Tag Archives: Math Coach

Recap: NCTM 2017

San Antonio, CA , April 2017
I have summarized each session with some simple (•) bulleted notes, red underline to encapsulate my major take-aways, and occasionally a brief italicized commentary.


Math Task Makeover with Desmos Activity Builder — Michael Fenton (Desmos), Jed Butler (Heritage HS), Bob Lochel (Hatboro-Horsham High School)

  • The Big Take-Away = Use Desmos activities to generate intellectual need to learn the lesson objective.”
  • Generate need for Graph of a Linear Inequalities ….

  • Generate need for Definition of Ellipses …

  • Start with informal investigation, then move to formal language.
  • Teacher facilitation is key.
  • Where to Learn more: learn.desmos.com

I’ve got to starting using the overlay function!


Numberless Word Problems in the Elementary Grades — Brian Bushart & Regina Payne (Round Rock ISD)

  • The Big Take-Away = Have students make sense of word problems prior to computation by removing the numbers.”
  • The origin: Press kids to stop just circling numbers in word problems and applying random operation.
  • Not all day every day. It is a tool for sense making.
  • Focus on the relationship and the operation, formal language, and what the question would be, not the answer.
  • #numberlesswp

This makes sense for secondary grades as well.


Rich Tasks as Landmarks for Students to Use in Navigating Their Mathematical Learning Journey — Peg Cagle (LAUSD)

  • The Big Take-Away = Students’ work on Landmark Tasks throughout the year that should be visible in the classroom so that students can map their learning.”
  • We don’t take advantage enough of narrative in math class.
  • “Imagine shrinking down an entire map to the size of an index card. All the details get lost and the map becomes unreadable. What are the landmarks that will help students navigate the mathematical landscape”.
  • Peg presented the criteria for a Landmark Task …

  • … and presented us with a LandmarkTask …

Tied Up in Knots: In your groups, measure the length, in centimeters, of the piece of rope that you have. Then tie a single overhand knot and remeasure the length. Repeat the process several times. Create a data table, graph and equation relating the number of knots to the the length of the rope.

  • … then she analyzed the task according to the criteria …

  • … and showed how this landmark was made visible in her classroom.

  • The Speech Bubbles were created by the students to make comments on other groups’ work.
  1. This is the second year in a row at this conference that I have seen Peg give a year-long, big picture vision of using tasks in the classroom.
  2. This is also the third presenter who has mentioned some variation the Speech Bubbles. Time to use them in my classroom.
  3. Peg made a statement that has me thinking deeply and that I have quoted several times already: “Students have ample amounts of robust evidence that they are not good in math.” We need to help them overcome that.

Changing Teacher Practices: Transforming Teaching 101 to PD 101 — Audrey Mendivil (San Diego County)

  • The Big Take-Away = Shift from Professional Development to Professional Learning.”
  • 5 Principles of Effective PD
    1. On-Going
    2. Support during implementation
    3. Model new practices
    4. Variety of approaches and active engagement
    5. Specific to discipline/grade level
  • Shift from Professional Development to Professional Learning

  • How to Change:
    1. Small Steps. Stick to only 2-3 short term goals.
    2. Rethink Our Norms:

  • Why PD often FailsHow can we set-up for success?
    1) Top-Down Decisions: How can you include teachers in the decision making process?
    2) Little or no support in transferring ideas to the classroom: What support is available?
    3) Idea that teachers need to be fixed: How are you communicating your why?
    4) Lack of variety in delivery modes: How can you differentiate for teachers?
  • Essential Elements. Audrey took us through a terrific activity for those who create Professional Learning experiences. She gave a sets of cards that were color coded, and asked us to work together to sort them into 4-6 groups, and then name the groups.
    She then shared how she grouped them (which is what the color scheme was for). The idea was to take ALL the things that we want teachers to know and do and rather than create a checklist for them, cluster these concepts into Themes or Essential Elements and have teachers learn that.

