End of Semester Round-Up: MATH

The end of the semester is drawing near. We have two more weeks of teaching and learning, and then one week of summative examinations. All grade levels take summative exams for every subject, which is a lot of testing for a 17-year-old, let alone for a 6-year-old. My grade 6 students are beginning to study now — cramming for long tests that will dominate an entire week of their lives. I’d love to work in a school where there was less emphasis on testing. At least at this school, nationwide standardized tests are only taken every three years and are barely mentioned until a week beforehand. (And amazingly, I might add, the kids do fine on them!) However, while big standardized tests are de-emphasized, testing in our classrooms is rampant. Teachers here are very used to the modern status quo of testing constantly to monitor progress and hold students accountable for their learning. But anyone who has studied education theory in the last couple decades would know that testing, and homework too, are often correlated will lower achievement — not to mention lower self-esteem and self-efficacy. I’m a big fan of Alfie Kohn in particular who said, “When test scores go up, we should worry, because of how poor a measure they are of what matters, and what you typically sacrifice in a desperate effort to raise scores.” He has written a lot to call into question taken-for-granted features of modern schooling. His articles “Rethinking Homework” and “The Case Against Gold Stars” are inspiring, but unfortunately, there are more teachers and administrators who ‘believe’ in homework and extrinsic motivators (despite the mounting evidence against them) that getting a school to move away from them would be like taking a fish out of water. Or maybe a shark, because they would put up a nasty fight!

I have a math co-teacher, and because he has been here a lot longer than me, I easily fell into the non-leader position upon arriving here last year. My co-teacher is old-school — worksheets, tests, memorization, etc., and I find myself slipping into those ways more often than I’d like. I also fear that he views students’ math ability as fixed, rather than flexible. I’m taking a free online course through Stanford University called “How to Learn Math,” and it’s all about teaching for a growth mindset, instead of a fixed mindset, which means that teachers need to understand that people are capable of learning math and being successful in math class, even if they never have before, even if they’re behind, and even if they seem to be stuck at a certain math level. Teacher expectations have en enormous impact on student learning. (A famous study was done by Rosenthal & Jacobson in 1968, which showed what is called The Pygmalion Effect. You can read about it in this Wikipedia article.) I’m learning a lot of really good ideas for helping students understand the value of mistakes and to view themselves as growers and learners, while at the same time expecting them to respect each other as fellow growers and learners.

I went to school to become a teacher not afraid to shake things up. As it turns out, I’m a total wimp. I’m so concerned with stepping on others’ toes that I shy away from doing things that I know are better for my students. Although at the same time, it would be difficult to be a total radical while co-teaching with someone who is not. It would be confusing for the students, and it could create tension. Again, I’m a wimp. My activists idols certainly never stopped what they were doing to avoid awkwardness. I have found that as a teacher, I really crave inspiration from a role model. I’m not great at being the ringleader of a revolution; I need someone to get behind. I wish I could be a leader. I wish I could teach with fellow Critical Research Academy grads and with Liz Pearne (who says things like, “Let’s start a revolution!”). I wish that I could:

– eliminate homework

– stop grading tests

– assess projects and individual assignments based on learning over time, rather than on achievement

– be more constructivist when it comes to designing lessons

– lead other teachers toward a more theory-based model of education

Little things that I can do now:

– I’m giving a math quiz today, but their scores won’t count toward their grade in the class.

– I’m going to congratulate students on their mistakes, and ask them to explain how they fixed them, to show that mistakes are the only way to learn.

– I’m not going to assign homework tonight.

On a positive note, I really like my students, and they’ve been doing some great things. This week they’re working on a project for which they must ask a research question, gather data via survey, and decide on an appropriate graph to display their results. I’ll post photos of the finished products!

I could use some encouragement for breaking through (or at least lightly bending) the status quo next semester. Do you have any suggestions or thoughts?


6 thoughts on “End of Semester Round-Up: MATH

  1. Although I don’t have any suggestions (sorry!!), I wanted to at least mention that I think it’s amazing and admirable how much thought you put into teaching. If the world had more mindful, learning-focused educators… I think we’d be MUCH better off πŸ™‚

    Keep on keepin on (even if you are taking baby steps).

  2. What an interesting post! I’m glad Carrie pointed me towards you. And I have to say, I agree with Alicia’s sentiment–it’s heartwarming to hear how much you care about your students. I think you’re doing the right thing by not causing chaos by trying to change methods too fast. That said, I’ll bet there are a few good ways that you can continue moving the class activities more toward a growth mindset (Carol Dweck is awesome). I’m certainly no expert in childhood education, but I’m happy to share ideas that seem to work in other walks of life.

    Regarding tests, is it really the tests that are bad? Or is it a mindset problem–the mindset that your score on a test somehow defines who you are? For students with a growth mindset, I would think that a thoughtful test is a good thing. It’s an opportunity to see how effective your learning methods have been. A chance to try new approaches to studying and see which work best for you. No tests would be like being on a soccer team that never plays games. Just as in soccer, until you compare your progress to others (over multiple occasions), how do you know if your improvement methods are effective? For me, It’s not about whether I’m better than Johnny or Sarah, but about being the best ME possible. Feedback is helpful.

