Monthly Archives: October 2015

Assessing Higher Order Thinking by Brookhart

Before this year began I was out shopping at a used book store and came across “How to Assess Higher Order Thinking in Your Classroom” by Susan Brookhart. My assessments always haven’t been strong and was one of my priority areas for this year so I picked it up.

Brookhart's Text

This week on fall break, I procrastinated from planning and sat down and read the book cover to cover.  It was definitely worth my time because I think I’ll be able to make better assessments the rest of the quarter with her work in mind. I’ve never had formal training on creating or using assessments so Brookhart’s work was more helpful to me than it might be to others.

Assessment should be based on three principals. 1) specify clearly what you are assessing 2) Design items that require students to show this knowledge or skill 3) decide what you will accept as evidence [aka rubrics] (pg 17). I’ve never sat down and made a list of what I was specifically assessing by Bloom’s or DOK – its always been by standard and never intentional. My last assessment made this clear as students were assessed on the same skill way too many times so the test became too long and students gave up. Using Brookhart’s blueprints (like the one pictured below) will give me a better outline of what I want students to do and then I can backwards plan from there.

Brookhart Pg 21

Brookhart also suggests assessing with “novel” situations to assess transfer of learning. While I agree that is the best way to assess for transfer I have yet to create or find a complete enough assessment bank to make that a realistic and consistent goal. Looking forward however I can plan with the idea of novelty in mind to ensure an accurate assessment of learning.

She also focuses on feedback and saying that we need to make explicit when we are commenting on thinking versus format to ensure that students have a better way to move forward (pg 52). This year I’ve been working to improve my feedback focusing on giving students questions, but I can also improve by making sure I’m giving feedback on thinking and/or format.

The rest of the text breaks down different kinds of thinking to assess (logic, creativity, problem solving etc.) and provides a few worked examples of each type. Most of these were really helpful and I’ll go back to as I create assessments. Looking at her work on logic was the one area that stood out most. When I reflected upon my work with Construction Castles, I noted how students struggled and weren’t given enough feedback. Lo and behold – Brookhart knew that was coming and says we must build in formative assessment into long term projects so students can ensure they are on the right track with their thinking and working.

It all isn’t perfect though – Brookhart’s section on assessing judgement lacked any math examples. I need an example or two of how that would look and hoped I would see it to make the implementation faster but I’ll have to build specific items and compare to what she says is best practice to assess judgement.

All in all – Brookhart’s text will definitely be helpful provide insight into how I assess what my students are learning and how they are thinking but seemed at times a little incomplete at times from a math teacher’s perspective. I’ll be coming back to this once I craft a few blueprints and incorporate that work into my unit plans.


Geometry: Constructions Unit Reflection

In Geometry this year we began our first unit with constructions to frame our work and build the course from there. This was the first time I’d ever don constructions, let alone in class. Next time will be a trillion times easier for sure.

We began with a quick review of how to use compasses, straight edges and protractors because I don’t know the last time students worked with them.

I relied heavily on Juile’s Construction booklet for notes to add to our INBs and used the directions and worksheets from Math Open Reference. We only did constructions through creating perpendicular and parallel lines – we didn’t inscribe any triangles or hexagons in circles yet.

We ended our unit with Cheesemonkey’s Construction Castles assignment as an assessment. Good news, it was a great way to assess what students know about constructions. Bad news: Students showed they hadn’t mastered constructions -the average grade on the assignment was a failing grade….. After being graded, students were allowed to make up and improve their work for over two weeks, but only two students did so.

Even with that academic hurdle, we were still able to have productive conversations about the work and why some wouldn’t receive full credit before we finished the project. While that was helpful for some, that conversation should’ve happened before work began – which now with pictures can happen next year.


“Constructions: In Space!” – 6th Period. Students could do anything – and this group went to space. They also wrote out the construction near each which was super helpful to see.

Also titled: Castle - from the inside.

“The [castle] Wall” – 6th Period. This was my favorite key for sure. Each student had a place to write which construtions they did. I legit smiled when I saw this after being confused for so many projects before.


“Hogwarts: Did you know they don’t need doors?” Also, it comes in plaid. – 3rd Period I liked this because it had things clearly labeled while also making an explicit key.

We didn’t get to use Euclid the Game in this unit because our Castles took too much class time, but I’ll use it as a review for Semester 1 and for the AZMERIT in May.


  • Students conquered new and challenging things.
  • Construction Castles was a good assessment of what students knew and how constructions relate to one another.
  • Some of the other assessments used also required students to build off previous skills and apply them to new situations. In particular, the assessments at the beginning of the unit and on constructing a perpendicular bisector were strongest to assess student mastery.

Grows for 16-17:

  • First, review this edited unit for ideas to improve
  • Scaffold Construction Castles – give students daily targets to achieve instead of big goals. This was one of their first experiences with anything this open and it needed more structure for them to eventually be successful
  • Don’t start the year with this unit. We had students change schedules after MAP testing so they were placed in the correct math course. While great for students, it meant that a lot of students came into class in the middle of the unit. It was incredibly challenging to continue the unit where everything was built on top of the previous skill. Consider a logic unit to begin the next year – its still relevant but not necessarily content. Plus, this is coming back to bite me in the butt now.
  • “Copy what I do” isn’t a good way to make this unit work….don’t do that again because literally no one understands what they were doing – they were just doing. I’m pretty certain that this is going to come back and bite us later :/
  • Add in technology before the end (and don’t drop it when things get rough)
  • Intentionally separate this unit from parallel and perpendicular lines. It is already in practice, so let’s make it a reality.