  1. This was yet another session at NCTM that focused on Vision and the need to put the WHY in front of teachers.
  2. The re-structuring of the norms resonated with me. I’m still thinking deeply on this one. The norms drive the culture of the meetings, so they offer great leverage.
  3. In her call to keep the list of goals short, Audrey discussed the need to set short-term, intermediate and long-term goals. This falls in line with the concept of “leading and lagging indicators.” Student data may take awhile to improve (lagging) so what are the improvements in teacher moves that we can credit to our PD (leading)?
  4. The objective of the card sort activity gets at the heart of what I see killing most PD in districts … too many short-lived initiatives. Keep the broader concepts in mind. Bigger, slower moving targets are easier to hit. 

The Struggle is Real: Tasks, Academic Status, and Productive Problem Solving — Geoff Krall (New Tech Network

  • The Big Take-Away = Developing a culture of productive struggle requires holistic vigilance on the relationships between Quality Tasks, Effective Facilitation & Academic Safety.

  • Protocols for Problem Solving
    1) Make it visual
    2) Estimate Before Solving
  • Record what students know…
    vs what they are assessed on.
  • Promoting Access:
    Example: Make the smallest (or largest) difference by filling in numbers 1-9 no more than one time each.

I am challenged by Geoff’s two graphs of the linear regression of student growth. My Claims-Based Grading needs a little more work in the area of reflecting cumulative knowledge rather than recent learning.


Logarithmic Earthquake Project: An Algebra 2 Project with Real Applications — Tanisha Fitzgerald-Williams & Beverly Heigre (Notre Dame High School)

  • The Big Take-Away = Have students view videos of earthquake damage and do their own research on Richter Scale, before formal presentation of calculating Magnitude difference with Logarithms.”
  • Step 1: Research

  • Step 2: Calculations

 

 

 

 

  • Step 3: Student Groups make Presentations
  • Note: Tanisha & Beverly also have students offer possible humane response to victims of earthquake presented.
  • There is a google drive folder available that contains materials for this projects: goo.gl/Y197YR

Clothesline: The Master Number Sense Maker — Chris Shore (Me)

  • The Big Take-Away = Number sense and conceptual understanding of current content can be taught simultaneously with Clothesline Math.”
  • I presented the power of the Clothesline to teach Algebra, Geometry and Statistics.
  • clotheslinemath.com
  • #clotheslinemath

There were at least 5 sessions at NCTM Annual in which the Clothesline was a part or the focus of the presentation. 


Fun Sidenote: The ceiling rafters and the carpet print of the convention center had the same Geometric Pattern. I am sure there is lesson to be created out of this.


There are videos of keynotes, ShadowCon and Ignite
at NCTM’s Conference 2017 web page.


The city of San Antonio enhanced an already fantastic trip!

 

 

 

Recap: Greater San Diego

logo-gsdmcThe Greater San Diego Math Council resurrected its annual conference. After a two year hiatus, Jason Slowbe, Sean Nank and their Council colleagues did miraculous work to bring GSDMC 2017 to life. This Glorious Day was worth all their efforts.


Opening Session (Four Bursts)
Rather than one keynote speaker, four presenters gave brief talks.

Observe Me
pic-kaplinskyRobert Kaplinsky (@RobertKaplinsky),
Downey USD, CA

Robert made two strong points:
1) The #ObserveMe practice, which calls for teachers to invite others to observe them. The key here is that very specific feedback is called for from colleagues.
2) The need for teachers to gain new perspective. Robert shared the story of Febreze. It is a very effective product that initially had a tough time selling, because people were nose blind; in other words, they did not realize how badly their houses smelled. Similarly, teachers will not buy into professional development until they recognize the need for change.  Therefore, we really need to do the work on changing teachers’ perspectives on the results of their practices.

Music Cues
pic-matt-vMatt Vaudrey (@MrVaudrey),
Bonita USD, The Classroom Chef

Matt is well-known for his use of Music Cues to save on transition time in the classroom. In fact, he showed how as much as 21 hours of instruction time a year (a whole month of school!) can be saved with the use of these cues. In my own class, I personally use four of the cues that Matt offers in his Google folder.

