The Alberta Math Curriculum is extensive, and for the sake of organization and accessibility it is structured in a very linear, segmented format. Considering how we might connect key skills and concepts with the broader discipline of mathematics in ways that engage diverse groups of learners and breathe life into the Mathematics Curriculum requires not only that we engage with the central ideas of the discipline but that we become intimately familiar with the curriculum document. Thankfully, this work is incredibly engaging. Both the “Introduction” and the “Conceptual Framework for K-9 Mathematics” contain such gems as:

“A problem-solving activity must ask students to determine a way to get from what is known to what is sought. If students have already been given ways to solve the problem, it is not a problem, but practice. A true problem requires students to use prior learnings in new ways and contexts. Problem solving requires and builds depth of conceptual understanding and student engagement.” (p. 14)

“A true sense of number goes well beyond the skills of simply counting, memorizing facts and the situational rote use of algorithms. Mastery of number facts is expected to be attained by students as they develop their number sense. This mastery allows for facility with more complex computations but should not be attained at the expense of an understanding” (p. 17)

The “Conceptual Framework” outlined by the Alberta Mathematics Program of Studies aligns perfectly with our inquiry-based approach to pedagogy at Connect. It also reinforces the importance of coaching students to develop both computational fluency as well as mathematical habits of mind through problem-solving.

With these “mathematical process” outcomes in mind, we introduced the “button” problem (adapted from nRich) in order to encourage students to consider how a systematic approach to problem solving might help them recognize patterns or connections that could lead to generalizations. As is often the case with this inclusive approach to mathematics, the focus on “looking for patterns” also resulted in specific *skills-based* revelations from students as they worked towards solutions including:

Here is a glimpse into some of their observations and conversations.

It is important to note that though the work of some of these students in attempting to develop algebraic representations of factorial (!) extended well beyond the scope of the Grade 7 math curriculum, the intended outcome of this work was simply to have *all* students *organizing their thinking systematically* such that they could be certain in each case, that they had found all the possible ways of buttoning a given number of buttons. We encouraged students **not to suppose** that there were 6 solutions to 3 buttons,

*In the Galileo Educational Network’s recent digital publication: “Focus on Inquiry”, they elaborate on the difference between a strictly “thin or superficial knowledge that comes from a general, surface acquaintance with important concepts or ideas”, and the “deep knowledge that engages [these concepts] within the central ideas of a topic or discipline” (see Chapter 1: Knowledge Building within Discipline Based Inquiry). Textbooks, and curriculum, for the sake of organization and accessibility, are generally structured in very linear, segmented formats. Teaching is a practice that engages the teacher as a liaison between these individual concepts and the depth and breadth of the discipline within which they exist. Teaching in the inquiry-based classroom requires that students solve problems, construct explanations, and work with simple concepts to construct more complex understandings. *

*One of the biggest challenges of this work can be communicating what this work looks like, and how it connects to those individual concepts. This year, as a teaching team, Jocelyn Monteith and I are focused on trying to tell that story.*

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Our first few challenges have focused on developing students ability to “tinker” or to persist with “trial and error.” We recognize that many students can be reluctant to use a trial and error approach as they may feel they are only using it because they do not know the “right” way to solve the problem. In reality, trial and error involves trying something out and then using it to gain further insight into the context and to get a better idea of what to try next. This is often the start of working systematically.

Students responses to this problem were varied. We encouraged them to share their attempts, strategies, ideas, and frustrations. At first many were quick to assert that they had “finished” and to ask whether they were “right.” We challenged them to find a way of concluding unequivocally that they were right with questions like “how do you know *for sure* that it is not possible to hit all of the orange tiles within the given parameters?” Some students expressed frustration at their inability to use a quick formula to solve the problem. Some students appreciated that the emphasis was not on speed but on careful consideration following multiple attempts and an awareness of their thought process as they determined what adjustments to make. Here are some examples of student thinking:

A recurring question among some students as we worked through this problem was “how is this math?” It is a major misconception among young mathematicians that computational fluency *is *mathematics due to the fact that developing a high level of accuracy and automaticity in basic computational and procedural skills is so much of a focus in mathematics in schools. This introductory activity was a good reminder that higher-order skills such as problem posing, problem representation, solving complex problems, and transferring math knowledge and skills to problems in non-math disciplines are no less valuable. (See also: The Problem With Math Problems: We’re Solving Them Wrong)

Levasseur, Kenneth, and Al Cuoco. “Mathematics Habits of Mind.” Teaching Mathematics through Problem Solving: Grades 6-12. Ed. Harold L. Schoen. Reston, VA: National Council of Teachers of Mathematics, 2006. 27-37. Click to download

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As our Outdoor Education programs at Connect have expanded over the past few years, our OE teaching team became increasingly concerned by consistently low participation of girls in our classes. Though our school demographic is 65% male, female numbers in Outdoor Education were significantly lower than what we would expect even accounting for this imbalance. For example, the Grade 8/9 term 2 trip last year had only one female student participant.

Upon further consultation with girls in the fall of last year, many of them expressed some hesitancy around the idea of participating in an elective that they felt was typically dominated by their male peers. Some identified barriers to participation as a lack of confidence, concerns about their ability to “keep up,” about their physical appearance in the backcountry and about being “the only girl” in a group dominated by boys. A handful of students suggested that they would be more likely to consider participating in an OE elective if there was an “all-girls” option. It was with this in mind that in term 2 this year we split the Grade 8/9 OE class into two, single gender options in an attempt to increase female participation.

With some recruitment and encouragement, we filled 26 spots in our “all-girls” term 2 Outdoor Ed elective. We ran parallel but non-overlapping programs for both groups including a day trip to Kananaskis and an overnight ski trip to Mosquito Creek in Banff National Park. At the conclusion of the term we asked students to comment on their experience. Here are some of the girls’ reflections:

*“I appreciated the all girls class because I felt like there was a tighter bond between classmates. Everyone was included, and people didn’t feel judged because they were a girl. I really felt that it was a comfortable, safe environment to develop my back country skills.”*

*“I appreciated that it was all girls in this elective because I have never done this elective before and many of us were in the same boat. I guess I always felt that guys would all have had more experience with these things and I would look awkward for being new at it.”*

*“I liked being in a group with all girls because I felt that we were much more supportive of each other than a group with both boys and girls. E**veryone was very comfortable and felt accepted. I feel that with the boys there would have been more competition.”*

*“I liked this all girls elective because it made me have more connections with other girls in the school. Mixed gender OE electives feel kind of intimidating with so many boys, they sort of bring down my confidence in myself.”*

