The Glorious Aftermath of a Design Project (3/3/15)

posted Mar 3, 2015, 10:17 AM by Ellen Crews   [ updated Mar 3, 2015, 3:10 PM ]

I have nothing to do. I am sitting in my morning math class doing nothing. My students are selecting a gym for me in a problem that requires them to solve a system of equations. Aside from occasional humorous remarks about the likelihood of me ever going to a gym, they are not interacting with me at all. They are discussing the problem and figuring it out for themselves. Cool! To be fair, I need to admit that last week was a struggle. We completed a design challenge on buying a car which ended up being much more complicated than I had ever imagined. I spent so much time filling in gaps in their background knowledge, I began to seriously doubt whether the intended content was coming through. The whole experience proved very frustrating. Did they actually learn what I had hoped they would learn? The problem I handed out today is one that I created three years ago. In the past, students have struggled and needed me to push them in the right direction to get started. Today was different. Without prompting, at each table the students started discussing the problem and determining the appropriate steps to reach a solution. The only questions for me so far have been asking about the location of the stapler (I found it in the back of the room) and whether they could move on to the second problem when their group is done. I have heard some amazing questions including: “Which of these numbers represents the growth?” “How should we space the numbers on the y axis?” “Which variable should we graph on the x axis?” “Does this answer make any sense?” Great questions, however none of them have been directed at me. They are actually discussing math and trying to figure things out for themselves. Wow!             I spent the last two weeks tearing my hair out over a seemingly endless design project, wondering if I was wasting my time. This week, my students are barreling through complex systems without any help from me. They are explaining, arguing, erasing, demonstrating, and celebrating when they figure out the answers, all without me. I can sit back and watch them learn without intervening.             Next week we move on to geometric transformations, another design project, and probably a little hair tearing. My scalp and I are enjoying this week.

What A Design Thinking Project Reveals About Equity (2/20/15)

posted Feb 20, 2015, 8:21 AM by Ellen Crews   [ updated Feb 20, 2015, 8:25 AM ]

It seemed simple enough.  A design challenge in 8th grade math about buying a car. The idea is that students choose form a list of fictional buyers, empathize with the buyer, and select a car based on the buyer’s needs. To help with empathy, each buyer has a financial statement along with some other background information. For the math content, students had to calculate the amount of flexible spending money each month for their buyer, look at different payment plans, graph and compare the plans, and generate a linear equation to describe each payment option. I obsessed on creating a website with all of the necessary steps and information. I spent way too much time on the details, telling myself that it was worth it because it would help build both my technical skills and my standing curriculum. I looked forward to seeing the engaged look on my students’ faces as they tackled the real-world problem.  I didn’t see that look; I saw confusion. Students didn't ask questions. They sat and stared at the problem, not writing, not reaching for a calculator, just staring. I started a conversation with one group, asking them what they thought they should do with the information. “What is a ‘savings account’?” one student asked. I asked the entire class if they understood what a savings account is. Three students nodded, the rest shook their heads. So I spent the next several minutes explaining how and why people save money.  Further questions revealed that many students did not understand the concept of monthly income or bills. They also did not understand what a mortgage is, or that you can buy a car by making monthly payments. I had to explain taxes, interest, down payments, and why you might not want to spend every available dollar on a car. The situation caused me to reflect on some of the practice performance tasks that I have seen in advance of the new testing regime. Much like my design project, they make some large assumptions about students’ background knowledge. Unlike my project, however, standardized tests do not allow for assistance to fill in those gaps in background knowledge. So, is it equitable? In almost every aspect of adult life it is acceptable to reach out for more information when we don’t understand something, yet we require children to perform complex tasks without support. If we are really trying to predict future success, shouldn’t the ability to seek out appropriate support be a factor? It may be impossible to achieve equity on any test, because the playing field in the classroom, as in life, is never truly level. Now I have to go explain income tax to a group of teenagers.

Design Thinking in Math (1/18/15)

Jan 18, 2015, 6:26 PM by Ellen Crews   [ updated Jan 23, 2015, 9:56 AM ]

