You can assess whether your students can apply higher-level thinking skills. After I had exposed my class to several different types of “thinking” questions while doing math problems together, it was their turn to start asking the questions instead of me. Obviously, this is not helpful – if the math processes are the actions of doing math, it makes sense then that these actions will, at times, encompass critical and creative thinking. I wanted to understand why the results had been so poor, so I stayed to observe June and her students in their normal routines. Assessment is at the heart of teachers’ work as it focuses on paying attention to students’ mathematical thinking and acting accordingly. A visual scan of the classroom confirms an active learning environment. Are our students question askers? Here are my personal working definitions of each: Yes, these are deliberately economical. 7. Use these three strategies to get kids thinking and talking about their problem solving strategies while building that “oh-so-important” confidence, and you CAN conquer math word problems! . The range and variety of the student work, with all its understandings and misunderstandings will lead us to that point. 3. How tasks are given to students: As much as possible, tasks should be given verbally. In the math classroom, students can get on Sum Dog to practice learned skills independently after a mini-lesson. Over more than a decade, the author has developed a 14-point plan for encouraging students to engage deeply with math content. Jennifer Piggott shares some of her thoughts on creative teaching, and how it can encourage creative learners. Assessment for a Thinking Classroom ; Vertical Surfaces [docx from Rob Cop] Delta School District, Delta (May 9, 2017) Building Thinking Classrooms ; Good Problems; Global Math Department Recording; Vertical Surfaces [docx from Rob Cop] West Point Grey Academy, Vancouver (May 8, 2017) Building Thinking Classrooms Let’s think about the big picture of why we ask students to share their thinking when they are solving math problems. “Loving the Math, Living the Math” on LearnTeachLead is here. Originally posted on Matthew’s Olridge’s blog, here. To the former: problem-solving classrooms will always have an element of creativity, unless we force our own methods, techniques and processes on our students. Students using new thinking tools, or subtly tweaking a solution path or process they may have got from talking with their classmates. Here is a acronym to help students remember the strategies involved in solving such rigorous problems. Kady Dupre has worked as a classroom teacher, instructional coach, and intervention teacher in elementary grades. In each class, I saw the same thing—an assumption, implicit in the teaching, that the students either could not or would not think. I want them always probing the mathematical world around them with their confident judgments. Textbooks and workbooks usually show problems vertically. A forest of arms immediately shot up, and June moved frantically around the room answering questions. A balanced math program with strong foundations and a spirit of questioning will always lead to interesting lines of inquiry-questions, leading to more questions. For a long time, I felt like creativity was that certain “je ne sais quoi” of the math classroom, a “know it when I see it” type of thing. Further compounding the problem, critical and creative thinking are, at best, ill-defined. More information and examples of … Numeracy is often defined as the ability to apply mathematics in the context of day to day life. Room organization: The classroom should be de-fronted, with desks placed in a random configuration around the room—away from the walls—and the teacher addressing the class from a variety of locations within the room. Rather, it occurs constantly and is an integral part of daily classroom practice. If there are data, diagrams, or long expressions in the task, these can be written or projected on a wall, but instructions should still be given verbally. When I think of the 6 Cs, it touches on most of them: Critical Thinking, Creativity, Character (because being in a time-sensitive situation really is a test of character), Communication, and Collaboration. But teachers often show them horizontally (15 – 9 = 6). Typically this binary is set up as “making” versus “assessing” or “judging.” I believe that both are intrinsically tied together. There will be patterns and trends in the strategies and tools that individual students use that further differentiate more “unique” or “divergent” work which will perhaps “more” creative. One day in 2003, I was invited to help June implement problem solving in her grade 8 classroom. examples, and applicable classroom handouts can be found on these websites. That the students were lacking in effort was immediately obvious, but what took time for me to realize was that the students were not thinking. The teacher should answer only the third type of question. They can use the progress reports to reflect on their learning and set their own pace. Practice questions: Students should be assigned four to six questions to check their understanding. It did not go well. Waco, TX: Prufrock Press. Since critical thinking doesn’t end when an individual project does, you will want to give students sufficient time to evaluate their thinking strategies. The first one I gave her was a Lewis Carroll problem that I’d had much success with, with students of different grade levels: If 6 cats can kill 6 rats in 6 minutes, how many will be needed to kill 100 rats in 50 minutes? When I thought this, I probably didn’t have a broad enough definition of creative thinking. Work on these problems to improve your strategic thinking. In his judgment, here they are: Here’s a nice quotation on critical and creative thinking: “These two ways of thinking are complementary and equally important. Not $1.25, not $1.27- $1.26. 