Tag Archives: Re-Cap

Recap: Twitter Math Camp ’16

TMC LogoThe annual Twitter Math Camp is always amazing. This summer’s conference in Minneapolis, at Augsburg College. was no different. My great disappointment was only being able to stay for one full day this year, but the one day did not disappoint. 

As always, portions the Math Twitter Blogosphere (#MTBoS) rallied from around the country in genuine excitement to see and learn from each other after another year of digital friendship and collaboration. Thanks go out to Lisa Henry (@lmhenry9) for being the lead on this terrifically special event.

Michelle NMichelle Naidu (@park_star),
Saskatchewan Professional Development Unit

A packed room on the topic of intervention was surprising to both me and the presenter, because the MTBoS dialogue mostly revolves around first instruction. The large audience is a testament, though, to the need for reaching ALL kids in the era of 21st Century Standards. Michelle is leading a very successful intervention program in Canada which is focusing on some basic premises:

Differentiating for All Students is like Cowboys Herding Cats, but “it’s a good feeling having the herd [of students] arrive on time without losing a one.”

Early Intervention on the Pre-Requisite Skills (Readiness) that are required to be successful in the current curriculum is the first and most important intervention move. Pre-Assessments on prior content are then necessary to help improve students’ chances for success. Back at home we call this Boot Camp. Michelle affirmed that this work is good, and also inspired me to go back to my site and push to make it a priority.

Unpacking Standards Collaboratively serves two purposes. (1) It allows you to throw out material that is not in the standards, which buys you time for intervention/differentiation (Grade Level)  and (2) It helps you focus on the pre-requisite skills needed for students to learn the new material (Readiness).

Intervening on Readiness = Differentiated Content
Intervening on Grade Level = Differentiated Product

SnowballI also saw an interesting take on the Snowball Activity. Students write down one comment and one question about a topic (notice and wonder), then wad up their papers and throw them around the room. Each student picks up a “snowball” and adds another comment and question. This is done again, until there are three of each. After the fourth toss of the snowballs, the students do not write, but instead debrief publicly as the teacher summarizes the comments and questions on the board. This is a strong way to have ALL students reflect on learning.

Jose Vilson (@TheJLV)JoseV

Jose’s most solid point was that public conversation on math education reform often does not include educators, especially those teaching the marginalized. He accurately stated that if the medical system in America were being discussed on cable news, there would be a doctor on the show, but you never see a teacher on TV talking about education.

In many ways, Jose was calling us out to be activist on our campuses for the changes that we in the Blogosphere write so much about, particularly for students of color. He made a claim that really stuck with me: “We say that we teach math to all kids, but students of color are taught a different type of math than white students.” I know this is true on my campus, While my school is relatively diverse, the lower-level math classes are disproportionately populated by students with Hispanic surnames.

I asked a question of Jose, preluding it with a statement that prejudice on my campus tends to run more along income lines than racial lines (although, racism exists everywhere). Students are accepted and succeed as long as they behave like ‘these kids.’ So I asked, “How do you get teachers and staff to be more accepting of ‘those kids,’ so that they can remain authentically themselves and still learn?” Jose’s response was, “Teach the adults to recognize ‘different types of genius.'” I love that phrase! He went on to explain that kids in poverty are often times going to bring the norms of their own sub-culture to class, which is many times in conflict with the rigid, quite, patient, controlled environment of traditional school. If we can respect that and honor ALL students’ intellects, while also teaching proper social behavior, schools will break down a lot of walls and reach more marginalized students.

Audrey McLaren (@a_mcsquared),

Audrey showed samples of student work from her classes, in which she has students BUILD activities and graphs in GeoGebra and Desmos. The best example was Sticky Points. I love how the challenging of students to create the special points for a function like the x-intercept(s), the y-intercept, and the vertex demands that the students do some algebraically manipulation. The graph offers an immediate feedback loop until students do it correctly. This builds their algebra skills and conceptual understanding simultaneously. I’m using this idea in my class this year for sure.

Desmos Sticky points

Edmund Harris (@Gelada) and Myself (@MathProjects)

Edmund Model.png
I thought Dr. Harris asked for “mathematician modeling!”

I was honored when Dr. Harris, of the University of Arkansas, asked me to present with him on Mathematical Modeling. Edmund and I have been friends since our first Twitter Math Camp (TMC13), and I always look forward to our laughs and deep mathematical conversations. Edmund wanted to share the theoretical meaning of mathematical modeling, and he asked me to add my take on how the teaching of it manifests in the classroom.

