What #Mathissippi Learned at MCTM

Last month I had the opportunity to attend the annual Mississippi Council of Teachers of Mathematics (MCTM) conference in Ellisville, MS. Davis Parker (’15) and Dylan Jones (’15) attended as well, and have shared what they learned below. Take a look, and steal some ideas – specifically…

  • Using Algebra Tiles effectively!
  • Creating “Secondary Circuits” centers-alternative
  • Meaningfully infusing Statistics into Algebra I
  • Using Plickers for quick data collection and sharing!

Dylan’s Findings

My name is Dylan Jones, I am a second year teacher in the Mississippi Delta, teaching 6th – 8th grade mathematics to 50 of the most passionate and energetic students I know. I have had the pleasure of being sent on many professional development experiences on behalf of the Sunflower County Consolidated School District. Recently, I had the privilege of attending the 2016 Mississippi Council of Teachers of Mathematics at Jones County Junior College in Ellisville, MS. At this conference, I made connections with iReady representatives, engaged in many sessions to enhance my classroom, and got a chance to participate in a state wide Professional Learning Community (PLC) with fellow math educations across the state.

The purpose of this blog post is to share some of the information gleaned from these sessions. Since I found most of what I attended to be extremely useful, I have narrowed down my post to include the following sessions: 1) How to use Algebra tiles and 2) “Circuits”.

In my short time as a second year teacher, I have been able to incorporate technology into my classroom, increase the level of confidence and rigor, and fully implement secondary centers. One thing that I have always wanted to figure out is how to increase my use of manipulatives. While at the MCTM conference, there was a session on the fundamentals of algebra tiles. I signed up, made friends with the teacher next to me, and we began our journey together! My partner teacher has used algebra tiles for over 10 years now, so she allowed me to hog all of the tiles as I was learning the rules. Each tiles represents a variable (x, y, xy, x2, and y2) and then there are unit tiles to represent the numbers in the equations. I received a template and the facilitators started to walk us through some equations. Right before my eyes, for the first time in my adult life, I started to visualize the zero pairs when I solved for the variable in the equation. The facilitator took us through over 10 different equations, I was blown away. I couldn’t stop thinking about how I wish I had these when I introduced 7.EE.1-4 to my seventh grades in the first nine weeks. Below I have included some pictures to show you how powerful algebra tiles could be in your classroom! I ordered the set from EAI education, here is the direct link, and I used my EEF card and they were delivered in a week.

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While I was still reeling from the algebra tiles session, I saw a session for “Secondary Circuits”, to which I though was a cooler name for center rotations. When I arrived at this sessions, I was told that it was not about centers, but yet a way to make work more rigorous, engaging, and where students can assess themselves. I was sold! The facilitator starts passing out what look like worksheets, but have two to three columns of boxes with problems in the top. The facilitator asks us to solve the top left box, use that answer to find the next box, so on and so forth. So I am sitting with about 25 other math teachers and there is not a sound. We are all trying to solve these algebra problems and use out answers to advance our progress. I get stuck about 75% through the first circuit. The facilitators looks at my paper and says that I am operating on the target level question because I completed 75% of the circuit. The facilitator then explains that if a students can complete less than 50% of the worksheet, they are not operating on the grade level question target. If a student completes 60%-75% of the worksheet, they are operating on the grade level target question and if a student complete above 75% of the circuit, they are operating above the grade level target question. For better representation, here is a link to the facilitators TeachersPayTeachers website, where some of her circuits are free! I have also included a picture!

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Davis’ Findings

The annual MCTM conference in Ellisville was a unique opportunity to learn and share with other math teachers from the state. Over 300 teachers, representing every corner of the state, were there with the goal of improving their student’s outcomes and to change the way our students see and interact with mathematics.

With nearly 50 different sessions available to attendees, there was a great variety of information to be gathered. The most impactful session I attended dealt with the use of statistics in Algebra 1. The presenter walked us through the process of refreshing students’ knowledge of basic statistical analysis—box and whisker plots, mean, median, and outliers. Often times, statistics is taught as a system of rules and formulas with very little student input. It is rote and boring. The presenter, Dr. Jennifer Fillingim of Madison County Schools, completely flipped this script. Rather than simply copy notes of the board, students were actively engaged in the learning process and contributing to the creation of knowledge.  Through pointed questioning, the presenter was able to draw the needed information out of students, building on prior experiences. Going forward, I am planning a statistical analysis unit for the start of the second semester. We will use statistical techniques to analyze our performance from the previous semester, which will allow us to not only learn the material but also think more critically about how we can improve during the second half of the year.