12. Thus, my early efforts to build thinking classrooms was oriented around problem solving. Robert Kaplinsky, a math teacher and author on the “open middle math” talks about how math teachers can unlock student thinking and interest in how problems are posed to students. 10. Critical Thinking A - Level 2. When businesses hire employees, the employee will never be given a math problem to be solved. Guide students to formulate ways they might adjust their critical-thinking strategies with the next problems they solve. The following day I was back with a new problem. It does not elaborate which! And there is an optimal sequence for both teachers and students when first introducing these pedagogies. But if you are a student, and you are doing a mathematical problem or task, you are making something new every single time. The type of tasks used: Lessons should begin with good problem solving tasks. We redesigned Thinking Blocks and packed it full of new features! How hints and extensions are used: The teacher should maintain student engagement through a judicious and timely use of hints and extensions to maintain a balance between the challenge of the task and the abilities of the students working on it. The teacher should answer only the third type of question. Yet I believe both are relatively unexplored areas with our young student mathematicians. I believe critical and creative thinking are both essential to doing math. The questions should not be marked or checked for completeness—they’re for the students’ self-evaluation. Inquiry to me means: asking good questions. So this wraps up the top 5 ways that you can use problem solving tasks in your classroom. Obviously, this is not helpful – if the math processes are the actions of doing math, it makes sense then that these actions will, at times, encompass critical and creative thinking. Busy math teachers can listen to this quick episode to get an introduction to open middle math … How does this happen in the math classroom? Age 11 to 14 Posing Questions and Making Conjectures. That is why our classrooms should be open thinking spaces. Click your grade level below to get Solve and Explain problem solving tasks for your classroom. What is critical and creative thinking in the math classroom? I don’t buy this false binary. They will be given a PROBLEM to be solved. I have a dislike for overly complicated frameworks and definitions that clutter and obscure important concepts. Helpful idea: Have students cut out numbers and place in the empty boxes like pieces to a puzzle. With 'S.W.E.E.P' the students can better perform on constructive response questions on their state-mandated tests. They will pick the best representations for their mathematical work, and their own idiosyncratic mathematical voice will come out. 13. Here is the lone reference to critical and creative thinking in the Ontario curriculum: The star below the achievement chart is a footnote explaining that critical and creative thinking are present in some, but not all, math processes. other, and extend their thinking. Students can improve their argumentation skills while they practice explaining the logic behind their problems. It will always be our job to consolidate purposefully, and to offer suggestions as to more efficient or effective solutions. June used it the next day. They need to work together in harmony to address perceived dilemmas, paradoxes, opportunities, challenges, or concerns (Treffinger, Isaksen, & Stead-Dorval, 2006). Some kids have trouble changing the … The problems posed should have multiple solution strategies, encourage investigation, promote reasoning, and require students to provide justifications for their thinking. See: Treffinger, D. J., Isaksen, S. G., & Stead-Dorval, K. B. What she wanted from me was simply a collection of problems she could try with her students. The role of teachers in teaching critical thinking is debated- see Daniel Willingham’s piece here. Benefits of this practice are various. Though computational thinking is often associated with computer science, its process guides problem solving across a variety of different contexts. What is critical and creative thinking, and why is it so important in mathematics and numeracy education? She had never done problem solving with her students before, but with its prominence in the recently revised British Columbia curriculum, she felt it was time. Since they have to explain their thinking, this is a great way to catch any misconceptions and give feedback to individual students. To help teach computational thinking in the classroom, this article will review four project examples in math, English language arts, science, and social studies. Doesn’t that sound like critical and creative thinking, combined in one neat mathematical package? When used explicitly and consistently, Visible Thinking routines will promote active thinking and deep learning. 