Social Justice in Math Education
pic-susie-hSusie Hakansson (@SusieKakansson),
TODOS

Susie told the story of “Carol” and all the barriers to accessing rigorous math courses that she confronted as an Asian girl. Then she revealed that “Carol” was really herself and the experience she had growing up in the American school system. She called for more equity in access for all students, particularly in STEM courses.  “Don’t let test scores, skin color, or adults low expectations to prevent students from taking rigorous math courses.”

The Converging Future of Math and Computer Science
pic-pierre-bPierre Bierre (@pierrebierre),
AlgoGeom

Pierre  drew our attention to the growing number of computer Science courses being offered on high school campuses. Pierre went on to also share how programming can be a terrific problem solving tool in math class. This was a good primer for the number of sessions at the conferences that dealt with programming in math classes.

These quick presentations set a terrific tone for the conference experience.


Math Coaches Panel 
Brenda Heil (@BrendaHeil)
Bethany Schwappach (@MsSchwappach)
Chris Shore (Me) (@MathProjects)

panel-pic

Brenda, Bethany and I each offered up a 10 minute introduction of our roles as math coaches and a particular point of emphasis for math coaches to focus on. The rest of the session was open to questions fielded by our facilitator, Sean Nank.  The conversation was rich, and I learned a great deal from my panel colleagues.

brenda-slideBrenda is a TK, K-1 Coach in Escondido. Her biggest point was avoiding the badge of same… “If I work with a math coach, it means that I suck.” She instead insisted that math coaching training should be advertised as a resource for everyone.

Bethany is a Technology Coach for El Cajon.  She did something interesting by surveying math coaches, prior to the conference, with the question: “What are some of the greatest challenges Math Coaches are assigned to tackle?” The number one response was differentiating professional development for teachers. So Bethany offered two terrific ideas. The first was a Badge System for online “Anywhere, Anytime” PD, much like the structure of online mastery courses for students. The other was the promotion of omnipresent communication of the math coaching program to teachers.

bethany-slide-badges

bethany-slide-comm

I am a Secondary Math Coach in Temecula.  I declared that a math coach’s job is all about relationships as I shared out how many people I deal with to my south (teachers I serve), my east-west (coaching colleagues) and my north (administration). Because of this, the most important question to ask any of them is “How may I best serve you?”

relationship-panel

I also offered three axioms that I believe all math coaches should base their work on. Each of them are quotes from famous researchers.

  • Axiom #1, Dr. William Schmidt, University of Michigan: The greatest determining factor in the quality of the education that students receive is the decisions that the teachers make on a daily basis.
  • Axiom #2, Dr. Kenneth Leithwood, University of Toronto: Indeed, there are virtually no documented instances of troubled schools being turned around without intervention by a powerful leader.
  • Axiom #3, Dr. Maggie McGatha, University of Louisville: The meta-research shows that math coaches are effective. We see small bumps in years 1 & 2, and large spikes in years 3 & 4.

The second one seem to resonate with this crowd.

berray-tweet

From the questions and conversation I learned that …

  • …no two math coaching job descriptions are alike. Everyone’s daily routine was unique, but we all had a common goal… improve classroom math instruction.
  • … most math coaches are tossed into the position with very little support and training. Everyone, including administrators, deem this job important, but seem to be figuring it out as they go along. It was awesome to discover that San Diego County offers math coaching training. This is an idea that should spread to other counties as well.
  • … everyone is optimistic. Math coaches acknowledge that education has a long was to go in improving math instruction, but that we have all seen significant progress despite the challenges.

Clothesline: Algebra, Geometry & Statistics
pic-luevenos
Daniel Luevanos  (@DanLuevanos) &
Chris Shore (Me) (@MathProjects)
clotheslinemath.com

I loved presenting with Daniel. He is a Clothesline Math enthusiast who has developed some terrific ideas, particularly on systems of equations.

pic-daniel-system-1
We demonstrated fractions, algebraic expressions, linear systems, solving multi-step equations, vertical angles, special right triangles and statistics (average, range, standard deviation).

pic-twitter-clotheslne-gsdmcMy favorite moment was during the Call to Action when Daniel challenged the teachers to use the Clothesline to enhance their own understanding of mathematics. So I surveyed the room by asking “How many of you today learned something about mathematics itself, not just the teaching of it?” Ninety percent of the room raised their hand!