*“I really appreciated that this elective was gender specific so that I could open myself up more and ask more questions. **I think that it was a more “carefree” zone for a lot of people. Most girls, like me, came out of their comfort zone more than usual so the experience impacted me it a bigger way.” *

*“I really appreciated the gender-specific focus of this elective because its not an everyday thing where you get to be in an all girls group and it felt really supportive.** Everyone could laugh off everything.”*

* “I did appreciate the gender specific focus because I found that as girls we were able to get more help and support than we would have if it was mixed gender. I also thought it was easier to try new things in girls outdoor ed, which was awesome, because I needed to try a lot of new things. Also, this way I didn’t need to worry so much about my appearance on the backpacking trip.”*

*“I really really appreciated the all girls elective because I am not comfortable around guys in general, and it usually limits my participation in group activities. When they made a girls elective I was really thankful because I could be more of myself and that is something that doesn’t happen all the time so I was really grateful for this experience and if they have this next year I would definitely participate.”*

*“Thank you for the all girls elective! Usually, this elective is an elective that mostly boys do and it pressures girl not to join. With the all girls focus it promotes girls to sign up. This was also the biggest number of girls in a outdoor ed term so that shows that the girls appreciated it too.”*

*“When I was in mixed OE, the group dynamic was a lot different. There were so many more boys, and they dominated pretty much everything. This term everybody was a lot closer and I think it was a lot easier to be ourselves. Both the mixed and gender-specific groups have their pros and cons, but the girls-only was a really valuable experience for me.”*

The “all-boys” elective also really enjoyed their experience, but none of them indicated that they noticed any difference in their experience between the mixed and “all-boys” groups. One of them commented that there were so many boys in the mixed electives that it was really the same environment as usual.

The “all-girls” Outdoor Ed option this year ultimately resulted in an increased number of female students at Connect that were willing to try new and challenging activities and students overwhelmingly felt more comfortable and confident in developing their outdoor skills. The space that was created with the “all-girls” elective was clearly one in which an increased number of female students were provided with the opportunity to gain experience and expertise and this translated into a surge in female sign-up for our Term 3 mixed electives. We are truly grateful for having been able to provide this opportunity for our students.

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The inclusion of Inuit Games in our Physical Education program began four years ago with the simple idea of introducing students to some less conventional sports and helping them connect physical activity to community and culture. Our goal was to design a unit that would coincide with our school’s Peace Festival; a two week long celebration of peace, understanding and community. This *Inuit Games Video Podcast* discovered online provided an excellent starting point with our classes as we worked through some of the more basic events as a group.

As it has evolved throughout the years, our Inuit Games unit has increasingly encouraged students to develop an appreciation for different ways in which aspects of physical fitness can be practiced and tested. It has also provided us with an important opportunity to draw connections between physical activity and the humanities as students are able to recognize and identify cultural influences on sport. Perhaps one of the most valuable outcomes this term however, has been the acknowledgement that many of the Inuit Games activities are “impossible to beat.” Students are generally up against themselves in games designed to test individual perseverance and endurance. The Inuit Games effectively personalize physical challenges, differentiating and scaffolding automatically based on student effort and comfort level. This year, the Inuit Games unit lead to some incredibly thoughtful conversations about how specific activities support the development of an intrinsically motivated athlete mentality. Students recognized that when competing agains themselves they generally experienced feelings of success and personal accomplishment more often than in environments in which they were battling peer. They also commented that the way Inuit Games were set up, they more readily engaged with the goal of beating their own record rather than someone else’s.

In particular, our Inuit Games unit has emphasized the following broad range of curricular outcomes for Alberta Physical Education:

- Acknowledge individual attributes that contribute to physical activity
*(Functional Fitness)* - Describe positive benefits gained from physical activity/l physically, emotionally, socially
*(Well-being)* - Demonstrate basic skills in a variety of games and more challenging strategies and tactics
*(Games)* - Improve and refine functional quality of skills in a variety of activities with increased control
*(Locomotor and Non-locomotor skills)*

I’ve included an overview of the activities we included as part of our unit this term, as well as a mini-edit showcasing students from Grade 4 – 9 working through the different events! Would welcome any feedback or questions!

//www.scribd.com/embeds/192733269/content?start_page=1&view_mode=scroll&show_recommendations=true

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“*Tell me and I forget, show me and I remember, involve me and I understand” *has been a perfect starting point from which to extend our conversations around what types of learning opportunities we were providing for students. Historically, our teaching in physical education has been didactic and demonstrative with rare opportunities in which students were collaboratively invested in their learning beyond attempting to follow a set of instructions. Our shift toward a more inquiry-based approach to developing physically literacy focused on encouraging students to invest in seeking information through questioning, rather than just merely waiting for it to be “delivered”. From the teacher’s perspective, this involved carefully designing a context and framework for specific units that might draw student questions out, and help focus thinking.

Physical and Health Education Canada identifies that “individuals (persons with unique abilities and characteristics) who are physically literate move with competence (proficient performance) in a wide variety of physical activities that benefit the development of the whole person (physical, cognitive, social).” An inquiry-based approach seemed perfectly designed to emphasize the individualized development of each of these unique characteristics. Our focus, was on developing a framework for each lesson in which the focus would always remain broadly centred around:
**Setting the Stage**

- acknowledging and celebrating students’ unique abilities and characteristics
- acknowledging the foundational importance of fundamental movement skills
- emphasizing connections between sport and physical activity and,
- accommodating students’ broad range of physical, cognitive and social skills

We began by defining our key understandings of how our teaching practice would shift as a result of our emphasis on inquiry-based pedagogy for both students and parents. The video we put together was brief and emphasized with both students and parents that the inquiry-based approach to PE above all would strive to ensure that there would be opportunity within each unit for students to take initiative in personalizing their learning experiences through tasks appropriate to their interest and ability.

The Physical Education Curriculum is a massive document. Even with the generosity of its most recent re-design which provides many rich and broad entry points into an exploration of health, activity and physical literacy, it can be difficult to navigate. With the understanding that we wanted to begin as teachers with curricular topics that had enough richness and complexity to embrace the full range of children’s background, experience, abilities and previous knowledge, we began by reviewing and re-framing the curriculum so that those topics could be clearly identified. The end result was a more condensed scope and sequence that identified key learning outcomes specified by the curriculum for each grade from 4-9. Click here to view!