Logo Pear DeckWe started by surveying the audience on Pear Deck, prompting for their definitions of mathematical modeling. The vast majority of the responses fell into two categories:

  • Representing a Real-Life Situation
  • Applying the representation to make Predictions.

It turns out that these are quite accurate if we include them BOTH, but the two are not necessarily a comprehensive list, as Edmund explained.

The professor started by claiming that shepherds in the field used to count sheep by using stones in their pocket by which a small stone represents one sheep and a larger stone represents 20 sheep. This, he asserted, is an example of abstract modeling. (Leave it to the Brit to bring sheep herding into a math discussion.) Then he drew this diagram on the board:

Edmunds Model Diagram

Edmund teachingHe explained that you start with “something to be modeled,” (noticed he did not say a real-life situation) and then you create an abstract representation of it. This is a back-and-forth process of verifying the accuracy of the model’s description of the something as well as the “thing” that we want to do with it. (Use rocks to keep track of the sheep). So the audience was responses were spot on… collectively. Yes, modeling is Representation AND Application, but not necessarily just Representation OR Application. Furthermore, Edmond wanted to make it clear that modeling does not have to apply to only “real-world” examples. He claims that when we discuss the transformations of a family of functions, we are also modeling… using an abstract representation to “do something” to the original parent function.

Modeling Tweet Me

In my investigating of what is expected of school teachers when it comes to modeling, I studied the common core documents and found very persistent, clearly defined attributes of Mathematical Modeling:

  1. Modeling is a process.
  2. Modeling is a verb.

In other words, using a model that is already provided is a good and healthy step in the learning process of modeling, but it is not modeling itself unless the students are generating the model themselves.

Modeling Tweet Heather

Modeling Tweet Jasmine

Thank you, Edmund. It was a pleasure working with you, my friend. You always make math appear so joyful.

I had several conversations throughout the Camp, but two that stood out were with …

Math Modeling
Edmund Harris (@Gelada), Brian Miller (@TheMillerMath) & Alex Wilson (@fractallove314)

TMC Bar ModelingThe first night of TMC16 was a huge social event by Desmos. Edmund, Brian, Alex and I had a beer-laden discussion about modeling that proved quite passionate (read as: table pounding, finger-pointing, and all in good fun B.S. calling). It was such a blast to throw ideas around with people of high intelligence, strong convictions and the deep desire to get this thing that we call teaching right. Cheers to changing the world one math lesson at a time.

Intellectual Need for VocabularyPic Dan M
Dr. Dan Meyer
Dr. Meyer completed his dissertation last year. Knowing how much those with a doctorate enjoy talking about their research, and being truly curious about it, I ask him to share his findings with me. He joyfully did, including some of the back story behind it. In essence, Dan studied the effectiveness of giving students the academic vocabulary after first posing a task that required its use, rather than front loading the terms. He called this method Functionary. His study showed that the both Functionary (using the vocabulary to communicate) and Traditional methods (making flash cards to memorize definitions) were equally effective in teaching students academic language found on traditional assessments. The Functionary method, however, showed superior results when students were asked to communicate their thinking using the vocabulary terms or to complete less traditional (more CCSS-like) tasks. You can listen to the Defense of his Dissertation on Dan’s Blog

As always, I highly recommend this event to any math teacher. I hope to see you all at Twitter Math Camp in  Atlanta, July 27-30 2017.

Recap: NCSM 2015

NCSMI spent a terrific week in Boston for the 2015 NCSM & NCTM conferences. I am recapping the NCSM sessions here. I already summarized the NCTM sessions in a previous post.

As with my other Re-Cap, I have summarized each session with some simple (•) bulleted notes and quotes to encapsulate my major take-aways, and occasionally a brief italicized commentary.

While I have been to several NCTM conferences, this was my first NCSM trip. For my new position as math coach, this was experience was very worthwhile.

What the Research Says About Math Coaching? — Maggie McGatha

  • Maggie-McGatha2013Positive, small student increase in 1-2 years, strong spikes after 3-4 years.
    Math Coaching works, but you must be patient. This was my biggest, most encouraging take-away of the conference.
  • Positive teacher growth on incorporating Questioning, Engagement, Conceptual Understanding, Group Work, Discourse & Technology.
  • Spectrum of Coaching
    (least directed is most effective, all are needed)

most directed ——————————- least directed
Model lessons          Co-Planning           Data Reporting
Resources                Co-Teaching           Reflecting

Ironically, the most directed (lesson resources) is what teachers request most often, even though it was the least effective service from math coaches. It still showed teacher growth and student improvement, so this is the logical place to start with teachers. As soon as possible, though, it is better to work side by side with the teachers on these lessons.  The ultimate coaching service, though, appears to be the debrief… having teachers look at student results and contemplate their effect on student learning.

