Year: 2014 (page 3 of 5)

This is the presentation proposal I submitted last Thursday to the NCTM conference committee. Would you attend this workshop?

Description:

Effective mathematics teaching is more than just teaching procedures; students must have opportunities to grapple with rich mathematics. In this workshop we will collaboratively investigate using rich math tasks to explore students’ use of the Common Core Standards for Mathematical Practice as part of formative assessment for learning.

Objective:

Participants will walk away from this workshop with a source of rich mathematics tasks they can use in their classroom, and a flexible and useful protocol they can use to interpret student thinking about these tasks as part of formative assessment practices. Participants will also explore the power of teachers collaborating together to make evidence based decisions and improve their own practice.

Focus on Math:

The participants in this session will be given appropriate rich mathematical tasks and samples of student work, all along the continuum of algebraic reasoning from grade 9 to grade 12. Participants will not only be able to use these tasks in their own classrooms, they will be able to apply the protocol for looking at student work for their own students’ work, and build their school teams’ capacity for collaboration at the same time.

I’m not an expert on standards by any means, but I know that the standards in British Columbia (where I was trained to teach) were coherent and made sense. You could follow the threads through the years and understand why they had been designed that way. I know that the Common Core content standards in Math have the same level of coherence.

I don’t know if they are always appropriate, or how one even defines appropriate given the strong relationship between what set of standards students learn under, and what they are therefore capable of learning in later years. I know that recent research suggests that young kids are capable of learning higher level math than what is currently expected, with many or even most kindergarten classrooms practicing skills with students almost all of whom have those skills. I believe in play based early years teaching, but this doesn’t preclude teachers from focusing on problem solving and pattern finding and continuing to develop students’ number sense.

What I do know is that the Common Core Standards for Mathematical Practice (SMP) are not pedagogy-neutral.

These non-content standards require students to be able to make sense of problems and persevere in solving them. This requires teachers to offer opportunities for students to problem solve (this is how some people define “doing mathematics”).

Students have to be able to construct viable arguments and critique the reasoning of others. While this could be done entirely through paper and pencil means, it is far easier to teach students to do this by regularly engaging them in dialogue and giving them opportunities to discuss mathematics together.

Students have to be able to model with mathematics, which again means that they have to be given opportunities to do mathematical modelling. The type of mathematical modelling described in the standards requires students to be able to make sense of problems resulting from everyday life, which means that teachers should be using examples of problems that result from the cultural contexts students live in (it’s not everyday life if it’s someone else’s life).

These are just three of the eight SMP, and the other five SMP also have pedogical signficance attached to them as well. The SMP require that some teachers teach differently than they do, and that therefore hopefully more students will get opportunities to grapple with mathematical ideas.

What I think we need to be careful to recognize is;

• Even though the standards and the increase in testing happened at the same time, these are two different issues. I can like the Common Core standards, and also think the testing is excessive.
• Many of the “Common Core Math problems” that have been shared via social media have either not been very good problems, or have had insufficient context to explain them. However, none of these problems is “Common Core” since the Common Core is a set of standards, not a set of curriculum. Standards define what kids are supposed to know and when; curriculum is a tool used to align specific mathematical examples to those standards. The fact this has sometimes been done poorly is not the fault of the people who wrote the Common Core standards, and in fact, these kinds of poorly written problems have been plaguing education for many years.
• Value added measured (eg. teacher evaluation programs), privatization of education, ALEK, and a number of other issues that have risen across the USA in recent years are also not actually related to the Common Core Standards. Again, I can support the standards and not support people excessively profiting off of education.
• Children being given problems that are too challenging or being given insufficient support when attempting these problems at home is again not the fault of the Common Core. Every standard in the Common Core has a range of possible curricular resources, and hence challenge levels, and educators just need to be careful when selecting amongst these. If students are being sent home assignments that they cannot reasonably be expected to do with miminal support from their parents, then these are the wrong types of homework assignments to assign. Homework is probably not appropriate at all in elementary and middle school, but fortunately the Common Core does not come with a requirement to assign homework.
• There is tonnes of interesting and rich mathematics available that falls under the set of content defined by the Common Core. Almost every puzzle or challenging problem on this website, for example, is aligned to some Common Core standard.
• The Common Core is not going to solve the problems of inequity, poverty, and racism in our education system. It is unreasonable to expect a set of standards to do this.

tl;dr: Strategic inquiry is a lesson study structure.