 


21st Century Conference Ideas
I also want to give a quick shout-out to the GSDMC President, pic-slowbeJason Slowbe, and the rest of the Council for their willingness to experimentation with some new conference formats:

  1. Opening Session Burst: Instead of one keynote speaker, four presenters gave brief presentations within the same hour as the MC greeting.
  2. Genius Bars: Presenters were made available outside of their sessions for participants to meet and ask questions.
  3. Panel Sessions: 3-4 panelists share brief introductions and presentations (15 min), then the remaining hour was open to question by the audience.
  4. Working Lunches: People received their box lunch (part of the registration fee) and then were allowed to sit in the session rooms. Many of these rooms had exhibit presentations.
  5. pic-philippClosing Session Reflection and Evaluations: Closing speaker. Randy Phillip (@rphilipp), asked us all to reflect on one idea that we would take back to our classrooms. After giving us time to ponder, he asked for volunteers to share out publicly. It was an excellent way to have participants reflect on their conference experience and increase the chances of us committing to improve our instructional practices.

How Deep for Teachers?

 

26570883 - flood level depth marker post with rain falling into the surrounding waterRecently, I conducted a training with a school district in West Virginia.  It was for new teachers (1st-3rd Year) in all subjects K-12. There were approximately 75 participants and 20 mentors. One of our activities dealt with Depth of Knowledge. I showed the typical D.O.K., but I wanted them to have a more meaningful experience with D.O.K. levels in mathematics.

DOK Chart

The activity I created was inspired by the work of Robert Kaplinsky. I love his Tools to Distinguishing Between Depth of Knowledge Levels. I particularly like his example of sums of whole numbers:DOK RK sampleThis is a simple and clear example of the D.O.K. progression. However, it does not show D.O.K. Level 4, so I contacted Robert and he directed me to this Problem Post of his, How Many Soda Combos are There on a Coke Freestyle Machine? 

DOK Soda

Perfect! I compiled these four into one document, scrambling the order, and asked the teachers to discuss the problems in their table groups and to assign a D.O.K. level exclusively to each one. I was intrigued at how different their responses were compared to what Robert (and myself) considered the problems to be. I noted that the group was a broad range of grade levels and subject areas, so I thought I would conduct the same activity with a collection of high school math teachers that I was scheduled to train in California  the following week. I was very curious if math teachers would view the problems differently than non-math teachers. Indeed, they did. However, they also disagreed with Robert and me. Below, are the all responses from the groups at each training, as well as Robert’s determination. Notice the variety of responses that was generated within each training.

DOK RK Response

The choices that earned  the most votes looked like this.

DOK RK tops

Notice that there is not a single example in which all three parties agree. I have no profound analysis of these results; I am simply sharing this very curious experience. I am still pondering the outcomes and their meaning many times over. So much so, that whenever I hear the phrase “D.O.K.,” I smirk and scratch my head.

Recap: Twitter Math Camp ’15

What happens at Twitter Math Camp never stays at Twitter Math Camp! 

TMC logoHow can it? We all met through Twitter, speak through blogs, ride a communal wave of a passion, ache to change the world through math education, and respond to the annual call of Lisa Henry (@lmhenry9) to gather each summer for the most exhilarating, unique and educational professional development event that any of us have ever experienced. Collectively, we form the universe know as the Math Twitter Blogosphere (#MTBoS). With this kind of excited learning and a vehicle to share it loudly with the world, there is no way to keep TMC a secret. 