The Galileo Inquiry rubric has always been a guiding document in my practice. For Physical Education, we focused on four characteristics identified in that rubric that aligned closely with the work we could and would be taking up in PE. They were:

**Authenticity**: We wanted to make sure that the problem(s), issue(s), or exploration(s) undertook in PE were significant to the broad range of disciplines within the physical education field (athletics, physiology, coaching, etc.) and that the tasks undertaken provided students with the opportunity to*create, produce, understand*or*perform*something relevant to students and to the discipline (outcome oriented).**Communication:**It was important to us to provide students with opportunities to support, challenge, and respond to ideas and feedback from classmates during class, and to allow them to select ways of expressing their understanding appropriate to the task (including the use of technology when relevant).**Active exploration:**We wanted to design learning tasks that would*require*student autonomy, collaboration, problem solving, management, and the recruitment of outside expertise while allowing for multiple/flexible approaches to learning.**Ongoing assessment:**Our goal was to embed regular opportunities for students to reflect on their learning throughout a particular unit, using clear criteria that they helped to establish. We also wanted to encourage them to use those reflections to set learning goals, establish next steps and develop effective learning strategies.

After an introductory class. Students had 5 days to choose a skill and work at improving it. They had unlimited resources, could work individually or in groups, and had to track their progress via video through Edmodo submissions. This glimpse provides an overview of some of the skills students worked to develop through the videos they submitted.

The re-thinking of our PE programs at Connect led to an inevitable re-examination of our assessment practices, something that has continued to evolve over the past 12 months from a tri-yearly quantitative approach to a more ongoing, formative, qualitatively reported outcomes-based assessment with an emphasis on triangulation of data through the collection of artifacts (done digitally via Edmodo), through observation (on a daily basis), and in conversation with students (via bi-annual 1-on-1 interviews with teachers). *More to come on the evolution of our assessment practices in PE… *

**Resources**

I’ve embedded some sample plans from last year’s program as an example of our approach to planning for inquiry in PE…

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Grade 9 OE Student

Grade 8 OE Student

Outdoor Education on a very basic level is about developing learning experiences designed to enhance students’ knowledge and skills in natural settings. Although outdoor programs have always been an important part of our school, the question of how to deepen the quality of the experiences we provide is one that has recently led to many recurring debates and conversations among our staff team. Late last year, it was suggested that a focus on creating more opportunities for students to spend time immersed in the heart of the local backcountry might be a good way to help regenerate connections to nature that can be so easily severed in our technology-enhanced, production-driven urban environments.

This year, we expanded our Outdoor Education Electives program in order to attempt just that. With the goal of equipping students with the skills, understanding and awareness necessary to spend lengthier periods of time in the wilderness, we practiced tent/shelter set-up and take-down, thermo-regulation, backcountry cooking, packing, navigation and leave-no-trace principles. OE students were also held to high standards with respect to demonstrating leadership, initiative, organization and teamwork in order to earn the opportunity to participate in a final 3-day backcountry experience through Elk Pass. Although explicit outcomes for the OE elective were identified as: “the development of skills necessary to ensure safe and sustainable wilderness travel,” it was our ultimate hope that the experience might result in heightened social, cultural and environmental awareness and connection. We didn’t just want to travel safely in the backcountry, we wanted to reconnect with the heart of this place we live in and cultivate an appreciation for how everything belongs.

As an OE team we really tried to tread carefully, so to speak, as we prepared for and hiked Elk Pass this June with students. We were intentional about shifting our focus away from the destination to the moment and to things we too often grow accustomed to overlooking. The resulting student and teacher reflections were pretty powerful. Although there is always more work to do, this experience renewed my conviction that while there is something immeasurably important about providing opportunities for students to find themselves in the outdoors, it’s not just about getting kids outside. It is our approach to natural spaces and our motivations as we move through them that have the potential to create or bypass the conditions for truly thoughtful ecological experiences.

**Skip to 7.00 min for student reflections **

*In the end, our society will be defined not only by what we create but by what we refuse to destroy.*

John Sawhill

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Thanks for your reply, Deirdre; I look forward to your full response.

I address the one point you make here about memorization.

Memory is the seat of learning. No memory, no learning. Those opposing memory work would do well to — at minimum, acknowledge its importance (I presume you do not disagree, but I note that there is no hint of it in what you have written.) And, having acknowledged this, to explain why memorization of times tables is not a particularly good use of memory.

I can tell you why, to the contrary, it is a good use of memory.

Early-years learners are passing through a rapid acquisition phase during which important facts are committed to memory, establishing the foundation upon which later synthesis of cognitive understanding takes place.

The ease with which these particular basic facts are automatized at this age contrasts the difficulty faced by those who must do so later in life — students who fail to memorize these elementary facts at this stage may struggle mightily with them later, and many will simply fail in the effort and never master them.

The goal of education is UNDERSTANDING. And understanding cannot grow in a vacuum — it requires context. Context necessarily entails factual content about things, processes and relationships, committed to long-term memory.

Our long-term memories are very well suited to storage and retrieval of such trivia. (Long-term) memory is not the ANTITHESIS of understanding — it is an integral part of understanding. Understanding is functionally impossible without a well-stocked memory. I don’t think any of this is controversial in the least.

WNCP Math and the like forces children to adopt inefficient and ad-hoc mental approaches to even single-digit arithmetic, and in multiple ways.

How different is memorizing multiplication tables from WNCP’s rote work? “Rote” means “repetition”. The demand for children to revisit the same “strategies” by rote in WNCP is simply astonishing.

Grade 5 students are expected to “apply mental strategies” and use skip-counting, doubling, halving and looking for patterns, to “determine answers” (i.e. NOT facts they have yet mastered) “for basic multiplication facts to 81” (WNCP K-9 Framework, p104).

“to 81” = “the 9×9 times table”.

Five years is FAR too long to force children to obsess over the mechanics of single digit arithmetic without closure! The 2008 NMAP report warns against “any approach that continually revisits topics year after year without closure”, an indictment of WNCP Math, which specifies NO point at which these are to be mastered.

http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

Now it doesn’t take a PhD in brain function to know that working memory — particularly for abstract facts — is extremely limited. Famously, humans can reliably hold about seven digits in their heads but few can do the same with fourteen digits. It is a very small working space.

A year ago a paper published in cognitive psychology quantified the rather obvious consequences. A team of researchers led by Dr. D. Ansari of UWO separated children according to whether they performed single-digit arithmetic with automatic recall or strategies. They collected longitudinal data on the same children years later from their SAT Math scores. Those who had, years earlier, committed the fundamentals to memory, significantly outperformed those who had been trained to use ad-hoc approaches.

http://www.jneurosci.org/letters/submit/jneuro;33/1/156http://communications.uwo.ca/media/singledigitmath/

Some contend that those ad-hoc approaches constitute “understanding”. In fact the WNCP Framework itself, in outcomes specifying that children “demonstrate understanding of” such-and-such a concept, the corresponding achivement indicators specify that the children are to show multiple strategies.