Almost every tine that I have gotten into a discussion about design thinking in the content areas, the excitement in the room is almost palpable. Teachers share their project ideas and stories of engaged students developing creative solutions to a variety of complex problems.  One content area, however, seems frequently to be excluded form this celebration of innovative teaching and learning. Math. How does design thinking work in Math? When this question comes up, the simple answer often is, “It doesn't.” How sad. As a member of the team designated to lead my school into the world of design thinking, it seemed almost unbearable to think that, because of my content area, I would not be a full member of the club. Shuttled to the outskirts where I could watch others bask in the glow of this enlightened approach while I continued to stress the importance of solving for x. Math teachers know that they have a long list of very specific skills that they need to teach, and often worry that former students will be the only ones in the room who cannot use the area model to multiply polynomials. The mere idea of deviating from our slog through the mathematical standards to engage in design projects is daunting, to say the least. Many of us agreed that it simply cannot be done. The solace offered by those more experienced than I was to pull in small components of the design cycle wherever I could.   I was preparing to teach a lesson that had proven to be engaging and meaningful for students in the past.  The idea was, if you are given the cost of a single, double, and triple cheeseburger, can you develop a linear equation that will allow you to find the cost of any burger? The final step was to calculate the cost of a burger with 100 patties.  As I was preparing the lesson, it struck me that the goal, teaching linear progression, could be met with less structure.  I showed students pictures of burgers of increasing sizes and asked them to find the problem. I was hoping that someone in the class would come up with finding the cost as a problem so that my students could reach my intended goal. The students worked in their team to develop problems and share them with the class.  The complexity, creativity, and relevance of the went beyond anything I had imagined. How many calories are there in large burgers? How does the sodium content compare to health recommendations? What percentage of the fat comes from the cheese? And yes, some wanted to look at the cost. Wow! Each group developed a “needs statement” defining who needed what information and why it was important. Students brainstormed about how they could solve their problem, and determined what data they would require. Without any direction to do so, students did online research and began solving their problem. Did all of them include a linear equation in their plan? Of course not! I had to walk from group to group and push their thinking until they realized that graphs and equations would be an excellent way of describing their work. It was a little contrived, but in the end students met my learning goal and engaged in a little design thinking.

Evolving Assessment (1/15/2015)

posted Jan 15, 2015, 1:28 PM by Ellen Crews   [ updated Jan 15, 2015, 1:32 PM ]

When I started teaching, it was at a school which struggled with long-term “Program Improvement” status. As such, there was a strong emphasis on continual assessment. “Assessment drives instruction” was the foundation for much of our planning.  This phrase, however, had developed an alternative interpretation with could best be summarized as, “The assessment drives instruction.”  I worked with a team to write benchmark exams for the district which closely mirrored the content and format of the state’s standardized assessment, with a goal of accomplishing the dual purpose of predicting student performance and preparing students to be successful.  Additional chapter tests were created using the same process.  The formula was multiple choice, and we carefully crafted questions that would predict future performance as well as wrong answers that reflected students’ foreseeable mistakes.  After each test, our assessment software would generate a detailed report on the outcome, and we could look at trends for specific questions or standards.  In addition, each student was assigned a color which reflected their overall performance.    A few years ago I surveyed my students and, among other things, they reported a high level of test anxiety.  They had been through years of tests like mine, with teachers continually stressing the extreme importance of successful performance.  To combat their fears, I made some immediate changes. I stopped giving chapter tests and replaced them with smaller, more frequent assessments.  I also stopped using the words “test” and “quiz,” calling my mini-assessments an opportunity to “Show What You Know.”  The multiple choice questions were gone, and students could earn partial credit for showing appropriate procedures.  I also stopped preparing students for the district’s benchmark exams. I administered them without warning, telling students, “Just do the best you can and don’t worry about it.” Surprisingly, scores did not suffer from this lack of preparation and emphasis.  Student anxiety, as measured by subsequent surveys, decreased and students started enjoying math class. The next year, my team decided to institute a weekly assessment, and made the shift from grading with points to using a rubric.   We were looking at mastery of the content standards, while emphasizing the Eight Mathematical Practices found in the Common Core State Standards. This was very different that the tests our students had taken in the past, and our students became increasingly frustrated.  They did not know how to demonstrate their thinking, and all of our suggestions and examples seemed to go over their heads.  We shifted to a new rubric which emphasized process over mastery.  For the next few months we focused on the Mathematical Practices and increasing students’ willingness to tackle complex problems.  We changed the names of our assessments to “Show What You Can Do” to emphasize the importance of process over outcome.  Gradually, as students became more comfortable with this new type of assessment, we moved back to grading on content. This year, I started at a new magnet school and worked with a team to develop a general rubric to guide grading across all content areas.  I adapted this rubric to fit with what I what I valued in math.   The assessments also changed.  I have moved away from weekly assessments, and instead throw them in whenever I want information.  I try to assess with two questions at a time.  One question relates to concepts that students have experience with, and I consider that assessment to be summative.  The other question is based on concepts to which students have had little or no exposure. These I count these as formative.  Students may use their notes as a reference, and may ask questions during the assessment. If I do not have the time to provide individual feedback, I do provide an example a response that would receive a 4.  Students have the opportunity to review the example and reflect on how it differs from their own work before having a second chance at the assessment. I’m still not sure of the overall impact of these changes.  I have noticed that many students are putting in more effort than before, and really striving to do the best that they can.  Students who tend to struggle have learned to at least try, because they know that they can get a score of 1 or 2 for their efforts.  And I have a frequent source of information about my students’ progress to help drive my instruction.

