If you’re here it means you like reading blogposts that I write. Check out my guest blogposts and the Mathematics Teacher site at NCTM for the next month or so. I’ll be trying to incorporate some of the advice and challenges I’ve faced in teaching with PBL and some of the ideas that I’ve shared with others.

# Category Archives: NCTM

# NCTM 2015 – Reflections

I know I’m a little late but I did want to post my own handouts and talk a little bit about my experiences at NCTM Boston this year. I want to thank all of the great speakers that I saw including Robert Kaplinsky, Ron Lancaster, Maria Hernandez, Dan Teague, The Young People’s Project (Bob Moses’ Group), Deborah Ball, Elham Kazemi and of course the inspiring Jo Boaler. One of the things I thought was great about Jo Boaler’s talk on Thursday night was that even though I had heard a great deal of what she had said before, there was a different tone in the room. I’ve been a fan of Jo’s since I first read her research in 2001 when I started my doctoral work on girls’ attitudes towards mathematics learning. What I felt that was different that night was that she was no longer trying to convince people of anything. There was a different message and that was “join the revolution” and the audience seemed to be on board and excited. It made me feel very energized and empowered that a huge ballroom full of mathematics educators had bought into her ideas and were enthusiastic to make change happen.

Some of the best times I had were spent just connecting and reconnecting with people – some who I met for the first time (MTBoS folks and other Twitter folks I met F2F which was really nice) and others who were old friends who mean a great deal to me. I forget how much the mathematical community of professionals enriches my life and makes me proud to do what I do. Thanks to everyone who reached out to find me and say hi – or tell me a story, talk to me about what they are doing or ask a question about what I am doing. You are all inspiring to me.

I left the conference with exciting ideas about teacher observation for PD, how teachers can share problems with each other better on the internet (awesome resources at Robert Kaplinsky’s problem-based lesson site), great ideas about agent-based models to add to courses, and ways in which teachers can talk to people about the Common Core and gain respect about the difficult work we do in teaching. Overall, I felt like it was an amazing time.

I want to thank everyone that came to my session. Although I had an unfortunate technological snafu and was unable to do an exercise I had planned where we were going to analyze a segment of discourse from my classroom using the framework of the MP standards (which would’ve been great), I felt that at least the resources that I shared were worthwhile for the people that came. Here is a link to the powerpoint presentation and the handouts I gave.

Weekly Learning Reflection Sheet

I’ll just put in one more plug for our PBL Summit from July 16-19 this summer – we still have a few more spots and would love to have anyone interested in attending!

# PBL at NCTM 2014!

One of my major goals in attending the NCTM annual conference this year was to see how widespread PBL had become in terms of mainstream education practices across the US. I have to say that this year there were quite a few sessions that had PBL in the title or as the central theme and I was excited to see that! Here were some of the workshops:

Problem-Based Learning (PBL) Is More Than Solving Problems – in this session the speakers were giving just a beginner’s view of what PBL is and can be in the classroom.

Change the Classroom, Not the Students – Attaining Equity Using PBL (OK, this one was mine)

Bring Back Problem-Based Learning into Methods Courses! – in this session the speaker makes an argument for using PBL methods in courses for teacher candidates and spoke about the positive experiences of preservice teachers with PBL.

Amplify the Mathematical Practices -this session focused on middle school PBL practices and how they stressed the CCSS MP standards. This was sponsored by Amplify’s Math projects.

Making Mathematics Culturally Relevant to Students Using Problem-Based Learning – in this session, the speakers gave an example of culturally relevant pedagogy striving for equity in the classroom. Again arguing that PBL allows for furthering equity in the practice of PBL.

Setting the Scene: Designing Your Problem-Based Classroom – in this session, the great Geoff Krall (emergentmath.com) gave a great talk summarizing a lot of his methods relating to PBL and his protocols in getting students to work through problems in their learning.

The Hidden Message: Micromessaging and Mathematics – I wanted to attend this session so badly, but I had to leave early on Saturday morning. This session has so much to do with my own research relating to how we talk to each other in mathematics classrooms and how PBL can allow for better communication without the micromessages. (Tujuana if you read this – get in touch with me!)

Promoting Equity through Teaching for a Growth Mindset (Jo Boaler) – in this Session Prof. Boaler reported on her work in math education with Carol Dweck’s Mindset research. You should check out her new website youcubed.org if you are interested in all the resources that she has shared freely.