Achieving Equity: Instructional Strategies to Reach All Students (Chicago) — Ruth Seward, Jessica Fulton, Lynn Narasimham

  • RuthSewardThe third largest district in the country has a very structure, organized, intentional professional developement program.
    If a district this large can provide sustained PD for its teachers, then my district should be able to do the same. We just need a plan and a system to implement it. My district has both, but they need to be revisited to include some of the following.
  • Focus on Engagement, Application and Communication
  • Accountable Talk… Just as teachers should question more than tell, we should have students do the same with each other, also.
  • 3-Reads by Harold Asturias
    1) Read aloud to a peer.
    “What is the problem about?”
    2) Read the problem again.
    “What is the question in the problem?”
    3) Read it a third time.
    “What information do you know and not know?”
  • Hierarchy of training:
    Facilitators ->Teacher Leaders -> Teachers
    PD is given to Admin as well as Teachers.
    PD for teachers includes Elbow Coaching (Co-Planning, Co-Teaching, Co-Reflecting)
  • The Five Dimensions of Mathematically Powerful Classrooms
    5 Dimensions
  • We were also shown an example of the types of activities that are promoted in their teacher training. We were asked to place the Decimal/Percent cards in order from least to greatest, and to fill in any blanks. Then we had to match the set of Fraction cards, followed by the Area Model cards, and finally the Number Line cards.
    This would be a great activity to open the year with in ANY class, even an upper level, in order to accelerate number sense and set norms for group work.

Percent activity

Engaging ALL Learners in Mathematical Practice through Instructional Routines — Amy Lucenta & Grace Kelemanik of the Boston Plan for Excellence

  • Amy LucentoThe Standards for Mathematical Practice create open doors to struggling students, not walls.
    This is such a simple, yet profound concept. It was the heart this presentation, and one of the best principles pitched at the conference. I’m a fan, because it is one of the three principles that I shared in my presentation at NCTM .
    SMP doors
  • Not all SMPs are created equal. #1, followed by #2, 7, 8.
    I have heard many people say that the 8 Practices should be a shorter list. It was interesting to see their list.
    SMP scal e2

Hey! What’s the Big Idea? — Greg Tang

  • tang-montageProgressions is the Big Idea?:
    Concepts -> Algorithms -> Speed
    Greg really pushed for a balanced, reasonable approach to teaching math. I have always emphasized the first two, but was challenged to put more effort into the back end. This was one of the Biggest Ideas that I brought home.
  • Number Sense is Key, and can be enhanced through number games.
    I am now addicted to Kakooma
  • “Generalizing your thinking is what makes you smart.”

Reinventing Algebra in a Common Core World — Eric Milou

  • MilouProvocative Statement #1: Dr. Milou laid out an Algebra sequence that pushed the introduction of Quadratic functions to Algebra 2.
  • Provocative Statement #2: Teachers need to to start a grassroots revolution to address the Common Core’s failure to limit the bloated list of standards in high school, since no revision/feedback mechanism exists.
    I was very impressed that NCSM allowed a dissenting view, and I loved the courage with which Dr. Milou spoke. While I find his suggestion having merit in terms of math progressions, I don’t see how it  addresses the glut of standards, so I agree with him that there needs to be a feedback mechanism to address that issue.

Sense-Making: The Ultimate Intervention — Janet SutoriusJanet S

  • Removing the mathematics from context and focusing on procedures prevents students from using their own common sense and sense-making abilities to do mathematics. Struggling students need a contextual framework the most.
    I have always said… naked math comes last.

Hot Topics: Intervention — Matt Larson

  • Matt LarsonDo not pull struggling students out from class. Give them additional learning, instead.
    This was a round table discussion with a big name in the field of math ed. He described some field studies he was involved with in Chicago regarding elementary intervention structures. The big take-away here was to not have intervention students miss class time. Build the time into the day when they receive additional instruction on unmastered topics, and give those who have mastered the topic an enrichment activity.

Occam’s Razor — Eric Hart

  • hart_ericFocus on the Math first (methodology second)
    This echos what I learned from William Schmidt, about focusing on the mathematics, not the methodology.
  • “If we could switch from telling to questioning, we would change the world of math education.”
    A college Professor said this! In public! I pressed him on this statement, which I whole-heartedly agree with, but pointed out the obvious … college math is taught almost entirely through telling. His response was, “That is changing.”
  • Which form of the Quadratic Formula is better? Doesn’t the less conventional one make more conceptual sense?
    This pic got a lot of response on Twitter.
    Quadractic Pic
  • Students in other nations do not spend as much time on factoring as U.S. students. They use the Quadratic Formula to get factors them plug them into the equation.