Yes, some call it “understanding”. But I call it “clutter”.

Thanks Dr. Craigen,

I wanted to begin by acknowledging that it seems we agree on several points. Learning is without a doubt the cultivation of memory. However I would argue that there is an important distinction between rote memorization and experiencing something memorable. Memory is formative and compositional. It requires judgement, connecting, shaping and reflecting. It is a creative, inventive process of making sense of experience.

You have written that memorizing times tables is a good use of memory. I would suggest that finding ways of making multiplicative concepts memorable is a much better use. My experience with “times table memorization” in schools is that it typically involves recitation with no conversation, no questioning, and no opportunity for students to recognize or identify patterns and connections between multiples. I have noticed that the WISE site lists John Mighton’s JUMP math program as a resource. I have used JUMP myself on occasion and recommended it to students, specifically because Mighton sets out to cultivate memory very differently to the way it is done in traditional math workbooks. As a basic example, he asks students to practice counting by 2s and 5s and guides parents to ask their children what they notice. He discusses multiples of 4 and multiples of 6 as connected to multiples of 2 and multiples of 2 and 3 respectively. The formulation of memory is connected to discovery and he creates opportunities for the students to notice patterns of fundamental importance and articulate them in their own words. The work the students are involved in goes beyond recitation in an effort to commit the basic facts to memory. This is worthwhile practice.

I think perhaps the essence of our disagreement is not whether students should have basic facts committed to memory (it seems we agree, they should) but as to how this is best achieved. You wrote “understanding cannot grow in a vacuum — it requires context.” Absolutely, but I would add that committing factual content to long-term memory also requires context. This is what having students “skip-count, double, half and look for patterns” can provide. To be fair, I didn’t always think this way. Here’s some personal context because I think it’s an important part of the story.

I was successful in math class as a kid and through high school. My parents insisted I recite multiplication tables on long car rides and I had a gift for recall. Anyway, my high school IB scores exempted me from first year math in university. The four post-secondary math classes I did take boosted my overall average. I am not a mathematician, but I guess that makes me a relatively successful product of the system. Two years into my teaching career I found myself in a Grade 4 Math/Science classroom. Although my students had arrived from schools all over the city, my own success with classroom mathematics had made me pretty confident.

Half of my students came in overwhelmingly excited: “I already know my 9s tables,” while the other half were clearly dreading math. I had had them fill out an introductory survey and at least 50% had noted that they hated the subject. The first problem we introduced that year involved calculating costs of purchasing a variety of candies using either addition or multiplication. We just wanted to get an idea of where students were at with their understanding. It was a bit of a disaster.

Student: 3 x 32 cents = 15 cents

Me: The price of one candy is 32 cents. You decided to buy 3 candies and you have calculated that it will cost you 15 cents, does that make sense to you?

Student: Confused stare.

Me: How did you get 15 cents?

Student: Well 3 x 3 is 9 and 3 x 2 is 6 and 6 + 9 is 15.

Me: Why did you multiply 3 x 3?

Student: Because there’s a 3 on the bottom and a 3 on the top.

Me: But what does that 3 on the top represent?

Student: Blank stare.

Me: Does the “3 on the top” represent 3 cents or 30 cents?

Student: Blank stare.

“Alignment” mistakes from students using conventional multi-digit addition algorithms were also excessively common. It seemed they weren’t thinking, just executing.

Student: 24 cents + 13 cents = 154 cents

Me: How much is a quarter?

Student: 25 cents

Me: How many quarters in a dollar?

Student: 4

Me: You added less than a quarter to less than a quarter and got more than a dollar?

Student: Blank stare.

Some struggling students attempting to add double digit numbers were in tears because they just couldn’t remember what “carrying” meant and what column the number they were “carrying” was “meant to go in” (“my teacher just told me to put it there”). One student had successfully used multiplication to determine the cost of purchase of a whole variety of different candies but kept coming back to me to ask “is this right?” When I asked her if she could think of a way to verify whether she was correct using an alternative strategy, she couldn’t.

I’ll be honest, for the first few classes I did a lot of showing and telling. I figured, that’s how I had learned so it should probably work. I would be sitting next to students saying: “so these 3 candies are worth 10 cents each right? If you want all 3, you will have to add 10 cents 3 times to find out how much you owe. Since they all cost 10 cents though, you could also just multiply 10 by 3 right? Because that’s 3 tens. Three multiples of ten. Right?” The kids didn’t often have much to say though and I couldn’t shake the feeling that they still didn’t really “get it.” They were doing what I had asked alright, but relatively thoughtlessly. They also seemed determined that multiplication was a series of isolated concepts you memorized and then moved on from. “We’ve already done 5s and 6s so this year we do 7s.”

One weekend early on I was telling my husband about the “trick” I was going to use to teach my students how to remember multiples of 9. He responded with “why do they have to do it your way, that’s not how I do it.” Again, I am embarrassed to say that it had simply not occurred to me that there was a different way to remember multiples of 9. It did occur to me at that point however, that it might be worth reading a little bit more about how to teach math, so over the next few weeks I read as much as I could about how students construct mathematical understanding. I spent quite a few nights at the school until 8 or 9 with my teaching partner, reading and researching and thinking and we finally decided to have the students “review” multiplication with a hundreds chart. We had envisioned that the students would start by coloring multiples of one, two, three, four etc. on the hundreds chart, that it would help them recognize patterns and make connections between numbers and that it would help them remember.

We asked them to start by coloring in multiples of one and were shocked again when we were met with 50 blank stares. The students had no idea what the word multiple meant. So instead of coloring, we talked about what it means to multiply something and what constitutes a “multiple.” We used students as examples: “What would happen to Joe if I multiplied him by 2? If I had 3 Jessicas standing up here how many multiples of Jessica is that?” and then asked students to propose definitions for “a multiple of one” based on their understanding. As a group we reviewed their definitions and then added, verified or refuted their various conjectures through conversation. The result was a more engaged group of students than I’d seen all year. The conversations led to discussions and debates and lots of “Oooooh, now I get it!” I was hooked, the kids were hooked, it turns out math is really cool.

A few weeks into our conversation about multiples I had a group of students trying to figure out how many different ways they could make a box filled with 3, 5, 7 or 9 truffles and one little boy came rushing over brimming with excitement..

J: “Mrs. Bailey I discovered something!!! You can’t fill a box with two rows if you have an odd number of truffles!!”

Me: “YEAH J! Why do you think that is? Do you think it’s connected to something we noticed about multiples of 2?”