One of my roles in my current job is to help facilitate team meetings for two schools. In these team meetings, our objective is to collaboratively study our individual impact on student learning, and work together to design instructional strategies for improving the learning outcomes of students.

This means we collaboratively:

1. Look at student work.
2. Take the time to notice things about the student work that everyone agrees on.
3. Ask more inferential questions about the student work.
4. Identify a specific area that we should focus on for this student.
5. Offer suggestions as to what we would do if we were the teacher for this student.
6. Make a plan that includes a plan to re-assess students.
7. With the assessment information from our plan, if necessary, revisit steps 1 to 6.

Teachers definitely need to collaborate in this process. The most important reason to collaborate with other teachers when studying the impact of your own teaching; other teachers can offer insight and feedback that you cannot see yourself. Also, when you first start looking carefully at the impact of your teaching, it can also be disheartening sometimes to see how little impact you sometimes and having some colleagues to reflect on this and offer support is invaluable.

There is evidence to suggest that teachers improve faster when they work together to plan and reflect on their teaching. Two central tenets of John Hattie’s book, Visible Learning for Teachers (2012), are that teachers should know their impact, and work together to improve each other’s teaching. A highly effective model, Hattie suggests, is for teams of teachers to norm around what it means to be successful in their subject area, look at sources of student data, and collaboratively create instructional plans to attend to trends in that student data. In Ilana Horn’s summary of her research into professional learning of math teachers, she suggests that teachers learn most about teaching when their conversations are centred around teaching, students, and mathematics.

I have a proposal. I would like to form and facilitate an inquiry group of 3 or 4 other people from the online mathematics community. We would start the inquiry process for next September. 

Here’s what would make your participation ideal:

• You are interested in studying your impact as a teacher,
• You have enough time to meet once a week (or once every two weeks) for about an hour or 90 minutes,
• You are teaching a course which is substantially similar to everyone else that participates (or alternatively, happy to help someone study their teaching in a course you are not teaching),
• You are able to give your students a pre-assessment before you start teaching, and the same post-assessment after you teach a unit,
• Have the technical know-how to upload your student work, minus personal identifying features, into a shareable space,
• And are able to participate using our chosen communication technology (Google+ Hangout or BigMarker are my two suggestions for now).

Here are two other ideas to make our work even MORE ideal:

• All participants are teaching the same course using roughly the same scope and sequence. For example, we could all teach the Common Core aligned Integrated Algebra 1 using the Mathematics Design Collaborative scope and sequence.
• All participants use the same pre-assessments and the same post-assessments (but are obviously free to sequence and teach the unit topics as they see fit).

Benefits:

• Your teaching will improve (probably),
• Your students will likely benefit,
• You will have a source of other people teaching roughly the same content at roughly the same time, which will make collaboration around resources and lesson planning much easier.

If you are interested in participating, fill out this form here: http://wees.it/inquiry.

First, give an exit slip to your students based on a critical math concept for which you want to check for understanding.

After class, sort the exit slips into piles based on the method students chose to use (whether they used it perfectly or not). Choose two examples from the student work that highlight one or two probable misconceptions students still have on the chosen critical math concept.

Remove identifying information from the student work, photograph it (or use a document camera) and show it the next day in your class. Ask students a question about the work that requires them to think about the work. “Which one of these two examples is correct?” is not a very good question because it can be answered by guessing. “Why do I really want these two students to talk to each other about their solution?” is a better question because if students answer it, they will have to think about the concept a bit differently.

Ask students to think about their own answer, write it down (if necessary), then turn and talk and share their work with a partner while you circulate and listen in on student discussions. Select 1 – 3 students to share their thinking with the whole class.