And that was just to name a few! So much wonderful information out there to learn and share. The variety and number of sessions that connected to the pedagogy, content or philosophy of PBL was overwhelming and honestly very invigorating for me as someone who has taught with PBL for over 20 years. Seeing the interest and enthusiasm for this type of classroom practice has given me renewed energy to get me through the rest of the year!

# What I learned over my NCTM break!: Part 1

Wow! What an amazing three days I spent at the NCTM annual conference in New Orleans! I can’t believe how much I learned (which actually never amazes me and always humbles me – one of the many reasons I love going to these conferences.) I also hate leaving and knowing that I missed at least 20 sessions that conflicted with ones that I did go to, so now I’m catching up and trying to email the speakers that I didn’t quite get to see or get in contact with while there.

One of my major a-ha moments was in Gail Burrill’s session on logarithms. You’d think that after 25 years of teaching that you’d understand how much you understand about logs right? Oh, no! So she had us all have a very large number and we were doing an exercise where we had to put a post it note with that number (mine was 72, 753) on a scale of powers of 10 {10, 10^2, 10^3, 10^4, 10^5…}, her argument being that one of the main reasons to teach logs is to have a different scale for very large numbers. So after all of these teachers did this, we analyzed where all of our numbers were on the scale – particularly between these numbers. Since my number should’ve been between 10^4 and 10^5, I knew I put it in the right place – but oh no, I had it in the wrong place relative to the middle. She asked us to calculate the middle of those two – 10^4.5 which was 31,622 and yes, I admit that’s very close to where I put my post-it. I could blame the person who put their’s up first which said 75,289 and I just put mine by there’s but I won’t. I just didn’t really think. But I know this was a light bulb moment for many of the teachers in the room. Students don’t really understand how a logarithm is an exponent in the first place and we were doing this exercise without even using the word “logarithm.”

Then we went down to the section below that was between 10^3 and 10^4 and checked some of those numbers. They were very off too and Gail asked us what number we expected to be in the middle. At this point, some of us pulled out our calculator (yes, I admit, I did) but some of the smartees in the room just said “3,162” and I finally got it. By just dividing by 10 and looking at the scale in this nonlinear way, students would be able to make the connection between the algebraic properties of exponents and what a logarithm was. I thought this was an amazing way to introduce logs. Has anyone done this before? Thanks so much Gail!! I think I’m going to write a problem for my curriculum about this, it’s such an insightful experience.

More reflections to come – just can’t do it all at once – catching up on school work!

# Handouts – Front and Center

I always try to make it easy for people to find both my slides and handouts when I give a talk – so Here’s my powerpoint presentation from my talk entitled, “Change the Classroom, Not the Students: Creating Equity with PBL” which I’m giving today at the NCTM Annual Conference in New Orleans – great to be here. I also have 2 handouts which include my framework for a relational PBL class and the results of my qualitative dissertation – I’d love to hear any comments and questions and start a discussion with PBL teachers. (I do not include the videos I used in this public version of the powerpoint, sorry)

Schettino Sample Problems Handout NCTM2014

There are actually a few talks here today that I would highly recommend and seem to be related to this topic of creating a classroom that allows for discussion and interaction at the level of creating equity. One of them is on Friday, and is entitled “The Hidden Message: Micromessaging and Mathematics” and it seems to be about managing the way we talk to each other in the classroom and making sure all voices are heard. I’m definitely going to that one! Unfortunately, Jo Boaler is presenting at the exact same time as me! I don’t know if I should take that as a compliment that I was put as the same time or not

Well, hope everyone has a great time! Enjoy the conference!

# Defying Gravity as a Means to Learning from Mistakes

There’s a lot of blogging, writing and research (and anecdotal stories) out there these days about trying to foster the value in students for the appreciation in failing. I even wrote a blog entry two years ago entitled “modeling proper mistake-making” way before I read anything or watched any videos on the Internet. From teaching with PBL for over 17 years, I am a pro at making mistakes and watching students struggle with the concept of accepting the idea of learning from their mistakes. This is so much easier said than done, but it is clearly something that grow to love even if only for a short time.