He paused, then his eyes lit up: “YA! Because multiples of 2 are always even, not odd.”

Me: “Awesome why don’t you go and add that conjecture to the board.”

J rushed off delighted with himself to add his conjecture to the ever increasing list of mathematical “conjectures” that we would review and debate at the end of class.

I’ve told this story about J a few times in the last several years for a couple of reasons. J came into grade 4 terrified of math. Every time we talked about numbers he’d nod frantically while blinking back tears. Most of J’s classmates had recognized ages ago (Grade 2 maybe) that odd numbers couldn’t fill a box with two rows. Much earlier that year we had, as a class, approved the conjecture that “all multiples of 2 are even” and J had nodded, writing it down in his book. J had even practiced his “two times tables,” at home. He was proud that he could remember “all twelve”. But he was remembering twelve different multiplication equations as isolated facts and they meant very little to him in a mathematical context. In a traditional math classroom this would have been overlooked. In the inquiry-based classroom however, we designed mathematical investigations such that it came up again and again until J finally had an opportunity to understand. While some of our students were writing conjectures about the frequency of prime numbers and how to identify least common multiples, J was discovering, really discovering, that odd numbers can’t be split in half evenly.

Someone once told me that every time a child has an “A-ha!” moment, a fundamental brain shift has occurred. I’m sure there’s no empirical evidence to support this statement. I have only taught math to a couple hundred students thus far in my career so my sample size is low. But everything I’ve seen in the classroom and everything I’ve experienced in my own learning supports that statement. “A-ha!” moments are fundamental to the cultivation of memory.

School is a lot more interesting and seems an awful lot more real and personal when kids are rushing around bursting with discoveries than when they are sitting at desks rushing through math facts. I guess maybe what I’m saying isn’t so much “don’t teach memorization” as “make math memorable.” Situating the development of basic skills more intentionally within mathematical conversation, encouraging student formulation and articulation of ideas and guiding students toward discovery has been, in my experience, way more powerful, more exciting, and more memorable, than having them practice reciting and writing their multiplication tables.

I agree that students should be provided with the opportunity to study multiplication early on. I also agree that by Grade 5, if these opportunities have been effectively designed, students should have already committed most multiplication facts to memory. My grade 4 students were able to point out that if you “knew” multiples of 2 you knew multiples of 4 and 6 and 8, and that if you knew multiples of 3 you knew multiples of 6 and 9, and 5s were fairly straightforward so that really only left 7×7 (“and by the way Mrs. Bailey, 49 is one of those numbers and that’s why you have to work harder to remember it..” “One of what numbers?” “You know, it’s not really connected to anything. Kind of like a prime number, but not, because it’s a multiple of 7”).

The word “rote” is associated with “mechanical or habitual repetition” of something to be learned. Synonyms include: mechanically, unthinkingly and mindlessly. I cannot subscribe to the idea that students should be taught to remember things “unthinkingly”. Yes to memory. No to “mindless”. I haven’t read the word “rote” in the Alberta Education curriculum. If I had, I would have thoughtfully ignored it. You mention in your critique the curriculum’s acknowledgement of multiple strategies but Alberta Ed uses the words: “such as” to suggest the different strategies students might describe or demonstrate. It is not prescriptive or prohibitive. It doesn’t mean that children need to memorize multiple different strategies for multiplying 6 x 7. It means that they need to be able to recognize that (5 x 7) + 7 and (3 x 7) x 2 are equal to 6 x 7 and that both of those are more efficient ways to calculate 6 x 7 than counting up by 7. If they work with these concepts regularly enough in meaningful ways, are engaged in conversations about what they mean, and are held accountable for what they know, where they struggle and what they should practice, 6 x 7 is easily committed to memory and the rest just follows because it makes sense. It’s not clutter.

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The recent push for a “return to basics” shift in math curriculum in Alberta is not unexpected. Our post-industrial society remains regrettably focused on relaying and assessing content over process. The deeply embedded desire to quantify student thinking for the sake of a neat, uni-dimensional continuum that claims to represent student potential results in the inevitable association of learning with factual and procedural recall. Quite simply, we’ve designed schools to train and measure our children. We group them by age, divide their days into standardized units and test them at regular intervals in order to compare them to their peers. Memorization is easy to measure in math so we convince ourselves we’re holding kids accountable by measuring their recall. This also allows us to rank and sort students effectively without actually engaging them in conversation, something PISA has effectively mastered. However, making a judgement about the quality of an entire math curriculum based on data snapshots from a moment in time is not only irresponsible it’s ridiculous. Advocating that because memorization scores have dropped, an entire curriculum should re-focus on memory work is incredibly shortsighted. We’ve already been there. It wasn’t awesome.

Drilling students on basic math facts and the memorization of assigned algorithms for the past several decades has overwhelmingly killed interest in mathematics, hampered intellectual development and misused teaching opportunities (more on the complexity of assigning “standard” algorithms here). Math facts worksheets have been painful for all but those gifted in regurgitation (and not the good kind of worthwhile pain that is connected to something important). As Paul Lockhart writes, “I don’t see how it’s doing society any good to have so many members walking around with vague memories of algebraic formulas and geometric diagrams and clear memories of hating them.” The test results may have been good but it is safe to say that a fair majority of “old system” graduates continue to dread the thought of trying to explain math to their children.

The inquiry-based shift away from an emphasis on memorization was in acknowledgement of the fact that the cultivation of deep understanding is now recognized to be much less straightforward than simple transmission and regurgitation. “Inquiry offers a way of thinking about things that does not begin with isolated bits and pieces, but with webs of relationships,” (Friesen & Jardine, 2009) meaningfully connected through experience and conversation. Although powerlessness has become a surprisingly seductive habit, society is slowly recognizing that it is no longer acceptable for high school graduates merely to be able to do what they’re told. Today’s students will have opportunities to collect, synthesize, analyze, connect and design and will need to be able to make use of these opportunities in order to be considered effective 21st century citizens.

Proponents of “back to basics” math education love to make comparisons between the importance of memory work and the necessity of “practice” in sports. It’s a good analogy. But advocating for a “back to the basics” math curriculum is very much akin to advocating for “less gameplay, more passing practice” approach to sport. When kids don’t get to play the game, passing loses it’s appeal pretty quickly.

