Learning from Peter – Part 5 of 5

Peter also talks about assessing what we value. The fifth post in this series will address this idea.

In addition to assessing the outcomes in our math curriculum, Peter encourages us to think about some of the challenges our students have in math class and then consider assessing them. For example, if you find that your students are struggling with group work, assess it, and then they’ll improve in this area. I will describe his strategy. He makes two columns on the board and writes Bad Group work and the other is Good Group work. Then he asks students what good group work looks like and lists the students’ ideas in that column. Then the students do the same for the qualities of bad group work. Then he draws a line, as a continuum, from the bad to the good columns. This is what it could look like:

Then a teacher makes several copies of this chart and, as students work, he/she puts a check mark on the continuum for each group in the class indicating their performance. The students receive immediate feedback and can adjust their behaviour. This formative assessment could be offered several times in a lesson/activity or over several weeks.

Sam Shah, a teacher in Brooklyn, New York, has created a SMART Notebook file that focuses on group work as well. He displays a page that looks like this:


The phrases you see here were created by students. Sam infinitely clones them so he can drag the comments into the four boxes (four groups) or out of the boxes as he assesses group behaviour. There is no paper used and it is quick and efficient way for a teacher to observe students and provide them timely and specific comments. Teachers save the Notebook file to keep track of this data.

Peter says it is very important to teach and give students feedback on these skills. As we expect students to collaborate more and more in math class, for example, those who don’t do this very well, could suffer academically. Imagine a student who doesn’t do his fair share of the work or misses some class time due to poor group behaviour. For both of these reasons this student probably will miss some of the mathematical concepts presented in class and then, on summative assessments, perform poorly. It is, therefore, our professional obligation to help students learn to collaborate, communicate, persevere, take risks, etc. to be successful mathematically.

Which skills would I emphasize, teach and encourage in math classes? First, I think the ‘soft skills‘ that help a person interact more effectively with others would be important. The 7 process skills in Alberta’s K-12 Program of Studies which include communication, connections, mental math and estimation, problem solving, reasoning, technology and visualization, would also be key. As well, since learning about Alberta’s Framework for Student Learning, I am reflecting on how to help students develop the seven competencies outlined in this document.


Again, the bottom line is, if you value it, assess it. I believe that this is the way to go but it will be challenging to determine the indicators of success for these skills and competencies and then determine ways to assess them.

You can read my other posts about ‘Learning from Peter’ here: Part 1Part 2, Part 3, Part 4

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Learning from Peter – Part 4 of 5

Along with shifting their practice to reflect the intent and philosophy of the revised Alberta Program of Studies, teachers are trying to figure out how to adjust their assessment practices as well.  Since this is such a hot topic for math teachers these days I’d like to share several of Peter Liljedahl’s ideas about assessment with you.

First, I’d like to recommend that you read one of his papers and one book. Peter has written a short paper, The Four Purposes of Assessment, which is a provocative summary about his current thoughts on assessment. He has also contributed to the book Questions Worth Asking About Assessment in Mathematics Classrooms produced by the BCAMT (British Columbia Association of Mathematics Teachers). As stated in the preface, “The book does not attempt to answer assessment questions in an authoritative, theoretical manner, but instead invites you into a deep, rich conversation with colleagues where the answering of questions happens after reflection and dialogue, and more than likely means that partial answers give way to new questions.”

Here are some ideas around assessment that resonate with me:

An important purpose of assessment is COMMUNICATION. Students communicate their learning to teachers and teachers give students feedback about their learning.  In order to do this successfully teachers begin by providing clear learning targets. Then teachers provide feedback so students know where they are in relation to the goals along with specific details about how they can get there. Peter uses a travel metaphor. Learners need to know where they are going, where they are currently and what to do to get there. He wants students to be the primary consumers of assessment. If they are, students don’t need to ask teachers what they need to do to improve because they will already know. He also reminds us that we report to parents several times a year but our primary focus should not be on parents, but on students.

Assessment should NOT be used to RANK students. This is a big piece of our past culture and we must consider letting it go. A former colleague of mine John Scammell, @thescamdog, shared this idea in his blog, Zero Knowledge Proofs. He has an example of how Peter emphasizes this first premise at the bottom of his blog post. If you’re curious, click here to read more about it.

Peter encourages teachers to liberate themselves from a point-gathering paradigm and shift to a DATA-GATHERING PARADIGM. If a teacher gathers points then he/she is assessing the same things for every student in a class. In this situation, students have exactly the same assessments reported in point-form. If a teacher gathers data then he/she is gathering a lot of data about students and determining the data and evidence that best represents each student. In this situation, the data does not have to be exactly the same for each student.

The controversial topic of second chances is related to these two paradigms. Generally, teachers functioning from the point-gathering paradigm struggle with rewrites or redoes because it seems unfair that students have different opportunities and resulting points. Teachers who function from a data-gathering paradigm are more comfortable with second chances since they are looking for data that is consistent for each student. Peter believes that we shouldn’t punish students for what they didn’t know along the way. If students demonstrate that they have learned a particular concept by the end of a course, then assessment should be dynamic and reflect this learning.

Peter makes the comment that marks often get higher if teachers use a data-gathering paradigm. He says that we aren’t ‘SOFTER’ but instead, the grades increase because:

  • Students receive more feedback about their learning and they can get better – they know where they are, where they are going and how to improve.
  • The data is more representative of student performance – teachers consider all the data and choose the most appropriate data for each student.
  • Students are given multiple opportunities to demonstrate what they know so they have more chances to do better.

Since this blog post is getting long, I’ve decided to add a fifth post in this series. It will address Peter’s idea that we must assess what we value.

You can read my other posts about ‘Learning from Peter’ here: Part 1, Part 2, Part 3, Part 5

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