Nank 2Mathematic Modeling with Strawberries and Video — Sean Nank

  • Sean had us participate in a modeling task that involved a video of himself cutting strawberries. The task walked us through each step of the Common Core’s definition of modeling:
  1. Identifying variables,
  2. Formulating a model by creating and selecting representations that describe relationships between the variables,
  3. Analyzing and Performing operations on these relationships,
  4. Interpreting the results of the mathematics in context,
  5. Validating the conclusions,
  6. Reporting on the conclusions and the reasoning behind them.

Nank Strawberries

The question was simple, “How long will it take to cut the strawberries?” The task, however, was rich and robust. While Dr. Nank allowed the lesson to be very student driven, he still paused before each of the 6 steps above, to direct us in the next segment. It was a great demonstration of how to scaffold the teaching of modeling, instead of the typical errors of “Here kids, now model.” or the “Let me show how modeling is done.”

  • Marilyn MansonMarilyn Manson Pedagogy: “Just shut up and listen.”
    Dr. Nank shared an interesting anecdote. He said after the Columbine shooting, Marilyn Manson was asked what he would say to the kids. He claimed that he wouldn’t tell them anything, he would  “just shut up and listen.” Sean was encouraging us to do the same while the students are working on the various components of modeling.

PAEMST Seminar for Awardees of The Presidential Award for Excellence in Mathematics and Science TeachingDan Meyer

  • Dandy CandyDandy Candy Lesson
    I have always loved this task. Dan took it so much deeper than I had imagined from his post on it. It was a delicious pleasure to participate in it with its creator.
    The conversation at my table of instructional leaders was how to get teachers to do lessons of this richness and quality. Our teachers back home all readily admit that they need as much scaffolding in teaching these kind of lessons as the students do in learning them.
  • When leading students through a task like this, wait for their questions. “Don’t give away too much, too soon. You can always add, but you cannot subtract.”
  • Dan shared Sean Nank’s/Common Core’s Definition of Modeling. (He also has a great post on modeling.)
    Dan also probed us for our take on it. There was consensus at my table that the definition was solid, but that modeling did not always have to be that comprehensive or limiting. There was also consensus that creating mathematical models from a given context to this degree needs to be done far more often in classes.
  • JerryI met up with Jerry Young of Oregon, a fellow awardee from 2001 whom I really connected with in Washington DC, some 13 years ago. This was a treasured highlight of the trip.

As you can tell, it was a great trip, from which learned a great deal. I am already looking forward to NCSM 2016 in San Francisco.

Recap: NCTM 2015, Boston

NCTM Boston CropI had the wonderful opportunity of spending a week in Boston for the 2015 NCTM & NCSM conference. I am recapping the NCTM sessions here, and the NCSM sessions in another post.

Since there was so much information, I have summarized each session with some simple (•) bulleted notes and quotes to encapsulate my major take-aways, and occassional a brief italicized commentary.

This was an enormously worthwhile trip. I highly recommend that you get yourself to San Francisco in April 2016, if you can.

NCTM President’s Address: Five Years of Common Core State Mathematics Standards — Diane Briars

  • Diane Briars“College and Career Readiness” in math calls for Statistics, Discrete Math & Modeling.”
  • Standards are not equal to a curriculum.
    We need to pay more attention to the tasks & activities through which the students experience the content, rather than simply focusing on the content itself.
  • 75% of teachers support Common Core, but only 33% of parents support it, and 33% of parents don’t know anything about it.
    So we have to get the word out.

What Decisions — Phil Daro (1 of 3 writers of CCSSM)

  • Phil Daro“Don’t teach to a standard; teach to the mathematics.”
    This was the most challenging statement of the conference for me, mostly because I’m still struggling to wrap my mind around it. I get what he means, but I have been so trained to state an objective on the board and bring closure to that lesson. He shared that Japanese lesson plans are simply descriptions of the math concepts of the unit rather than the typical American model of objective, examples and practice sets.