 

The second most valuable presentation covered the variety of useful technologies available for our classroom. Specifically, it further interested me in using Plickers in my classroom. Up to now, I’ve used a variety of different quiz-type apps such as Kahoot but have always been a bit underwhelmed. For those unfamiliar with Kahoot, it is a quiz app where students answer predetermined questions on their phones and received points for getting them right in a set amount of time. Students enjoy playing Kahoot, but it’s not ideal for teachers as not all students have functioning smart devices, and it does not give useful data on how students are doing. Unlike Kahoot, Plickers requires only the teacher uses technology (reducing tech issues significantly) and gives student specific data, allowing a teacher to more easily identify those students who are struggling. I am in the process of printing and implementing Plickers in my Algebra 1 classes, and I am eager to see how students respond. Certainly, there are issues of students losing their Plickers materials, but I think it will be a much better system than before.

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Kahoot’s ubiquitous loading wheel of death

 

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Plickers only needs one phone and gives useful student data

Overall, the most valuable aspect of the MCTM conference was not the individual sessions but rather the conversations with other math teachers. As a 2nd year teacher, I am always eager to glean wisdom from the veterans who have been in the classroom for many years, and I am hopeful that one day I will be able to provide the valuable insight to others that they have given to me.

 

Joy, Standards, and Relevance: Reflections from NCTM’s Annual Conference

How do we cover the myriad of standards for our grade level while also attending to student engagement and enjoyment? How do we make seemingly abstract math content relevant? The following post comes from Crystal Stone (Mississippi ’15) as she reflects on these and more ideas after attending the National Council for Teachers of Mathematics (NCTM) Annual Conference this past spring. Check it out and steal some resources and ideas! – EPS

I traveled to my first National Council of Teachers of Mathematics (NCTM) Annual Meeting in April. I didn’t know what to expect. I spent my four years in college studying English and attending literature classes only to be thrown into a middle school algebra classroom. Disoriented doesn’t begin to describe my experience. But my first year was almost over and as it was winding down and state tests were on the horizon, I needed to reinvigorate my creativity.

It turns out inspiration wasn’t hard to come by. I learned about the different ways other math teachers across the nation made algebra more relevant and more fun. This was probably most important for me to make happen for my students’ most dreaded unit of the year: functions. When I start flipping through my program booklet, I had just one goal: go to as many sessions on functions as possible.

My favorite session was a project that involved forced perspective photography. Forced perspective photography is an exercise where you create an optical illusion; you change the size of an object you’re capturing by moving the camera different distances. So for example,

The presenters gave task cards differentiated by grade-level and standard that they wanted to explore. I’ve included them here for you to consider:

What I love about this activity is that it not only makes math fun, but allows students to take ownership over their project. They can be creative and autonomous. It has enough guidance that it grounds them in the math behind the activity and forces them to draw on the knowledge that they’ve acquired throughout the year. But the investigation is also a practical one: in an increasingly digital and visual world, it’s important that students are aware of how images are manipulated and how they can manipulate those images themselves. My hope is that when I try this activity with my students next year they will thinking critically about the images they are creating and the messages those images are sending, too. The beauty of activities like these is they allow for teacher creativity. We can make these activities more math-centered or more interdisciplinary.

The forced perspective photography lab clearly isn’t the only activity I found that inspired me to be more creative and more relevant. I attended a session that discussed how to make flags into math problems. I was particularly intrigued by this session because I recently implied of a geometry project I adapted from Nicole Bishop’s classroom on redesigning the Mississippi State Flag. The presenter explained to us that flag typically have very specific proportions and we can resize them and create problems knowing these proportions. He showed us examples of problems ranging from Algebra I through Calculus. For example,

Even without knowing the exact proportions, we can fit these flags onto coordinate planes to analyze length and create equations. Here’s another image he showed us:

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And for those whose students need extra practice using positive and negative integers, there’s always the second quadrant:

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His discussion of flags didn’t stop there. He explained that he takes his students for a walk around places with a lot of flags represented in Canada where he teaches. He takes a field trip and allows culture of different people to be part of the conversation of their flags and creation of the transformations of the flags they view in class. You can view more about his presentation and find his worksheets here.

As a result of these particular sessions, I’ve been making changes to my curriculum for the upcoming year. I am considering how I craft interactive math walks this year. I plan to make my units diverse and interdisciplinary. What locations can we visit? Is there a way to incorporate technology? Can I incorporate social justice? These sessions helped provide me with creative examples of how others make the lessons more fun and will help me to create interactive lessons infused with social justice in more math-grounded ways.