5. The power of their thinking led them to this conclusion. This will require a number of different activities, from observation to check-your-understanding questions to unmarked quizzes where the teacher helps students decode their demonstrated understandings. Learn to conjecture, invent and solve problems. More alarming was the realization that June’s teaching was predicated on an assumption that the students either could not or would not think. To solve critical thinking problems, math teachers should model the way they think when solving a problem. 8. 14. Without the ability to solve problems, learning is ‘academic.’ Problem-solving, creative thinking, and critical thinking are both skills and habits that allow students to apply and transfer academic knowledge into real-world application. A thinking classroom must have something to think about. Many students gave up quickly, so June also spent much effort trying to motivate them to keep going. The star below the achievement chart is a footnote explaining that critical and creative thinking are present in some, but not all, . This sequence is presented as a set of four distinct toolkits that are meant to be enacted in sequence from top to bottom, as shown in the chart. Sign up for our newsletter and be the first to hear about new resources as they’re published to The Learning Exchange. Formative assessment: Formative assessment should be focused primarily on informing students about where they are and where they’re going in their learning. Your turn Student work space: Groups should stand and work on vertical non-permanent surfaces such as whiteboards, blackboards, or windows. I wanted to build what I now call a thinking classroom—one that’s not only conducive to thinking but also occasions thinking, a space inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion. “Voice” is not just for the English classroom). Measured Impact. about how the “best way to think critically is to think critically.” We are risking circular logic there, but think about it: the best way to learn to think, is to think. Learn to connect mathematics, its ideas and its applications. There are some astounding numbers floating around about the ratio of students asking questions, to teachers asking questions, in a typical math classroom. Why Students Need to Write About Their Thinking. Mathematical Language Routines A 'math language routine' refers to a structured but adaptable format for amplifying, assessing, and developing students' language. The role of teachers in teaching critical thinking is debated- see Daniel Willingham’s piece. When these toolkits are enacted in their entirety, an optimal transformation of the learning environment has been achieved in the vast majority of classrooms. This one page worksheet is on math terminology. From this research emerged a collection of 14 variables and corresponding optimal pedagogies that offer a prescriptive framework for teachers to build a thinking classroom. Summative assessment should not in any way have a focus on ranking students. Over 14 years, and with the help of over 400 K–12 teachers, I’ve been engaged in a massive design-based research project to identify the variables that determine the degree to which a classroom is a thinking or non-thinking one, and to identify the pedagogies that maximize the effect of each of these variables in building thinking classrooms. These are just a few of the Making Thinking Visible routines that can be used in the math classroom. 9. It does not elaborate which! 12 Strategies For Creating A Culture Of Problem-Solving In Your Classroom. Question askers are typically critical thinkers. My research also shows that the variables and accompanying pedagogical tools are not all equally impactful in building thinking classrooms. They need to use their basic math vocabulary and thinking process to answer the questions correctly. Here is an example of a student finding a new use for Minecraft as a thinking tool to represent data: Inquiry is also hidden in that little line in the picture from the curriculum above. Further, Poincare said something to the effect that mathematical creativity is simply discernment, or choice. How can we harness these two powerful types of thinking? 11. This is one of my favourite things to tweet now and again: This work came out of our LearnTeachLead project involving proportional reasoning: http://thelearningexchange.ca/projects/loving-the-math-living-the-math-part-1/. Introducing math games into the classroom is a great way to make learning fun, engaging and motivating for … My second presumption is that mathematical knowledge and skill gained as children grow older allows them to think creatively and critically. Vertical non-permanent surfaces such as whiteboards, blackboards, or windows present in some, but not all.! 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