Classroom

Set-up

Classroom Designs that Facilitate Mathematical Thinking

Create open spaces...

Creating spaces that are flexible and allow for easy movement, floor space, and vertical non-permanent surfaces allows for small groups of children to disperse throughout your space and engage with hands-on thinking tasks and problems. There is no one way to do this, but here are few some examples of spaces that are designed to promote this kind of activity...

Displaying learning...

Displaying learning in "real time" is an important consideration for building upon student thinking. Think permanent 'anchor charts' with a twist! There is no one way to do this, but here are few some examples of ways that are designed to promote this kind of activity...

Look What I'm Learning...

This board grows as the year progresses...key concepts, words, and more are recorded as a way to reference and keep track of the learning happening.

"Research suggests that students effectively learn language when it is introduced as students need it, to support and develop their communication. This means not preteaching vocabulary as part of the routines, and instead recording keywords and phrases as the need arises..."

(pg 38 - from book: Routines for Reasoning- Kelemanik, Lucenta, Creighton)

Online Portfolio Documentation

Use some format to create a digital portfolio of learning for students and parents to access as a highly effective way to engage parents, students, and keep track of 'hands on' learning.

Image source: http://loftinstechtips.blogspot.com/2017/10/seesaw-for-digital-portfolios.html

Student Strategy Discoveries

Post student "discovered" strategies which are named mathematically correct (example: Make 10 with 9) for reference. Teachers reference the student's name when the strategy comes up again during future discussions. Example: "Remember when Angela first discovered that you can make 10 with 9? That same strategy was helpful today when..."

Photo from: https://makingsenseofmathematics.com/2019/01/24/numberless-word-problem-using-a-student-centered-approach/

Accessing Materials...

Ideally, math materials and manipulatives are easily accessible by the students. The Studio at Grauer, Richmond BC, has some helpful images and descriptions about how they set up their math studio. Some of their ideas can be replicated in a classroom.

De-fronting the classroom...Vertical, Non-permanent writing surfaces...and random groupings...and more!

For over 15 years, Canadian professor Peter Liljedahl has been researching important, testable questions with over 400 teachers and their students in the area of building thinking mathematical classrooms.

Below are some of his KEY FINDINGS:

Defront, destraighten, and desymmetrize your classroom!

you know immediately when you walk into a room what to expect from the furniture layout - and that expectation shapes behavior
symmetrical, straight, and/or front facing furniture placement all convey expectations of ORDER and communicates students will be doing a lot of watching and listening centered on the teacher
defronting: position desks and tables so that chairs point in all different directions; cluster desks and tables away from the vertical surfaces
try not to stand at what used to be the front to give instructions or lead discussions
move around the room when you are talking to students

Use vertical, non-permanent surfaces for groups to stand at and work on! (pg 79)

What can you use? Windows, whiteboards, chalkboards, vinyl picnic table covers, shower curtains, melamine finished fiberboard, Wipeboards by Wipebooks, Better than Paper by Teacher Created Resources, and Dry Erase Surface by Post it
"What is left is an environment that not only supports thinking but also necessitates it" (Pg 63). See screenshot below showing time to engage and more based on the type of work surface used.

Form Visibly Random Groupings! (pg 45, 84)

making groups visibly random was necessary for students to both perceive and believe the randomness
random groupings allows for different students to step forward and begin to think
Benefits: increases willingness to collaborate, helps eliminate social barriers, increases knowledge mobility (sharing amongst groups), increases enthusiasm for mathematics learning, and reduces social stress
In K-2 form groups of two, in Grades 3-12 form groups of three
set up your method of randomization such that it tells students where to go
find a way to randomize such that the students know that you know what group they are in

"Although randomizing wrested the control from the teachers, making it VISIBLY RANDOM was necessary for the students to both perceive and believe the randomness." (pg 44)

How tasks are set up and given (pg 110-115)

Give the first thinking task in the first 3-5 minutes after you begin the lesson.
Give the thinking task with the students standing loosely clustered around you.
Give the instructions and thinking task verbally. This produces more thinking sooner and deeper with a reduction in questions being asked (at every grade level, context, and even with ELL).
Write on the board only the details that the students need to remember such as quantities, measurements, geometric shapes, data, and more. Ask yourself if what is written on the board would make sense to a student who comes in late.
Create tasks in a storytelling format if at all possible using a narrative, sense of chronology structure. Start with low-challenge tasks to ensure the groups start in flow.
Increase the challenge from one task to the next with incrementally small steps - this is called "thin slicing" of tasks. (Pg 154-155). Enter the lesson not just with a single sequence of progressively more challenging questions, but also a sequence of parallel tasks of comparable challenge level. (pg 163)

Mobilizing knowledge (pgs 141,145-166)

Groups are responsible for the learning of every member of the group.
As students are working, be "deliberately less helpful" - don't say or show anything another group could, model active interactions by suggesting groups talk to each other and see what they are doing.
Rather than shift the task the group is working on to something new, shift their mode of engagement with the same task to JUSTIFYING then explaining how they know they are correct.
Be watchful of which student work you would like to preserve for class consolidation - simply draw a box around the work you want to highlight with a red marker and ask students not to erase it. You can number these in the order you want to discuss them during the gallery walk.

Consolidating learning (pgs 171-183)

Pull all students to the center of the room or some vertical-surface free neutral area before consolidation begins and have a discussion about what they were asked to solve. "Can someone rephrase what you were being asked to do?" severs their attachment to, and ownership of, the work. not only does this increase the anonymity of the work, but it opens up the possibility for the teacher to take ownership of the gallery walk for their own purposes (pg 181).
Begin by reviewing the first 2 easiest tasks where student ideas are valued and expanded on using the existing work students created to demonstrate the details. Students stand in a loose cluster around the teacher, significantly increasing attention and engagement.
More time is spent at this entry level with decreasing amounts of time spent on each successive level until the highest level is barely touched upon in a 'gallery walk' guided tour fashion.
NOTE: if students are presenting their own work, very few, if any, of the other students listen. The fix? Ask "Can someone NOT in this group tell me what this group was doing her?" (pointing to a specific part of the board).

Additional Ideas for Tasks and Math Community Support...

"Building Thinking Classrooms: K-2" Facebook Group

"Building Thinking Classrooms" Facebook Group

(sort through using your professional judgement)