We read to kids and we encourage them to write things before they can spell. It’s what gives the importance of spelling proper context, makes it meaningful. The same should be (and is) possible in mathematics. Inquiry-based practice retains the rigour of strong work in mathematics without limiting kids to one perspective or strict procedural recall. Children work on problems using a variety of strategies. They are held accountable for justifying their thinking to their peers in class discussions. My experience with an inquiry-based approach to mathematics has never been that “basics” are ignored. It just structures learning so that things like arithmetic come up in authentic mathematical contexts. The emphasis is on conceptual understanding, not just procedures and practice of them. The result is that kids can not only think but can articulate their thinking. This video represents a range of grade 4 students explaining their solutions to a problem undertaken in class. Providing these students with the opportunity to share their thinking with peers and allowing their peers the opportunity to question their thinking led to some incredibly valuable conversations about efficiency, best practices, and worthwhile work in mathematics.

Inquiry effectively frames a question or topic of investigation, carefully guiding students to a solution but not directing their every move. I’ve continued to use the analogy of bringing students to a mountain and teaching them to climb but providing them with the freedom to discover their own way up rather than dragging them all up the main route. The approach involves checking in with students on a regular basis, discussing their experiences, missteps and difficulties, and supporting them as they work their way up (see Galileo Teaching Effectiveness Framework). Introducing students to a topic and subsequently abandoning them to their own devices is not inquiry, nor is it effective teaching. Nowhere in the current Alberta Math Curriculum does it state that students should “teach themselves.” High school students whose only strategies for adding 4+7 are counting up, or using their fingers are the result of ineffective teaching practice, full stop.

I recently posted the following quote to twitter:

In response I received the comment: “That way, arts graduates can appear to be competent math teachers.”

No. The opposite. The new approach asks teachers to challenge the curiosity of students with problems proportionate to their knowledge, guiding them toward strategies, conjectures, and conclusions that are mathematically sound and that they can justify with confidence.

Instead of: “Find the perimeter of a 4cm × 9cm rectangle,” we are asking: “Find a rectangle which has unit sides and a perimeter of 100. How many answers are there and how do you know you’ve got them all?”

Instead of: “Find the area

andperimeter of a 3cm × 8cm rectangle,” we are asking: “If the area of a rectangle (in cm²) is equal to the perimeter (in cm), what could its dimensions be?” or “If the area of a rectangle is 24 cm² and the perimeter is 22 cm, what are its dimensions? How did you work this out?”(via nrich.maths.org)

Instead of worksheets like this:

Students develop puzzles like this:

As an educator, it is no longer enough simply to hold the answer key. In order to effectively guide students through the process of thinking mathematically, teachers need to have wrestled with the same problems themselves and be familiar with the range of mathematical possibilities and conceptual connections that each problem might elicit. In grade 4, in lieu of repeated memory work we determined *what* was worth memorizing (ex. students agreed that it was particularly helpful to have memorized what we called “friendly numbers” – pairs that we add to give 10) and why.

I want to acknowledge that the task of moving beyond sequential, transmission-based math instruction can be overwhelming and intimidating, particularly without support or access to powerful exemplars. As Sharon Friesen writes in Back to the Basics, “it’s not just that teachers [and parents] don’t like math; they don’t know what’s happening because they can’t remember what the real work really is, All they remember of math is the equations and the rules and the facts they’ve memorized – the surface activities with all the relations forgotten…” Math teachers province-wide, most of whom are graduates of the “drill-and-kill” system, have recently taken on the difficult and uncomfortable task of attempting to introduce mathematics as the complex web of relations it is, often with very little support. It is fair to say that inquiry-based pedagogy is still new and inconsistently executed. The answer to any resulting challenges however, is not a throwback to an outdated curriculum or oversimplification of the complexity of mathematics.

WISE Math, an organization actively advocating for “back to the basics” mathematics instruction, have written on their main page that “in order to become a competent piano player, a child must practice regularly and memorize piano scales, ” stating that the same is true for mathematics. I do not disagree. Children who practice piano scales however, do not do so at their music lessons. In piano class, they play, they get feedback, and then they go *home* and practice scales because it makes a difference. They recognize that it affects the music. The new curriculum does not prohibit children from practicing math facts at home. It just acknowledges that there’s more worthwhile work to be undertaken in the classroom. WISE interestingly has an article linked to their website called “‘Drill and kill’ no way to teach math in 2011” which concludes with a quote I thought particularly apt:

“Do we need a high level of proficiency in math teaching? Sure. Is our goal one of raising student achievement and equipping kids with the math tools they need to function effectively in society? Absolutely. But we do this through effective, reflective practice, not by blindly adhering to outdated approaches that have characterized instruction for the past century.”

Also, this TED talk by 13 year old mathematician Jacob Barnett is well worth a watch:

Baroody, A.J. & Ginsburg, H.P. (1990) Children’s mathematical learning: A cognitive view. *Journal for Research in Mathematics Education. Monograph, *4, 51-64

“Cognitive research indicates that it is essential to distinguish between meaningful learning and rote learning. It is not enough to absorb and accumulate information. Children must be given the opportunity to assimilate mathematical knowledge – to construct accurate and complete mathematical understandings.”

Caliandro, C. K. (2000). Children’s inventions for multi digit multiplication and division. Teaching Children Mathematics, 6 (6), 420-424.

“The procedures [the children] developed were meaningful to them and flowed out of their deepened mathematical understanding. Their procedures will not be forgotten. Memorized procedures, in contrast, are frequently forgotten and have to be reviewed again and again.”

Carroll, W. (1997). Invented strategies can develop meaningful mathematical procedures. *Teaching Children Mathematics,* 3 (7), 370-74.

“By encouraging children to invent and use their own procedures, teachers allow them to use a method that makes them focus not simply on practicing computation but also on developing strategies for which computational approach to use[…] The reward of seeing students make sense of mathematical situations and the resulting appreciation of children’s thinking and capabilities more than make up for the difficulties.”

Friesen, S. (2008) Raising the floor and lifting the ceiling: Math for all. *Education Canada*. 48 (5), 50-54.

“I think it is important to note that students were not left alone to ‘discover’ the math for themselves. Rather, a series of lessons were designed to scaffold the student learning, ensuring that students uncovered and connected the underlying key concepts, worked through procedures related to measuring and calculating angles and arcs, length and perimeter, area and volume, congruence and similarity, and scale factors. They were asked to reason, to conjecture, and to justify conclusions.”

Friesen, S. (2006). Math: Teaching it Better. *Education Canada*, 46 (1), 6-10.

“While the task of creating classrooms in which students understand abstract and difficult mathematical ideas, see relevance in the mathematics they are learning, and achieve mathematical competence seems daunting, as a mathematics community we are further down the road in knowing what to do to achieve these goals. We have made demonstrable progress by working together – mathematicians, mathematics educators, and teachers who understand that mathematics reform is a complex matter. There are no easy answers.”

