second, it can require a lot of practice. It is not easy to tell others about something you think you could do to contribute more, to be a better team-member, and to take action and responsibility. The McMaster “mac sandwich” structure of i. say something positive, ii. Indicate an improvement, iii. Clarify how that improvement will have an effect on future contribution, professionalism, collaboration, productivity, is one of those carefully structured approaches. As stated and appreciated in the room, a growth mindset is not just for our secondary school students, but for us as teachers too.

PBL 3 – day 3, differentiation in higher ed! It sounds like every team was able to find their own direction and every person who wanted to was able to participate and produce what they felt was important. Very nice! Consolidating thinking around curriculum content (order, purpose, approach), and Achievement Categories, technology use, and formative assessment and summative assessment issues! How does it all fit together!? Just like the “real world” when teaching a new course means the course plan needs to be done before you have ever taught the course – normal! And even with teaching experience changes appear: new pedagogical approaches, a new curriculum, a new initiative from the education ministry/department or school board, means revising a course plan without having taught it yet – very normal! And frequent! ;-). Can’t wait to see what the teams learned, created, and decided upon in the final day presentations.

PBL 3 – day 2, what are the big ideas? what will student be able to do/show at the end?  how do we get students there through the course or unit?

Course Planning for secondary school mathematics -- curriculum development and implementation.

Sounds like backward design! If curriculum documents were written in an ordered, conceptually appropriate manner, showing the development of concepts from the beginning of the course to the end of the course, then we might not need course design strategies. But curriculum documents are not written that way. And textbooks are not written showing the same order of curriculum expectations in their chapters as we see in the curriculum documents. AND, teachers bring a LOT to the classroom – like their own ways of knowing mathematics, their own ways of listening to and attending to students’ learning needs and their knowledge of students’ engagement issues, or the use of rich learning tasks in optimal places in the course, and how formative assessment can inform instructional practice decisions, and how the context of the surrounding community and the school population matters when implementing context in problem-solving activities… and perhaps, just using the curriculum as a vehicle for building learning skills and a safe learning community in the classroom. All of this knowledge and ways of knowing (yes, just like Indigenous ways of knowing, or mathematical thinking ways of knowing, or the scientific method) means some kind of a strategy needs to be in place.

How many times has it been said by a teacher, “I didn’t get through the curriculum”, or to another teacher at the end of the course, “don’t put that on the exam because I didn’t teach it”, or “students did fine during the tests but failed the final exam”, or students say “but we used calculators and technology for the lessons, why NOT for the text or exam”, or “when will we ever use this?”, “why is this necessary?”…

If 1. The big ideas, or the essential questions of the course, or the main topics are understood, then 2. A final, summative, evaluation tool can be created that maintains a curriculum standard, a beacon and goal for learning for everyone in the course. Then 3. once we know where we are going, we can design the daily lessons, activities, tasks, assessments, and learning to build towards that ultimate goal, and we all get there.

PBL 3 – day 1, a new cycle – course/unit planning

Course Planning for secondary school mathematics --  curriculum development and implementation.

A new PBL cycle. This one is four days in length, and with a product at the end; an open-middled kind of task. However, even though everyone is working in their own way towards the same kind of final product, many differences will be visible across all the final products. PBL teams are working in a school department scenario developing a course outline for grade 9 applied and academic courses, or grade 10 applied and academic courses.

Yes, trust the textbooks and materials created for the curriculum, but trust in one’s own creativity, thinking, problem solving, and mathematical knowledge to develop a course outline that maintains the curriculum standard, and reflects the teacher’s pedagogical style...that can then also be responsive to students’ learning needs.

First on the list of action items for self-study: What curriculum development strategies exist? (e.g., like Understanding by Design or Backwards Design.) What is spiraling a curriculum all about? If the curriculum document is just a list of expectations, can the expectations be organized in a meaningful manner? (e.g., looking for the Big Ideas that anchor days of learning together into a cohesive unit). And how does assessment and evaluation work with, or drive, or respond to instructional strategies? (e.g., looking at Growing Success for insight.)

PBL 2 – day 4, what was learned….

Technology for teaching & technology for learning secondary school mathematics.

PBL 2 – day 3, specific technologies selected and application in curriculum expectations explored today.

Technology for teaching & technology for learning secondary school mathematics.