So in this passionate, collaborative, spirit, here is my Re-Cap of TMC15

{Note: All videos shown here were recorded by Richard Villanueva}


GOING DEEPER WITH DESMOS Session
Jed Butler (@MathButler), Michael Fenton (@mjfenton), Glenn Waddell (@gwaddellnvhs), Bob Lochel (@BobLoch)

Desmos Team

The “Morning Sessions” of the Camp consisted of 2-hour sessions that ran each of the first three days. Each 3-morning session was based on a topic. I attended the one on Desmos, the premier, free, online, graphing calculator. This was an enormously productive time that inspired me to SCHEDULE in advance, where and when to use Desmos in my curriculum this year. Here’s what I learned about Desmos ….

  1. Tours: These are built-in tutorials that walk you through the Desmos basics of Graphing Equations, Creating Tables, Lines of Regression, and Restrictions (domain & range). Just click the question mark in the upper-right corner.
    Pic Tours
  2. Desmos Bank: A communal site where teachers can share Desmos ideas and activities.
  3. Activity Builder: Eli Luberoff (@eluberoff), the founder and CEO of Desmos made a guest appearance at our session to announce the launch of the Activity Builder. In essence, this allows teachers to create lessons, constructed of a sequence of Desmos activities. Trust me, YOU WANT TO CHECK THIS OUT.
  4. Student Accounts: If students have a Google account (which all of mine do), they can log into Desmos through Google, which allows them to save their work and send their products to the teacher. That’s going to happen in my class this year.

GEOMETRY, Not an IslandJasmine
Jasmine Walker, (@jaz_math), Burlington, Vermont

Jasmine started her session with a statement that I very much agreed with: “Even if your school or district has not adopted an integrated curriculum, you should still teach geometry as if it has. Geometry is not an island; we should not leave algebra behind.”

She then posed the question, “How do you start the year in Geometry?” for which the room had a very uniform answer … with vocabulary. This led the conversation on how to start the year with rich math tasks that link algebra to geometry. There was not a great deal of time for solutions, but the conversation brought me back to the Desmos activity builder. Geometry, Algebra & Vocabulary can all be brought together with a Desmos activity in which students need to generate geometric shapes on a coordinate plane, with restricted equations.


WHAT DO YOU THINK AND WHY? Supporting Students in Sharing their Ideas
Dr. Ilana Horn (@tchmathculture)

Dr. Horn spurred a terrific conversation among a large audience about how we, the various teachers in the room, support students in the sharing of their thinking in math class. The class had some wonderful ideas, however, what struck me most was not anyone idea, but the fact that so many ideas existed in a collective body of teachers. It truly is not a matter of knowledge, but a matter of will in getting students to work together and discuss their ideas. I was also impressed in Dr. Horn’s use of Polls Everywhere. I saw the power of the simulataneous viewing of the classes’ thoughts. I have been contemplating the use of Pear Deck (a similar platform) in my class.

TMC Poll


Teaching the 8 Practices
Me! (@MathProjects)

I taught a session on teaching the 8 Standards of Mathematical Practice, in which I shared my SMP Posters, their corresponding Wordles, and the explicit teaching of the practices through “Dual Targets.” (my blog post forthcoming)  Meg Craig (@mathymeg07) posted about the implementation of #SMPTargets in her own classroom.

SMP Posters MPJ 1_Page_7


Growing Our Practice  (Keynote #1)
Dr. Ilana Horn (@tchmathculture)
(video Part 1, Part 2)

Lani PicDr. Horn is well known for studies on teacher collaboration as well as student collaboration, therefore, she often talks about how teachers think about teaching. She once again delivered on that point through the lens of how teachers’ perspectives affect their professional growth, parsing out the difference between good teachers and great teachers into three key qualities:

  • Problem Frames
  • Representations of Practice
  • Interpretive Principles

The great teachers have …

  • Problem Frames that are actionable,
  • Representations of Practice that include more student voice and perspective, and
  • Interpretive Principles that focus on connections among teaching, mathematics and student understanding

In other words, great teachers do not spend a lot of time and energy discussing things they have no control over; rather, they ponder how students think about and interact with mathematics, and what how the lessons and activities affect their learning. So Dr. Horn called for …

  • Teacher Agency
  • Empathic Reasoning
  • Ecological Thinking

This resonated throughout a room full of people bent on “growing their practice.”