Jardine, D.W., Friesen, S. & Clifford, P. (2003). “Behind every jewel are three thousand sweating horses”: Meditations on the ontology of mathematics and mathematics education. In E. Hasebe-Ledt & W. Hurren (Eds.), *Curriculum intertext: Place/Language/Pedagogy* (pp.39-49). New York, NY: Peter Lang

“All of us at the table knew, beyond a shadow of a doubt, that this solution was correct. But, equally, none of us knew at all why it was correct. One boy insisted, with an insistence that we all recognized in ourselves, “That’s just how you do it, ok?” […] Many of us in this classroom had, over the year, talked about that odd feeling of having learned, having memorized a procedure and knowing how to do it beyond question or hesitation, and yet suffering the terrible silence and feeling of cold and deathly immobility if anyone should have the audacity to ask a question about it.”

Kamii, C. & Livingston, S.J. (1994). *Young children continue to reinvent arithmetic – third grade: Implications of Piaget’s theory. *New York, NY: Teachers College Press

“Children’s first methods are admittedly inefficient. However, if they are free to do their own thinking, they invent increasingly efficient procedures just as our ancestors did. By trying to bypass the constructive process, we prevent them from making sense of arithmetic”

Madell, R. (1989). Children’s natural processes. *Arithmetic Teacher* 32 (7), 20-22.

“It is hard to follow the reasoning of others. No wonder so many children ignore the best of explanations of why a particular algorithm works and just follow the rules […]The early focus on memorization in the teaching of arithmetic thoroughly distorts in children’s minds the fact that mathematics is primarily reasoning. This damage is often difficult, if not impossible, to undo.”

Steffe, L. P. (1994). Children’s multiplying schemes In. G. Harel & J. Confrey (Eds.). *The Development of Multiplicative Reasoning in the Learning of Mathematics*. (pp 3-39.) Albany, NY: State University of New York

“[Children] can, indeed, be told to do something, but they cannot be told tounderstand[…]It is a drastic mistake to ignore child-generated algorithms in favour of the “standard” paper and pencil algorithms currently being taught in elementary schools. Other than the work already cited, there is solid evidence that imposing the standard algorithms on children yields discontinuities between children’s methods and their algorithms (Easley, 1975; Brownell, 1935; McKnight and Davis, 1980). even when they are to some extent based on operative arithmetical concepts, the standard algorithms become essentially instrumental for the children (Skemp, 1978) and pose a serious threat to the retention of insight (Fredenthal, 1979; Erlwanger, 1973).

Stein, M. K. (2007). Selecting the right curriculum. *NCTM Research Clips and Briefs. *Retrieved from: http://www.nctm.org/news/content.aspx?id=8468

But, efficacy for what? It is important to note that students tended to perform best on tests that aligned with the approaches by which they had been taught, repeating the well-worn finding that students learn what they are taught. Combined with the findings from the analyses of curriculum materials cited earlier, the research examined here suggests that students taught using conventional curricula can be expected to master computational and symbolic manipulation better, whereas students taught using standards-based curricula can be expected to perform better on problems that demand problem solving, thinking, and reasoning.

(Also, Cathy Fosnot’s entire series* *Contexts for Learning Mathematics, Christopher Danielsen’s Talking Math With Your Kids, the University of Cambridge’s nrich.maths.org and the Galileo Educational Network’s Math Resource List)

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Research suggests that when honour roll certificates are awarded, students will tend to adjust their approach to learning in order to achieve that required 80% or 85%. Far from this being desirable however, having students focus on attaining a standard percentage-based outcome each semester is fundamentally problematic. Quantified assessment of student understanding requires arbitrary judgements as to what is a “unit,” what is “worth” one mark, and what is worth five. These judgements often do not even have an explicit rationale beyond: “I am marking out of five, this is the best so it gets five, this is average so it gets three.” (Biggs & Tang, 2011) Multiple choice tests out of 100 are inevitably preferred for percentage-based grading because answers can only be right or wrong, questions can be equally weighted, and no one has to deal with the difficulty of quantifying a conversation. Then, because students inevitably focus on what is being assessed (or rewarded), their emphasis shifts to recall of the isolated details they will soon forget but that will help them pass the test with as many marks as possible.

I have to share a conversation I overheard last week in which two students were discussing a recent assignment…

Student A: “What did you get?”

Student B: “23/29. What’d you get?”

Student A: “25.”

Student B: “Man, I don’t even know what I did wrong.”

Student A: “I got an extra mark for my figures ’cause I labeled them.”

Student B: “I didn’t even know we had to label figures. Well that sucks cause I guess I’m two labeled figures away from an 80%.”

I had to interrupt them eventually just to ask what subject they were talking about. Upon learning that it was a science lab, I was curious about their research, the outcome of the experiment, what they had discovered, and what questions they had. I asked whether they didn’t think it a bit odd that their conversation hadn’t revolved around what they were learning and one student started to answer “yeah but that’s not the point…” before catching himself.

The insistence that the purpose of learning is the “cookie at the end,” is an interesting one. If this is the case, then the presence of the cookie should guarantee good quality work and given that these cookies have been around for a while it shouldn’t be too difficult to ascertain whether excellent work is a consistent product of this form of academic recognition. I will happily take this opportunity to associate a few cliche names with the school system’s recognition of their early efforts. (via The Creativity Post)

**Albert Einstein:** slow, lazy and expelled from school

**Thomas Edison: **too stupid to learn anything

**Ludwig Van Beethoven: **awkward and hopeless

**Bill Gates: **university drop-out

**Steve Jobs: **university drop-out

**Fred Astaire: **can’t act, can’t sing

**Charles Darwin: **rather below the common standard of intellect

Evidently they didn’t do it for the honour roll certificate.

The mother quoted in the Herald article (and the many adults who commented below), suggested that without an honour roll, children have “nothing to work toward.” I would argue that rather than “nothing,” they might in fact have the opportunity to find something much more genuinely worthwhile to work for.

What about the recognition though? Isn’t it nice to be recognized for great quality work? Isn’t it important for children who work hard to have it acknowledged?

Absolutely! However, as distinguished above, honour roll doesn’t recognize exemplary pieces of work, it recognizes an 80% average. I used to get 80% averages because I coloured in title pages and copied glossaries neatly. Honour roll too often recognizes students for knowing and doing what they’re told to know and do, or answering a standard number of questions accurately on the test. It is too general, too vague, and too transparent.