    Regarding homework, I definitely agree. How could the rote nature of most assignments be the best use of a child’s non-school time? And if homework needs to be assigned, maybe it’s not about what they learn, but more about the enthusiasm and thought process that goes into learning. What if their homework assignment for a week was, “Go learn about anything you want for the next week. And you should pick something YOU think is super exciting (not what others think is cool) because I want you to enjoy doing the research and sharing what you learn with your classmates.” They could present what they learned in a paper. They could make a poster using association methods to show their what they learned (ex. mind mapping). Maybe their big thing for the week is to perfect a song on their violin that they can share with the class. Anything really that gets them excited to go home and grow their brain in a productive way. And most importantly, instead of praising the quality of their output, you can focus the praise on their enthusiasm, persistence, teamwork, curiosity, honesty, bravery, modesty, or whatever other great character strength they may have shown in the process.

    And one of the best parts about changing mindsets is that you don’t need 100% support and coordination to do it. It works perfectly fine if over time the interactions become more and more about growing as a person. You might even find that sometimes you’re the one thinking in a fixed mindset! (I know I do sometimes) And that’s ok. Because every day you work on it, you get a little better. Sounds a lot like the growth mindset, right? πŸ™‚

    Looking forward to hearing what you think. And what you ultimately decide to try!

    • Hey Adam, thank you so much for such a thoughtful response. I do love Carol Dweck. Helping students develop a growth mindset is crucial for their success and self-efficacy. One idea that has come up a lot in the course I’m taking right now is the idea of constructive feedback. I agree that a test can provide a lot of information to a student, but that there are better ways of doing that. After a performance assessment of some kind, for instance, I could provide really specific feedback to students. I learned of a study where students who received feedback instead of a grade actually ended up performing better on future assessments. Giving a grade with feedback showed no difference from giving just a grade. Once students see a grade, the feedback is lost on them! So I really like the idea of giving feedback without a number or letter to label the kids. Now, of course, these kids are going to have to get grades. That’s life! But if I could limit that, I would. Or I should say that someday I will…when I have my own classroom again. Also, I like your idea of what homework could be, and that is an area where I really do have complete control (when it’s my turn to teach the math chapter). I’ll be teaching about percentages next, and that is one of the easiest areas of math to find and relate to in the real world. I’m brainstorming an idea where students must calculate sale prices or sales tax or tip amount when they’re out in malls and restaurants; and then they could make some sort of graph, to tie in what they’ve learned in a previous chapter. You’re right that adults get stuck in a fixed mindset too. Rather than imagine that I’m completely stuck, I need to remember that I actually have quite a bit of room to do what I think is right, even without stepping on others’ toes. I lack a little confidence sometimes, and I tend to gain confidence after having a good talk with inspirational people. And Adam, this counts! Thanks again for your comment.

      • I like your ideas for the math homework. I imagine the more useful they see it, the more they’ll be excited to learn.

        I’m also intrigued by the no-test concept. I can see how that could work very well through much of school. I just wonder, for kids that have never taken tests, how do they respond when they get older and natural differentiation kicks in? For example, some kids get into college ABC, some don’t. Someone gets promoted into the manager role at work, the other employees don’t. And some girls are happy to go on a date with me, and some aren’t πŸ™‚ Either way, adulthood naturally compares people. Leaving the question: Should we teach kids competition-coping skills? If so, when? And how? This, my friend… I have no idea how to answer πŸ™‚ BUT, I do believe that it’s teachers like you–learning new methods and testing the waters–that lead us to new, great ideas. Thank you for everything you do for “our” (the world’s) children.

      • I totally understand what you mean. My mom always jokes about kids who go to “hippie” progressive schools and then grow up not knowing how to stand in line at the grocery store. I believe John Dewey’s ideas about school being a place that mirrors society. If we’re preparing children to be upstanding citizens of society, then school should be a model of society — a place to practice. So yes, because kids will have to compete to get into university and/or to enter the workforce, I think that there must be a healthy amount of competition that will help them toward those realities. And in the 6th grade, I think a lot of kids can handle it. They also can handle receiving letter grades, so I’m not for completely eliminating tests for that age group. But maybe they don’t need one after every single chapter? Maybe cumulative exams at the ends of semesters to check in would be great. And let’s not forget that tests are not the only form of assessment. Kids can do projects and in-class work for teachers to observe, and the teachers can give meaningful and constructive feedback. I would argue, though, that tests are pretty much completely ridiculous for kindergarteners and maybe up to second-graders. As they enter into 3rd grade, sure, give them some tests so they can get used to what that feels like, but we can’t treat them like university students during finals week! Teaching is so much fun, especially at my school where there is a lot less pressure on us! The big kudos go to people like Liz and other American public school teachers who work their butts off constantly for 10 straight months! I, on the other hand, have the luxury of time to ponder things like this and write a blog about them πŸ˜‰

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