Math From the Heart, Not the Textbook (Keynote #2)
Christopher Danielson (@Trianglemancsd)
(video Part 1, Part 2)

Christopher laid down the inspirational challenge: “Find what you love. Do more of that.” He shared with us how he loves ambiguity and, therefore, was OK with playing the game of Which One Doesn’t Belong? For example, what students would choose and why in the set of four figures below, will offer up multiple answers.
TMC which oneChristopher is also the author of Common Core Math for Parents for Dummies. A much needed resource in responding to the darkside of social media.

“Find what you love. Do more of that.” — Christopher Danielson


Screen Shot 2015-07-24 at 3.05.23 PMTeacher Woman  (Keynote #3)
Fawn Nguyen, (@fawnpnguyen)
(video Part 1, Part 2)

Fawn did here what Fawn does best: She made us all feel wonderful about being teachers. She humorously poked fun at the tweets that many of us sent her, but also seriously shared her personal trimphs and tragedies. In the end, our diminutive twiter celebrity grew huge with inspiration. She tearfully read a complimentary letter from a grateful student, and then told us of her sister who is an engineer. An emotional Fawn, claimed “She makes more money than me,  but she doesn’t have that letter!”

“She makes more money than me, but she doesn’t have that letter!” — Fawn Nguyen


My Favorites
Several times throughout the Camp, there is time given for people to share a 5-10 minute presentation of a technique, activity or routine that they love. There were nearly two dozen amazing ideas.

Two of them I have already implemented in my class …

High 5’sGlenn Waddell (@gwaddellnvhs): Glenn was right. Offering the High 5’s at the door does more for my mood and mental preparation for the class than it did for the kids.

Music Cues, Matt Vaudry (@MrVaudrey): Playing Mission Impossible at the beginning of class and the Benny Hill Theme song at the end has drastically improved the time spent retrieving and cleaning up materials.

and two others I intend to use in the future …

Egg Roulette, Bob Lochel (@BobLoch): This looks to be a very engaging activity on probability and on making and critiquing conjectures.

Student Videos, Princess Choi, (@MathPrincessC): Having students make videos on math concepts, and then post them to a place where they may “like” and “comment” on each others is cutting edge.

I presented two of my own Favorites …

Neuron Stickers, Brain Surgeons & Wrinkle Sprinkles:  These are vehicles that that I used to cultivate a Growth Mindset in my students last year. (my blog post forthcoming) @mathymeg07 blogged about Strengthening a Dendrite and how to get inexpensive posters made.

Rally for Roatan: A pitch for the altruistic effort to bring textbooks and instructional supplies to the school district of Roatan, Honduras, and the roll-out of my new web page to support it.


MATH COACHES Roundtable
Chris Shore (@MathProjects), John Stevens (@Jstevens009), Chris Harris (@CHarrisMath), Hedge (@approx_normal), Jennifer Bell (@jkjohnsonbell), Nanette Johnson (@Math_m_Addicts), Robert Kaplinsky (@robertkaplinsky), Shelley Carranza (@stcarranza)

We eight math coaches had a wonderfully transparent roundtable discussion of what was working and not working at our sites. I was helpful to hear about so many successes, and to know that we shared many of the same issues. Listed below are the bulleted notes from that exchange.

“How do I move teachers along the WHY train?” — Nanette Johnson

Successes

  • 100% Handshake Introduction
    (Introduce self to every math teacher with a handshake)
  • Modeled Number Talks in 150 classes in 2 months
  • Acceptance of math coach at 16 schools
  • Teacher input (What do you think?)
  • Liaison/Advocate for teachers with District
  • Teacher invitation and openness
  • Self-Growth
  • Started Math Coach Network
  • Led Textbook adoption
  • Model Lessons (Geogebra, Desmos)
  • Teacher understanding of Common Core as teaching students to “Think & Communicate”

Resources:

  • #educoach: Wed 7pm Pacific
  • #k12mathcoach: 2nd & 4th Wed 6pm Pacific
    (starting in August 2015)
  • #elemmathchat: Thurs 6pm Pacific

Issues

  • Dismal lack of content knowledge in some cases
  • Missing teaching in the classroom
  • Coaching is more about psychology than math.
  • Drinking from a firehose, but only able to spit it back out
  • How do we collect data on effectiveness
    (Woodruff scale: 10 things)

Burning Questions:

  • How do I move teachers along the WHY train?
  • How do I use Behavior Economics to nudge change?
  • How do you measure effectiveness of PD?
  • What data do we have to show that we are effective?
  • How do I support myself at my getting better at my job?

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

Dr HornLani Horn (@tchmathculture): We finally had our long overdue conversation about the structure of collaborative student groups. Dr. Horn wrote THE book on this topic, Strength in Numbers. I have always used a great deal of group work, and recently Lani’s emphasis on “status” in the class has influenced my thinking a great deal. We had the controversial discussion regarding grouping homogeneously, heterogeneously or randomly which finally settled the issue in my mind. I will share the results of that dialogue in a future post. #cliffhanger

Edmund PicEdmund Harris (@Gelada): Edmund and I love comparing American & British education systems. (Dr. Harris is originally from Britain and now teaches at the University of Arkansas). This year, he was very hot on the treatment of homework in both countries. He insists that rather than it being either the traditional, boring rote or the new, mind-crushing, “common core” problems that end up on haters’ Facebook pages, that math homework should be a “joyful meditation.” I love this thought; now comes the challenge of making it happen for my students.

Edmund also is the Illustrator of a new book coming out, Patterns of the Universe, A Coloring Adventure in Math and Beauty. He is my go-to expert for anything that deals with Geometry, so I cannot wait until this book comes out. The preview below of his illustrations will get you just as excited.

“Homework should be joyful, meditation.” — Dr. Edmund Harris


TMC15 was a phenomenal four days at Harvey Mudd College in Claremont, California. TMC16 will be at Augsberg College in Minneapolis,MN, July 16 – 19. I can’t wait to reconvene with this crew, so that, as one participant shouted …

“My brain will explode with awesomeness!”

TMC Group

And just for kicks …

 

Common Core and The Land of Oz

Oz FourThe Common Core is a noble cause. Who would argue that teaching kids to think and communicate their thinking is anything but a virtuous goal? It’s like the Emerald City in the Land of Oz, and standing between us and that bright shining city is a Wicked Witch and a bunch of Flying Monkeys. We know how the movie ends, though; we will melt that witch and make it down the Yellow Brick Road.

I made this comparison for a news reporter after my keynote address at the Idaho State Math Conference last fall. My analogy made NPG News at the same time that my math coaching colleagues and I back at Temecula Valley Unified were developing a four-year plan for professional development and student support in our district. So we wove the Wizard of Oz theme into our plan.

It turned out to be more than a catchy metaphor. The theme is actually quite symbolic to the trials and potentials of rolling out the common core.

4 Year PlanLet’s begin with the Emerald City. The Common Core claims to teach students 21st Century skills. In our district, we have summed up those skills as the ability to “Think and Communicate.” This, then, is our noble cause, our shining city.

Along the Yellow Brick Road is the infamous Wicked Witch and her Flying Monkeys. Our number one issue for teachers in Year 1 of the roll out was the lack of resources, and therefore, the demand upon them to find and create their own curricula. We did not anticipate this phenomenon, but it quickly consumed our role as math coaches. Our first year will end (hopefully), with Units, Pacing Guides & Model Lessons in place, and with an infrastructure to share them among the 130 secondary teachers in our district. Since this is by far the biggest obstacle facing us, and the ugliest work to overcome, establishing the content, scope and sequence gets the tag as the Wicked Witch. In Year 2 (the first of the Flying Monkeys) our primary purpose is to change our method of first instruction. The Common Core is calling for radical shifts in how we teach as well as what we teach, so that will be the focus of Year 2. Year 3 then focuses on what to do for those students who don’t get it (Tier 2 intervention). Finally, while we continue with the work that we laid out in the first three years, Year 4 will emphasize enrichment for students who easily learn the material and on implementing student use of technology.