Summit Reflections with Identity and Empowerment in Mathematics

Hey y’all,

It was wonderful getting to see so many folks in our TFAmily this weekend and the Fall Summit. I got to hear some really exciting updates from our math folks across the region and also was able to spend a lot of time collaborating with some of us in the Identity and Empowerment in Mathematics workshop. I’d like to share some of the strategies, ideas, and questions we had in that workshop, but I first have to start with some of the broad themes I saw from this time together…

The first thing  on my mind is the clear connection between our workshop on the importance of identity and the stories from our opening speakers. Kimberly Merchant of the Mississippi Center for Justice spoke about how her teachers’ failure to push her potential led her to just sort of slide along for years, until a professor urged her to attend law school. She also mentioned the major motivation for attending college was to get as far away as possible from her home on the gulf coast. It makes you wonder how things might have been different had a teacher operated from a standpoint of cultural competence – building in a critical eye for Ms. Merchant’s community while also seeking out and affirming the positive models and history of the same place. How many Mississippi students view “escape” as the only viable option, leading to a continuous brain-drain from the region? How might Mississippi look in 15, 20, or 30 years if students right now saw the challenges but also the determination and leadership of those seeking better opportunities for these communities? Front and center when considering identity is the perception of this region as a place to escape, with little to offer – especially to those from historically oppressed communities. This message strikes me as overwhelmingly damaging to the students we serve here, and perpetuates a lack of trust or investment from students since their community is discussed only in terms of deficits. Ms.  Merchant demonstrates that these champions do exist in our communities, but we need to make sure that their stories shine through over the negative stereotypes.

The next speaker, Barbara Logan, is the incoming Executive Director for TFA Mississippi. She discussed the amazing language and analysis her 5 year old niece displays (in particular being able to critique the film adaptation of Alexander and the Terrible, Horrible, No Good, Very Bad Day versus the original story), but when she expressed this amazement her niece would only say (to paraphrase) “Of course I can do all of that. You teach me these words, why wouldn’t I use them?” And there is the powerful counter-narrative to Ms. Merchant’s story – the way that we perceive young people is reflected in their perceptions of themselves. For Barbara’s niece, she sees no reason why it is amazing for her to compare and critique and to do so with complex language since that is what is expected of her from the adults in her life. The same role of identity is at play when our math students are told “you are so far behind,” “come on, this is easy,” or “we just went over this.” These messages set the tone of “normal math students can do this. You lack the ability or determination of a normal math student. Something is wrong with you.” It is no surprise then that we see statistics like this:

“…more teenagers name math than any other subject as the course they find most difficult in school.”

  – Furner and Gonzalez-DeHass, 2011

This is where our Identity and Empowerment in Mathematics workshop comes into play. The purpose was to understand our own story with math, consider the implications this has in our work with students, and understand how we can build positive student identities towards mathematics. It is certainly not a feat that can be accomplished in 90 minutes, but we had a fantastic conversation to get us started. My own math story demonstrates the immense privileges I was afforded which helped me gain an appreciation towards mathematics. Indeed, much of our math identity comes from an intersection of race, gender, class, and community. I never had to contend with gender stereotypes that women are not meant to do math or that Asians must adhere to the “model minority” stereotype and excel at arithmetic fluency. Because I was offered Calculus in high school, I did not have to take remedial math courses in college or purchase new technology to succeed in these high-demand courses. How will my students cope when they attend college?

Ethan's Math Autobiography
Ethan’s Math Autobiography

Considering our own math autobiography is vital if we are to positively impact the identity of our students. There is a real danger of placing our own history and values on the shoulders of our students, and expecting them to operate and learn the same way we we did despite our separate lived experiences. And there again is that sneaking accusation of “normal math students can do this.” We are defining normalcy through our own experience, and demanding that students meet us there rather than us as teachers seeking to understand and empower them through their own unique assets.

At this point in the workshop, after building and discussing our math autobiographies, we  considered how culturally aware our students currently are and what our role is in this awareness. Through a set of student interview questions aligned to culturally-responsive teaching, we sought to understand how our students perceive the intersection of math, knowledge, and learning. There was a common theme from many of the teachers’ interviews, a few of which I’ve posted below:

“Broadly speaking, my higher students and my older students said they were more impacted by my class than my lower 6th graders have. The older students say that they can see that I care about them by sending positive messages home and by encouraging them to think independently. The other students said “I don’t know” or by helping me pass the class.” – Ms. A.

“I see two broad types of responses and attitudes towards math and school in general. My students who have had success in school and math feel very confident in their abilities and see the importance of learning and how it connects to their future goals. My students who have struggled have little to no confidence and don’t see much if any connection between what happens in school and what really matters to them.” – Mr. M.

“My non-honors students struggle with protecting something about themselves in my math class,whether that is their reputation amongst peers or their ego and pride. A good third of my students responded in technical terms: their understanding of math and knowledge as well as teacher relationships were cold and not personalized, i.e. that I am here to “help them learn better” or “teach them math”; math was discussed in broad terms and along the lines of “it is important to be successful in school.” I was surprised to see some students reply with a personal investment in math, for example that succeeding in math would make the family happy, but that was far less the case than the norm, and I’m curious to hear how others are helping students ‘humanize’ their math experiences in the classroom” – Mr. K.