What Does "Engagement" Look Like? (11/7/2014)

posted Nov 7, 2014, 9:59 AM by Ellen Crews   [ updated Dec 3, 2014, 7:43 AM ]

What does “engagement" look like?   I have been asking myself that question all week, and I am still not sure that I am any closer to a definitive answer.  During a group activity, I saw a group of boys all inspecting the inside of another boy's mouth (apparently he had a mighty fine canker sore).  Less than a minute later, they were all on their feet and arguing about how to create a graph.  Is that engagement?  I guess I could be a lot better about classroom structure and routines. I tend to find it amusing when students get up and do a victory dance when they get a problem right.  I don’t care (or notice) if they are walking around the room or lying on the floor while they work. My room can quickly turn in to a disaster zone.  There are times that students are leaning over their work, debating their next step, and there are times when they are looking into each others’ mouths.  Sometimes when I sit in a meeting, I look around at the room full of adult teachers and administrators.  There are times when we are adamantly debating our policy or next steps.  While I have never noticed anyone looking into anyone else’s mouth, I have seen people cheking email, tweeting,  playing solitaire  on their phones, or quietly writing blog posts.  Are we engaged?  Maybe engagement comes in waves.  To get true engagement, where students are totally immersed in the task, do they need the freedom to occasionally be off task? I'll keep asking myself.

Completing Your Own Assignments (10/28/2014)

posted Oct 28, 2014, 9:55 AM by Ellen Crews   [ updated Mar 5, 2015, 3:39 PM ]

I made a pledge to my students this year. I promised that I would do every bit of work that I assigned to them. I made this pledge after watching my own daughter struggle with two hours of math homework every night.  So this year I have completed every homework assignment, every exit-slip, every bit of class work, every quiz, and every test.  Last night I was up late because I realized that I needed to take all four versions of the Chapter 2 assessment before I gave them to my students this morning. What Have I Learned? There are nights when other aspects of my life make completing homework very difficult.  Some evenings it is almost impossible, and I can’t even imagine having to complete work in Language Arts, History, Science, etc. as well.  Students have lives that can be every bit as complex as our own, and need flexibility in the timing of assignments.  I will no longer assign work and expect it to be done the next day. Students take longer to complete assignments than teachers.  I heard somewhere that it takes students as much as 5 times longer than it takes their teacher to complete a task, and this fits with what I have observed in my own classroom.  Homework assignments now span a week, and I won't assign anything that takes me longer 30 minutes.  Last night it took me an average of 12 minutes to complete my own test, so students will have up to an hour.  We need to give students enough time to be successful. Doing the same thing over and over again is boring.  No wonder so many students hate math.  I need to continually remind myself to mix things up and provide variety in concepts, as well as the form of assignments.  Keep them guessing and keep them on their toes. I gather new insights every day, and am continuing to change as a result. Empathy with my students now guides my instruction.  Maybe I should invite them to teach the class.  It would be nice to have them empathize with me!

Stretching Their Brains (10/28/14)

posted Oct 28, 2014, 9:12 AM by Ellen Crews   [ updated Dec 3, 2014, 7:46 AM ]

Today, as I was beginning to conquer the mountain of student portfolios that still need grading, I noticed that I have begun to change the value I place on different components of an assignment.  I found myself rushing through all of the complex mathematics, and zeroing in on the student reflections at the end of each portfolio.     I feel I should warn readers; never ask students to evaluate the assignments that you create unless you are ready for some very pointed and incisive critiques.  Students pointed out many flaws in planning and execution of their latest project.  They also offered some very helpful ideas about how I could improve the assignment next year. Many ranted about how difficult the project was in one sentence, and then reflected on how much they had learned in the next.  They almost universally agreed that I should repeat the project (with their suggested corrections) next year.  What struck me most about their reflections, however, was the repeated use of the word "think."  Many of them felt that, even though there were not that many actual math problems to do, they had been required to think a great deal.  Some found all of this thinking time to be a wonderful change in their daily routine,  Others wished that I had directed them more, so that the work could have gone quicker.  One student wrote that the assignment had "strained [her] brain" but felt that all the strain had "stretched [her] brain a little." Here's to stretching their brains