These are some of my thoughts about teaching mathematics. The purpose of this blog is to help me reflect and become my best teaching self. #MTBoS #iteachmath
Although I haven't blogged in awhile, it is now time for summer and time for reflecting on what I might do differently for the coming year. It isn't that I'm not reflective during the school year, but time only allows my reflections to be scratched notes on the sides of papers - vague, barely legible scribbles that often say things like "that didn't work well" or "took too long". So, this blog entry (and a few others over the summer) will be my way to formally record my teaching reflections and perhaps, if you are a teacher, it may spark your own reflections as well.
Early this summer I had a 1-hour golf lesson with Mark Csencsits from Lehigh Valley Golf Pro. Initially I was nervous, because I hadn't hit a golf ball in a while. My old hitting style was more missing the ball than hitting it. I was lucky to drive the ball 100 yards. So, my goal for the lesson was to get better at driving the ball. As I was learning how to move my feet and shift my weight for optimum hitting distance, in the back of my mind I was also thinking about how I could use some of Mark's teaching techniques in my own teaching.
1. Find out what motivates my students. At the beginning of the year, many of my students are probably nervous. Anything new and unexpected can make us nervous. Before my lesson, Mark asked some questions about golf, but also asked about my other interests. When asked about why I like to read in the summer, I said that it is relaxing and enjoyable. This short conversation about my interests immediately made me less nervous, and that meant I was able to focus more of my energies on learning new golf skills later. Do I take the time that is needed to know what motivates my students? When they come in for help, what do I do to make them feel less stressed or nervous?
Rather than using the passing time between classes to get one last item done on my checklist this year, I am going to use that time to talk to students, to find out what motivates them outside of my classroom.
2. Letting students know that mistakes are a part of learning. During my golf lesson, Mark quickly picked up on the fact that I am a perfectionist. (Although this is a short blog, it will likely take me 2 hours or more to write and revise.) I have a sign in my room that says "Asking thoughtful questions is a primary way to open your mind to learning." But perhaps it should be modified to say, "Asking thoughtful questions and making mistakes are a integral part of learning." I need to find ways to have students understand that making mistakes is ok. For many of my honors level kids, they have rarely experienced this before; they approach learning from a fixed mindset instead of a growth mindset.
Perhaps a few statements in the survey at the beginning of the year can let me know which students will have problems with seeing mistakes as part of the learning process. Then, I can work specifically with helping those students see that it is ok to make mistakes as you learn.
3. Switch things up when something is not working. My golf lesson was short, 1 hour. Mark had to try several analogies and different tools to find one that worked to help me to understand how to shift the weight on my feet. (Reminder to self: pivot both feet toward the green and at impact have 90% of weight in the front leg.) I know what works best with students, but do I switch out my tools when I need to? Do I quickly recognize when one technique is not working with an individual student and move on to another?
4. Writing to Learn Near the end of my golf lesson I was given a clipboard and pen. The top of the page said "Student Notes". In order to get the video of my lesson, I had to send Mark a recap or review of what I learned IN MY OWN WORDS. (Those last 4 words were typed that way on my student note page.) Just like writing my ideas in this blog, putting pen to paper helped me to review the key ideas and made them more memorable. Does it take time to write to learn? (I am now on hour 3 of my blog.) Can it be a valuable part of the learning process when done correctly? (Umm...My bias is showing here.) So, why don't I have students write more as part of learning? Time and Time. It takes time to write and it takes time to read what students wrote. Does that mean I abandon the concept of writing to learn? No, but I need to find more ways to incorporate writing into what I already do.
Some Final Thoughts. First, if you haven't been a student in a while, you should. I am not talking about being a student in an education grad class, but being in a totally new element. Experience the growth mindset (and occasional frustration) that comes with learning something new. It will give you more empathy for your students. Second, when you are in that learning situation, think about teaching. Are there good things the teacher did that you could be doing? Are there bad things the teacher did that made the instruction less effective? Finally, be sure to share what you have learned with others. I learned much from the golf lesson and by the way, I can now consistently drive about 175 yards!