I’ve been a student now for 20 years. I appreciate recognition as much as anybody who is a product of this system and lives in it. I like working hard and inevitably am grateful if someone takes the time to acknowledge my hard work. I am particularly grateful when that acknowledgement specifically identifies something that shows familiarity with the work, or gratitude for its utility which typically is the point.

Recognition? Yes! When anyone does something exceptional we should be confident and intelligent enough to let that brilliant idea, interaction, creation or construction shine. But not by presenting them with some uniform piece of paper that 100 other people received as well. We are not all capable to the same capacity in the same context at the same time. We are not all great athletes, singers, scientists, or artists. I am not any of these. But I am thankful they exist and appreciative of their talents. I genuinely believe that we will only be capable of our best as a society when we are willing to let the best in each of us *be* the best. There is something in every child we can recognize; if we can’t find it, we simply aren’t looking hard enough.

A brilliant teacher once said “schools shouldn’t model the world as it is, they should model the world as it should be.” If we believe that schools should build a community in which students are encouraged to engage intellectually in the investigation of real issues for extended periods, if we believe that failure is part of learning, if we believe that students are not all alike and that schools should teach them how to capitalize on their individual strengths and those of their classmates as they discover who they are, then recognition in the form of honour roll makes absolutely no sense. As I wrote over a year ago, it is always troublesome to witness the living, cultivated detail of deepening understandings occluded in an overly technical and methodological obsession with quantitative outcomes of student work. Children are not flat, anonymous, trainable beings. Neither are they measurable entities, and every time we treat them as such we sell them short.

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I only remember a few specifics from my first few weeks in the classroom. I had big ideas but the execution was definitely messy. I remember trying to keep track of things that worked and didn’t in those first few months and the second category was certainly larger than the first. I remember the first time I gave the students a math problem that asked that they apply an understanding of place value. Within ten minutes, three children were crying because they didn’t understand and were afraid to get the wrong answer. Somehow I hadn’t anticipated that my fifty students from all over the city would have such varying experiences and attitudes towards learning.

I was so thankful to be partnered with Amy Park, an incredible teacher and leader in inquiry-based practice. Her early perspective and support during our team-planning blocks quickly became a lifeline. It became evident that my thinking was always amplified through conversation with Amy. A lot more seems possible when someone has always got your back.

A pivotal moment in those earlier conversations came from the acknowledgement that a majority of students seemed to be struggling with anything beyond simple computation in mathematics. They kept waiting to be told what to do. As I tossed out possible learning opportunities, I remember Amy asking the question “are we teaching students what to think or are we teaching them how to think?”

We realized these 9 year olds needed an opportunity to practice thinking. We needed to start by talking about the art of having a thoughtful opinion and being open with it. Two weeks into the year we decided to team-up. We gathered all 50 students in an open space in the school and asked them to share conjectures about how they might define: “multiples of one.” Hesitantly at first, we heard “any number with a one in it, every second number, every number that ends in a one.” As students saw their ideas considered and supported, momentum for participating in the conversation grew. Partial agreements about some conjectures lead to conversations about whole numbers. The kids debated whether zero and negative numbers could be considered multiples. We looked at whether two non-identical conjectures could mean the same thing and both be completely correct.

Further conjectures from our future mathematicians |

I learned more about mathematics and teaching that day than I could have imagined. I thought we’d have breezed through multiples of one. We didn’t even get past it. But what a waste it would have been to prescribe a definition and miss the magic of abstract discussion and debate among nine year olds. How could we presume to know what they understood, how would they know that they did, unless we allowed them to debate, to defend and to support their ideas?

I started my year with the expectation that my role was to help students understand exactly what it was that I wanted them to know; my goal was to track their progress and ensure that they were headed in the right direction. Unknowingly, I had intended to replicate my thinking in my students without ever having asked for theirs. That day in math class, I learned that even as a teacher, in a position in which I have theoretically earned the right to assume my expertise should direct the learning – inviting students to contribute blew my narrow perspective wide open.

As our year progressed, providing opportunity for students to engage in conversation and to push each others’ thinking continued. Our classes often combined to share their ideas and we found ourselves pushing desks and chairs out of the way on a regular basis. Conversations were always better when students weren’t at their desks so some old mats discovered in the gymnasium hallway were appropriated for class-wide “congresses.” We also found that students grew increasingly competent in advocating for different work spaces and were constantly moving back and forth between classes or pulling out the mats and lying on their bellies to discuss latest discoveries. It was sometime not longer after that I came across an article written by a university professor who had moved his classes to a nearby coffee shop in order to encourage his students to engage more readily in conversation and debate. He discussed the limitation of a desk-based classroom culture and the ease with which moving a to a less formal space shifted the attitudes of his students.

When we brought it up with the students, they quite willingly shared their ideas for how we might re-design our classroom space and the result was a unanimous vote in favor of completely converting one of our classrooms to a cafe-style area while keeping the other for what the students called the “university” – a space for more quiet, focused and individual thinking and writing. Our weekly blog had kept parents informed and involved in the process and that week we had bean bag chairs, arm chairs, and ikea side tables join the gym mats in what would become affectionately known as Barkley’s cafe. The cafe and university became fixtures at our school as the students helped us redefine what it means to be on task and engaged. It was the physical manifestation of a different kind of teacher-student relationship. One in which people could walk in right away and not know where the teacher was because we had become so much a part of the learning that we were also cross-legged on the floor listening to the students justify their thinking.

Barkley’s Cafe circa 2012 |

One of the best results of this change was witnessing students engage in conversation with guests to the school about the design of their workspace and the rationale behind it. I remember a teacher from a visiting school sharing that one of our students had told her that this space was different was because students here were treated like their ideas mattered and could make a difference.

Looking back I have to acknowledge that there were a few pretty key pieces that contributed to this change. First and foremost, it was the students that were willing to share their unique vision with confidence. I’ve since learned that every time I forget to ask the kids, it’s a mistake. Our school also supports a risk-taking culture that encourages teachers to keep taking a step forward,recognizing that every time that step is in the wrong direction that it was a valuable learning opportunity. A few months after the change, Amy and I were discussing our evolving collaborative practice with our principal and we made a point of thanking him for letting us move all the furniture down the hall. He responded with – “To be fair, you didn’t actually ask – although you’re welcome – we trust you.” In a way, that confidence had the same effect on us that ours had had on our students – we were empowered.

This change in our classroom environment was a product of co-designing learning tasks in which student voice had space and validity. Kids are so innately curious and creative. All that is left to us, is to foster an awareness of the possibilities that surround them, to let them ask questions, make decisions and make things different.

*I’m Deirdre Bailey and this is a story about bringing students into the conversation.*

Students share their work with visiting teachers at #ConnectEdCa |

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