Repeat this every day.

The objective of my presentation at NCTM in New Orleans was to introduce participants to social media, which was made difficult because participants did not have Internet access. As it turns out, this ended up forcing me into a couple of activities which were pivotal experiences for participants.

Here are my slides from my presentation.

Instead of trying to bring my participants to the Internet, I brought the Internet (or at least a portion of it) to my participants, and in doing so, provided them with concrete examples of how people use social media to interact.

I started my presentation by sharing some of the stories I have from my use of it, and who I have been able to interact with and how this has enriched my professional learning. If you use social media as a professional tool, then you have some of these stories too.

Next, I gave them an experience of what it might be like to participate in a live Twitter session. Participants were given a question, 30 seconds to find new group members, and 140 seconds (suggested by Dvora) to discuss the question in their small groups. This highlights that Twitter conversations are often with people you don’t know very well, and can be brief and short interactions.

I then asked participants to describe the attributes of our face to face conversations, and then speculate as to how these might transfer to an online conversation. I then highlighted for participants some of the features of these kinds of conversations. In particular, the conversations parallel conversations you would have with people face to face, but that conversations online can take place between participants who are separated by vast geographic (and cultural) differences.

Participants went around the room and read one or two of the four blog posts I had printed and put up on the wall, and put sticky notes up to comment on the blog posts. We then debriefed the experience with the main observation being that blogging is a lot like reading and responding to a letter from the editor.

Finally I wrapped up by talking about some of the specific projects that have been created through collaboration with other people in the online mathematics education community, and how our participation online has resulted in resources of real value in our teaching.

In the final questions at the end, one participant astutely observed that it would be easy to find a “how-to” guide online, but that he felt my “why-to” session was more helpful. There’s no reason to tell people how to do a bunch of technical details if they don’t see a reason to do them.

Everything in education these days is black and white, with no possible shades of grey.

Standardized tests are evil. Except when we agree with their findings. Or when they are used in research about teaching methods. Or when they highlight inequity in our society.

Lecturing to students is evil. Except when it’s coupled with peer instruction. Or when it is used to talk about peer instruction. Or when the lectures are short and have animations added. Or when the lecture is about creativity.

Common Core is evil. Except when it raises standards for students. Or when it communicates a common definition of what it means for students to do mathematics. Or when it encourages multiple ways of solving mathematical problems.

I recently read an essay published by the Carnegie Foundation for the Advancement of Teaching called “Getting Ideas into Action: Building Networked Improvement Communities in Education.” The basic argument of the essay is that while traditional research can be effective for finding out what works in specific circumstances, it frequently is too far away from practice to be useful in an educational setting, but that many of the ideas of research can be applied in practical ways through the creation of networked improvement communities (NIC) which use the design cycle to study and solve shared problems of practice. This to me does not say that research is useless, as it can inform this process, only that research as a tool for improvement is insufficient.

After reading the article, I thought to myself, in what ways is our online community of math teachers like or unlike a network improvement community? A clear and extremely important difference is that as a community we have no central objective. We also do not have many obvious structures which lead to sustained improvement and accountability back to the community. However, we do have a community of people who are all obviously interested in improving our own individual practice; quite simply it would otherwise not be worth the effort we put into our online participation.

Here’s a proposal. Let’s form some small groups of math educators (or alternatively, educators of math educators) who carefully study our practice together and think about improvements, using a process I learned about here at New Visions called Inquiry. This process is detailed in a book called Strategic Inquiry by Panero and Talbert (reading this book could be a useful starting place). We would meet once every couple of weeks (using a Google+ hangout, I guess unless there is alternate technology out there that is better) and take turns presenting on our work, and asking for feedback from the group. This will allow these small groups to collaborate around our teaching, our students, and mathematics, which Ilana Horn describes as among the most effective learning experiences for math teachers.

Anyone interested in participating?

Watch this video. Every time you feel you are confused, just pause and rewind the video and rewatch it. Do this until the video makes sense.