While it is perhaps easy to see a progression of lower math grades –> disinvestment in math –> limited cultural affirmation and identity awareness, I would ask that we instead see the opposite progression as the reality. When students do not recognize their potential as capable creators of knowledge, they lose investment in the purpose and process of the content, and ultimately fail to perform. While it is more obvious to see the student as failing math, we as culturally-responsive teachers must consider the ways that the math is failing the student: How are we affirming their potential as math thinkers? Are we designing tasks that reach all students through complex, multiple representations or approaches? Do we listen and incorporate learning when students voice frustration about systems and structures that frustrate them? Do our assessments push students to reflect on their strengths and next-steps or merely stamp them with a defining number to reflect how much they do not understand?

And that sort of self-reflection – not for the purpose of “shaming” teachers but rather so that we can continuously improve our alignment to student needs and assets – is what can help us stop this progression of disempowerment in math class from the very seeds of identity. This Thoreau quote often comes to mind:

“What lies before us and what lies behind us are small matters compared to what lies within us.
And when we bring what is within out into the world, miracles happen.”

And with that we dove into discussion of how our class structure can empower students. Here’s some of our brainstorming:

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From there, we considered six specific methods that are demonstrative of culturally responsive teaching in math. They, along with specific examples, can be found here. In summary, math teachers should:

  1. Use familiar modes of communication.
  2. Make analogies between new content and students’ lived experiences.
  3. Bring in community members to share math-related applications.
  4. Choose relevant contextual problems.
  5. Choose relevant instructional tasks and projects.
  6. Choose a relevant unifying theme or essential question for a unit.

And so all of this culminates with where we are right now – we have a real potential to empower students in their math identities and change the trend of math being seen as innate and inaccessible. The challenge is in how willing we are to look at ourselves and deeply consider from where our values about math came and how our class is impacting the identities of our students. Perhaps more than any other actor, math teachers hold the greatest power to unlock the latent potential of students and help students see themselves as capable leaders. We have to stop using the excuse that the failures of the past and the challenges of the future shackle us from doing just that. We need a stubbornness in conviction that insists that every one of our students has the capability to achieve excellence; that they are worth empowering. Because ultimately, the saying holds true:

“We see things not as they are, we see things as we are.”

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What is “interest”?

I think one of the questions that plagues teachers, and maybe math teachers in particular, is how to get students interested in the material. When we’re handed a curriculum and told to teach, it can be hard to find ways to get students on the hook.

I came across a great blog post the other day about interest in math classes. If you hop over to that link, you can find a brief overview of the psychology of interest.

One of the most useful ideas is the description of the two “appraisals” we make that lead us to decide something is interesting:

The first appraisal is an evaluation of an event’s novelty-complexity, which refers to  evaluating an event as new, unexpected, complex, hard to process, surprising, mysterious, or obscure. . . The second, less obvious appraisal is an evaluation of an event’s comprehensibility. Appraisal theories would label this appraisal a coping-potential appraisal because it involves people considering whether they have the skills, knowledge, and resources to deal with an event. In the case of interest, people are “dealing with” an unexpected and complex event—they are trying to understand it. In short, if people appraise an event as new and comprehensible, they will find it interesting.

As we attempt to interest students, I think we often focus on the latter—making sure students feel the material is comprehensible.  This was a nice reminder, I think, that we need to balance that, and also make sure the material is new, complex, and puzzling at the same time.

If you’re interested in talking more about these ideas, please sign up for the next “How Students Learn” webinar on December 11!

Math without numbers

Some great stuff happening in Joshua (’12)’s classroom:

I truly think the hardest part about Algebra for students is that they have to look for a meaning behind the numbers and variables.

As I’ve thought a lot more about that this year for my students, I decided that I would do some research, and what I found was a Common Core performance assessment from Illustrativemathematics.com that strictly asked for meaning. I fell immediately in love with the idea of no numbers, no vocabulary, just strict meaning of the problems.

Check out all his reflections here.

Happy first day! (and some motivation)

Many of our math teachers are kicking off their first day with students today–and I hope it’s going great.

To light a fire on your first day, I wanted to share some statistics about AP classes in Mississippi that I was looking at recently. In 2012, only 33 students in the entire state took the AP Calculus BC test. Of the students that took the AP Calculus AB test, more scored a 1 than scored a 3, 4, or 5 combined. And of the students that passed an AP exam in the state, only 11% were African-American–though African-American students made up just over half of the graduating class.

To the something better being started today!

Go get ’em!