We just recorded the biggest snowfall in the Lehigh Valley ever (over 30 inches) and despite clear roads, we are still having snow days! There are narrow roads in city portions of our area and there is too much snow for busses to make the turn onto some of those roads. This excessive (and unplanned) time off from work gave me time to think and to build something really cool in Desmos Activity Builder. If you haven't tried Desmos Activity Builder out yet and you are a math teacher, you are missing out. This is my 4th lesson built in Desmos Activity Builder.
The lesson focused on tangents to circles. In the past we would look at two big ideas, as illustrated below.
Big Idea #1: Tangents are perpendicular to radii at the point of tangency.
Big Idea #2: Tangent segments to a circle from a common point are congruent.
Usually we would discover these ideas using Geogebra or hands-on activities. However, I don't want my students to forget concepts from Algebra, such as equations of lines and I realized that with Desmos we could look at these concepts through the lens of coordinate geometry. Plus, I had time and welcomed the challenge of creating the activity in desmos. And it was quite challenging. (If you are interested in the details, let me know by posting a comment and I can send you the file with the hidden folders.)
What does the activity do and what does it look like? I could tell you, but that would ruin the fun of trying it our for yourself. So...here is the link: Tangents to Circles.
My students will be doing this activity in class on Monday (February 1st) and I will post back to this blog with a few comments of how things went. Be sure to return next week.
My summer was filled with a variety of professional reading, including:
In addition to reading
this book, I took an online course in blended learning. This book
showed me that many models fall under the umbrella of blended learning.
The most powerful blended learning models involve making a school from
the ground up and leveraging technology as a tool for teaching and individualizing
instruction.Little did I
realize that “flipping the classroom” (something I started doing 4 years ago
from time to time) is a blended model.
I first heard about Carol
Dweck’s book when I took a Stanford MOOC course by Jo Boaler called “How to
Learn Math” in the summer of 2014.People with fixed mindsets think their ability to do math is based on
their intelligence or innate ability - that they are born with it.These people get frustrated when learning
doesn’t come quickly to them.Failure
or risk of failure leads them to take an easier path. Growth mindset people
see failure as a part of learning and the effort needed to reach success
makes them smarter.Great ideas, even
though the reading felt like a stream of consciousness at times.
This book looked at innovators in several areas – social innovators,
entrepreneurial innovators and innovators in education.Allowing children time to play and
experiment was seen as important.Letting them work together to fail and learn from their failures was
necessary. The book looked at several college and grade school programs that do
this successfully.The short video clips
were interesting, but were a repeat of what could be read within the body of
the text.
This was actually my daughter’s summer reading book.She did not like it at all, but I told her
I would read it and I did.If I did
plan on writing a memoir, it would have been a very helpful book.A list of suggested memoirs found at the
end of the book looked interesting.Perhaps I will read one or two of these memoirs next summer.
But the most powerful and practical book was...
Make It Stick: The Science of Successful Learning by Peter C. Brown, Henry L. Roediger III and Mark A. McDaniel. Thanks to Daren Starnes (AP statistics teacher and super math presenter) for sharing this book during Best Practices Night at the AP Statistics Reading this past summer. Daren's presentation can be found at http://apstatsmonkey.com/StatsMonkey/ReadBestPractice.html. It is the fifth presentation in the list.
If you are not familiar with this book, click on the stack of books shown below to go to a video by Cathy DeHart which provides a good summary of the ideas from the book. Plus there are practical ways to implement those ideas to improve your learning and the learning of your students. My students will be watching this video for homework on the first night of school and I will be using EDPuzzle to embed questions within the video. This will model the same type of self-quizzing students should be doing as they learn new material.
My Plan to Make It Stick
Learning that is easy is stagnant and most likely boring. Think about it. What makes a student stay up late playing video games? It is the challenge of learning the strategy needed to make it to the next level that produces zombie-eyed students in our classes. "Making mistakes and correcting them build the bridge to advanced learning." (Make It Stick, pg. 7) Students get this for video games, because there is low-risk in playing the game. Your character dies, no problem. You have another life or you can always try again. The student wants to persevere. Unfortunately, students (and their parents) don't see mistakes in school as "the bridge to advanced learning". Applying the concepts from the book will hopefully change that a bit.