The Practices in Practice — Bill McCallum (1 of 3 writers of CCSSM)

  • MCCallumStudents understanding what WILL happen without doing the calculations is an example of Using Structure.
    I took this back to my classroom and immediately applied it in the students’ graphing of quadratic functions. One of the more practical things I took from the conference.
  • “A student cannot show perseverance in 20 minutes. It is done day after day.”
  • Noticing & Wondering applies to teachers looking at student work as well.
    Dr. McCallum was referencing an instructional practice made well-known by Annie Fetter of the Math Forum through which students are asked to closely analyze mathematical situations. He was calling on teachers to focus on and analyze student thinking (not simply answers) just as closely.

Five Essential Instructional Shifts — Juli Dixon

  • DixonShift 1: Students provide strategies rather than learning from the teacher.
  • Shift 2: Teacher provides strategies “as if” from student. “When students don’t come up with a strategy, the teacher can “lie” and say “I saw a student do …”
  • Shift 3: Students create the context (Student Generated Word Problems)
  • Shift 4: Students do the sense making. “Start with the book closed.”
  • Shift 5: Students talk to students. “Say Whoohoo when you see a wrong answer, because we have something to talk about.”
    I felt that I do all of these, but that I have been ignoring Sgift #3 this semester. Dr. Dixon compelled me to give this more attention again. 

Getting Students Invested in the Process of Problem-Solving — Annie Fetter & Debbie Wile

  • AnnieTeachers must stop focusing on answer getting before the students will.
  • Honors Students are used to a certain speed and type of outcome, so they need a different type of scaffolding when it comes to problem solving.
  • “If you are focused on the pacing guide rather than the math, you are not going to teach much.”
    This was one of several comments, including Dr. Daro’s, that bagged on the habit of being too married to a pacing guide of standards.

Motivating Our Students with Real-World Problem-Based Lessons — Robert Kaplinksy

  • Kaplinsky CroppedTo students: “I will only give you information that you ask me for.”
  • Chunking tasks (Teacher talks — Students Think/Pair/Share — Repeat) was demonstrated to allow student conjectures, critiquing reasoning and high engagement.
    Robert modeled his “In-n-Out” lesson. I have seen this several times, but I never get tired of it, because it is awesome. Every time I have witnessed this lesson, teachers cheer when the answer to the cost of a 100 x 100 Burger is revealed. I have never heard this from someone looking up an answer in the back of a textbook. Also, Robert expertly demonstrated how a lesson like this should be facilitated in class by chunking and by getting the students to think of what they need to know.

Getting Students to Argue in Class with Number Sense Activities — Andrew Stadel

  • vQWJdnFF“As the teacher, I feel left out if I don’t know what my students are thinking and discussing.”
  • Discussion techniques
    Andrew is known as Mr. Estimation 180.” In this session, he showed how to bring SMP #3 into a number sense activity. The new one that I learned from Andrew here was having students stand up … those that choose A face left, B face right, C face forward. Then find someone near you who agrees and discuss. Find someone who disagrees and discuss. That’s Bomb!
  • Calling for Touch Time with the Tools
    In other words, let’s get the kids measuring with rulers, constructing with compasses, building with blocks, graphing with calculators.
  • Chunking tasks to allow student conjectures, critiquing reasoning and high engagement, as I saw with Kaplinksy.

Using Mathematical Practices to Develop Productive Disposition — Duane Graysay

  • duaneDuane and other educators of Penn State created a 5-week course with the intent of developing a productive disposition in mathematical problem solving.
    There were a lot of data showing the effectiveness of this program which focused on teaching the 8 Math Practices. The most amazing and provocative result was shown by this slide in which student felt that the math was actually harder than they thought before the course, but that they felt more competent.

2015-04-18 08.46.25

(SA = Strong Agree, etc)

Shadow Con — A Teacher Led Mini-Conference

  • Michael pershan-219x181There were six worthy educators from the Math Twitter Blogosphere (#MTBoS) that each offered up a brief 10-minute presentation. The uniquely cool aspect of these talks is the Call to Action at the end of each. In other words, you have to do something with what you learned.
  • Michael Pershan’s talk: Be less vague, and less improvisational with HINTS during a lesson. Instead, plan your hints for the lesson in advance.
    This one resonated most with me, because I once heard that Japanese teachers have a small deck of cards with hints written on them. To draw a hint card, students have to first show effort and progress, then they may draw a hint card. They must use each hint before they may draw another. I accept Michael’s call to action.

 Ignite — Math Forum

  • IgniteThese were a series of 5 minute/20-slides mini-presentations that were more inspirational than informational. Apparently they are part of a larger movement (Ignite Show), but the folks at Math Forum have been organizing these Ignite Math Sessions at large conferences for a few years.
    If want to get fired up about teaching math, these sessions definitely live up to their name. 

Can’t wait for next year!