Can’t do it can you? It doesn’t matter how much you pause and rewind a video, if it doesn’t make any sense to you, watching it again isn’t going to suddenly change the video so it makes sense.

One critical job of the teacher is to find out where students are, and help them at that stage. Explanations that don’t make any sense aren’t particularly helpful. In fact, since our goal is to help students learn the mathematics, and not just the words that represent the mathematics, explanations may not be helpful at all.

PARCC recently released some sample computer-based test items for ELA and high school mathematics, so I thought I would check them out since NY state is still officially planning (eventually?) to use the PARCC assessments.

First, some kudoes to the team that created these assessment questions themselves. In general I found that the questions were looking for evidence of mathematical reasoning, and would be difficult to game with classroom test-preparation. What I think is missing is an opportunity for students to demonstrate the complete range of what it means to do mathematics, including asking questions themselves that they answer, but for an assessment with this function, this seems much better than the current generation of standardized tests.

If you want to stop reading this and preview the questions yourself, feel free to do so (if you are only interested in looking at the sample math questions, you’ll have to skip through the sample ELA questions).

Here’s my preliminary thoughts from attempting the first few problems myself.

1. Use of space is critical. The first assessment question does not do this very well. Look at the video below that explains my reasoning on this.

   
    

2. The second question has two issues, one of which is really very minor, the other of which is something PARCC should make an effort to fix.

   I’m okay with questions that use approximate models for mathematics, but it might be at least worth noting to students that these models are approximations.

   Taking a test on a computer is already extremely distracting as compared to taking a test on pencil and paper. Given that there is research that shows that people generally read slower and with less understanding on a computer, PARCC should make an effort to mitigate the platform issues as much as possible. Imagine if your work flickered in and out of existence while you were writing it down on paper?
    

3. I put the wording for the third question through a reading level estimation calculator, and it estimated that the reading level was grade 10. While it is reasonable to expect a certain amount of competence from students in this respect, we have to be careful that our assessments of the mathematical thinking of students aren’t actually measuring whether or not they can read the prompts in our assessment.
    
4. Question 5 assumes a certain amount of cultural knowledge, specifically knowledge of playing golf. Having worked with students who do not have the this sport in their cultural background, I found assessment items like this frustrating. Usually, the questions are doable without the cultural knowledge, but imagine you are a student who comes across a question that contains an idea with which you know nothing. Regardless of whether or not the knowledge is required to do the mathematics of the problem, it impacts student confidence and therefore their performance.
    
5. The sixth question assumes that students have some minor technical knowledge, which I would classify in the same genre as my fourth point; students with a minimal technical background may struggle with the mechanics of this task. This may not affect a huge number of students, but the assessment instrument should be as neutral as possible to allow the greatest number of students to interact with the mathematics of the task, not the mechanics of the task.
    
6. The seventh question has a video. It’s probably between 4 and 10 megabytes in size. Can you imagine what this will do to your school’s bandwidth if every student in a particular grade is accessing the resource at the same time?

There are some things which I think are obvious to me about the computer based assessment that PARCC is working on.

The first is that many of these questions are still going to require actual math teachers, with some experience looking at student work, to look at. Most of these questions are not just reformated multiple choice questions (although some of them are). While this increases the per-student cost of the assessment, I do not think that there are computer programs (yet) that exist that can accurately capture and understand the full range of possible mathematical reasonings of students.

Next, some of the more adaptive and social aspects of the work Dan Meyer and company have put together, are not present in this work. This assessment is intended to capture what students think now, rather than what students are able to do once given more information. This is still an assessment of the content students have learned, and does not appear to do an ideal job of making sense of how students make sense of problems and persevere in solving them, attend to precision, or any of the other standards for math practice (SMP). While it is clear to me that students will have to use these standards when doing this assessment, I do not see how anyone looking at the resulting student work is going to be able to say with any accuracy what is evidence of each of the SMP.

Unfortunately, unless the standards for math practice get captured somehow by an assessment (a goal of ours during next year with our project is to make an attempt to do this systematically), it is unlikely that teachers will use them.