1) Quiz and Quiz Often - Research shows that frequent low-stakes quizzes produce bigger gains in retention. So, I am going to have quizzes every week on our scheduled lab day for the class. With about 12 quizzes in a semester, I will be able to drop a quiz or two. This means students won't have to make up a quiz when they are absent. In addition, quizzes will count for 50% of my grade for the class, graded homework sets 30% and tests 20%. With each quiz only counting about 5% of the student's grade, they will be low stakes. Plus, tests counted 50% of the students grade in the past and now they are worth less. In the end, I will probably be asking the same total number of questions, but just asking the questions more frequently.
2) Interleaved Practicing - Why do students do poorly on cumulative tests? It is because the concepts are mixed up. However, practice is rarely mixed up. Students do all of one type of problem and then another type of problem. They don't have practice with recognizing the concept in a mixed up set of problems. Sure, my students will hate "mixed" practice. ("But Blah-Blah-Blah was in the last chapter, Mrs. Nataro.") But in the long run, they will do better. Plus, reviewing for the AP exam will really be review and not relearning everything from the fall semester.
3) Write to Learn/Explain to Learn - Although math has a beauty in the efficiency of its communication and its notation, there is much to be learned by explaining something to others and in writing about it. (Hmmm...I am writing now and learning now.) My students do a fair amount of verbal explaining in Geometry and much written explaining in AP Stat. I need to add more of the written explaining in Geometry and the verbal explaining in Stat. I am not quite sure how this will pan out yet. Perhaps by incorporating formal exit tickets from time to time in Geometry and doing a "think-pair-share" verbal class opener from time to time in AP Stat.
4) Give It a Try First - When I was a math student in high school, I didn't want to give things a try first. My motto was "Just show me what to do and I'll do it." But that type of learning is not long lasting. "When you're asked to struggle with solving a problem before being shown how to solve it, the subsequent solution is better learned and more durably remembered." (Make It Stick, pg. 86) Having students attempt to solve a problem before I show them how to do it will be challenging for me. It is hard to see students struggle and we want them to be successful. How much struggling is productive? I am not sure how I am going to make this part of my plan a reality...not yet.
5) Reflect and Learn - For many adults, this seems obvious. But how many times have you seen a student look at a grade on a test/quiz/assignment and then crumple it into a ball. I want to scream at the top of my lungs "It took me 10 minutes to grade your paper and write comments to you. The least you could do is look at them and try to learn something from your mistakes." OK, so screaming probably won't be good for my blood pressure. But I could have students completing the following sentence after every quiz. "I need to get a better understanding of BLANK." Then, they will describe what they will do to get a better understanding (such as, work through 5 examples of that type of problem and check their answer) or describe the conceptual error they made (such as, I thought the hypotenuse could be adjacent because it was next to the angle, but the hypotenuse is always across from the right angle. Adjacent sides must be one of the legs.)
Overall, I want to do less spoon-feeding and I want to provide my students with more opportunities for failure, because growing from failure = learning. Ideally the corrective feedback I give to students on their mistakes will lead them to recognizing and correcting their own errors.
Evaluating the Plan and Reapplying the Glue to Make It Stick
In the past my blogs have mostly been reflections on my teaching in general or some specific lesson I did in my classroom. That meant I only wrote when I felt like it and I didn't have a need to formally write and reflect all the time. Now I have a need to track the progress of my plan and blog about the reapplying of glue (or tape or velcro) needed to "Make It Stick". And in the process, I will be applying "The Science of Successful Learning" to my own teaching.
Additional Resources from Some Other Cool Teachers
As I was working on writing this blog, I came across some ideas from some other teachers that helped me refine my ideas and they may provide you with some useful ideas, too.
Attend their sessions weekly at 9 PM EST. Even if you have already begun your school year, you can still use some of the ideas in this recording of the Global Math Dept. webinar.