Last April, I had the pleasure of hearing Ed Burger at the NCTM national conference where he spoke about having students in his college-level classes required to fail before they could earn an A in his class. In his August 2012 essay “Teaching to Fail” from Inside Higher Ed (posted at 3:00 am, which I thought was kind of funny), he talks about attempting to make a rubric for the “quality of failure” on how well a student had failed at a task. I thought this was an interesting concept. I mean, in order to fail well, can’t you just really screw up, like not do it at all? Prof. Burger states that allowing students to freely reflect on their “false starts and fruitful iterations” as well as how their understanding “evolved through the failures” can be extremely beneficial. He also states:

“To my skeptical colleagues who wonder if this grading scheme can be exploited as a loophole to reward unprepared students, I remind them that we should not create policies in the academy that police students, instead we should create policies that add pedagogical value and create educational opportunity.”

Last year for the first time, I tried a similar experiment wherein I gave students an assignment to write a paper in my honors geometry class. They had to choose from three theorems that we were not going to prove in class. However, it was clear that they could obviously just look up the proof on the Internet or in a textbook or somewhere, since they clearly have been proven before. The proof was only 10 or 20% of their grade. The majority of the paper’s grade was writing up the trials and failures in writing the proof themselves. This proved to be one of the most exciting projects of the year and the students ate it up. I even told them that I didn’t care if they looked up the proof as long as they cited it, but I still had kids coming to me to show my how they were failing because they wanted a hint in order to figure it out themselves. It was amazing.

This past week I showed my classes Kathryn Schultz’ TED talk entitled “On Being Wrong” in which she talked about the ever popular dilemma of the Coyote who chases the Road Runner, usually off a cliff.

My students loved her analogy of the “feeling of being wrong” to when the Coyote runs off the cliff and then looks down and of course, has to fall in order to be in agreement with the laws of gravity. However, I proposed a different imaginary circumstance. Wouldn’t it be great if we could run off the cliff, i.e. take that risk, and before looking down and realizing that vulnerability and scariness, just run right back on and do something else? No falling, no one gets hurt, no one looks stupid because you get flattened when you hit the ground? Maybe that’s not the “feeling of being wrong” but it’s the “feeling of learning.”

Next blog entry on creating the classroom culture for “defying gravity.”

# First Day at Indy

What a great day at the NCTM national conference in Indianapolis. My colleague and I arrived late last night so I missed registration. However, since my talk was today at 9:30 am, I was supposed to be registered at least two hours before I was supposed to speak, so I needed to be up pretty early to get there to register in the exhibit hall. That was not a problem since I was so excited that I was up at 5:30 anyway. After registering, I went to a presentation of orchestrating successful class discussions in the math classroom which seas geared towards elementary and middle school teachers. This was very interesting because most of what I have read has been about secondary level reaching. It was interesting to sees the framework that they used and how important it was to try to anticipate what you. Thought students would say. Many of the ideas they shared were very similar to what I would have said.

I showed up to my room about 15 minutes early and people started coming in. I was very excited that there was interest in my topic. Because this one was a research session I had not planned many interactive activities because I had so much information to share. However, I encouraged people to be a part of the conversation. I think it went very well because many people shared thoughts during the talk and also stayed afterwards. I ran out of handouts and am hoping that those people with questions will contact me and we can keep the conversation going.

I got some great input from some members of the audience that I think will really help me improve my article. One fellow graduate student told me that he thought I would have a stronger argument for the self-referencing pronoun use being a positive sign of empowerment in the discourse if I used a chi-squared test inn the data I had instead of just looking at it qualitatively. Another preservice teacher told me that I should tr to make a distinction between social norms in the use of the pronouns and sociomathematical norms. I think this is a good point and something that I need to look into more in the current research.

Overall, this first talk was a great experience and I’m so glad it was so well received by those who participated. Hopefully, tomorrow will be just as fun and we’ll get some good responses from the crowd. Thanks to everyone that attended.

# NCTM national conference

# Documents for NCTM National Conference

Here are some links to documents that I will make public for my talks at the conference in Indianapolis this week:

Powerpoint Presentation for

Improving Classroom Discourse to Support Communication, Equity, and Students’ Agency

Handout for

Improving Classroom Discourse to Support Communication, Equity, and Students’ Agency

Powerpoint Presentation for

Problem-Based Learning (PBL): A Transformed Perspective for Standards-Based Geometry

Handouts for

Problem-Based Learning (PBL): A Transformed Perspective for Standards-Based Geometry

Emma Willard M225 Course Syllabus with Problem-Based Learning

Emma Willard M225 Course Curriculum Map

Emma Willard School Algebraic Geometry Problem-Based Learning Curriculum

M225 Curriculum 2010-2011