Reflection FrameWhile many of the obstacles listed above deal with the work of us math coaches, the work of the teachers is personified by the four main characters of Oz: Dorothy, Tin Man, Cowardly Lion and Scarecrow. Their training is structured around the four Essential Questions of a PLC (Professional Learning Community). Dorothy must go first, because she was all about direction (“There’s no place like home.”)  So she asks the question, “What do we want the students to know and be able to do?” The Common Core has defined this question very clearly for us, particularly when it comes to the Mathematical Practices. We summed up these practices on a Reflection Fame that we use to debrief with teachers after our elbow coaching sessions. Year 2 calls upon the Tin Man, because it takes a heart to care for those students who don’t get it, especially in secondary schools. We are now commissioned to deliver a “guaranteed and viable curriculum to ALL students.” Year 2 will focus then on Tier 1 interventions … reaching and teaching ‘those kids’ … within the classroom. In order to do this we must have formative assessment and data collection protocols in place to be able answer the question “How do we know if they know it?” The Lion personifies Year 3, because it will take Courage to deliver Tier 2 intervention in response to “What do we do when they don’t know it?” Then, to answer the question “What do we do when they do know it?,” the Scarecrow and his brain will be employed in Year 4, when all the mighty work of the first three years is in place, and we can focus on the needs of the advanced students and on teaching all students to Think with and Communicate through technology.

Finally, and most importantly, we turn our attention to the students results. These are personified by who else, but the Munchkins. We plan to establish Student Mile Markers. These will be Performance Task benchmarks that will be given each year with the Final Exams (but not necessarily counted in a grade) to be used as a gauge to our collective progress (that of students, teachers, coaches and administrators) down the Yellow Brick Road.

The Wizard of Oz gives us a nice frame to dialogue within, but it also offers an important lesson for all teachers. The Wizard gave Dorothy and her friends absolutely nothing, other than the realization that they already had inside each of them that which they had been seeking all along. As do we. Brains, Courage, a Heart, and a Direction Home.

Common Core Pathways: Redefining Algebra

PathwaysI have fielded a great many questions lately regarding the creation of Common Core Pathways (course sequences), especially in regards to the big question: to accelerate or not to accelerate. I appreciate the curiosity, because in this last year I did a great deal of investigating in order to help my school district develop our own pathways. I recently had a request to share our pathways “with commentary.” This makes sense, since there are many misconceptions of the Common Core out there that I had to sort through, and the rationale for these pathways will help others decide if these will work for their system. So I share four things:

1) A primer for the Common Core Pathways, particularly in terms of Algebra content.
2) The needs of my district that led to the development of three pathways.
3) The actual Pathways that my district decided upon, with links to resources that helped us get there.
4) Student placement.

I hope this helps.

A Common Core Pathways Primer

The Common Core spells out clearly what students are expected to know at each grade level K-8. Then for high school it lumps the standards together in High School Domains (Number & Quantity, Algebra, Geometry, Functions, Statistics & Probability and Modeling). This is done in order to allow high schools to structure courses in a Traditional Model (Algebra 1, Geometry, Algebra 2) or an Integrated Model (Math 1, 2, 3). At first glance it looks like CCSS is now delaying Algebra until 9th grade, after years of states pushing it in the 8th grade. This is because CCSS does not define Algebra as a course, but rather a domain across grade levels. Understanding this is key to creating accelerated pathways.

Traditionally, an Algebra course is seen as starting with the arithmetic (integers & fractions) and the simplifying of expressions (which many consider to be Pre-Algebra), followed by solving of equations, then moving onto linear equations and systems by the end of first semester, with polynomials, quadratics and rational expressions rounding out second semester. In other words, we go from balancing a check book to racing cars to launching rockets in a single year. However, the Core spreads these concepts out over several years. Arithmetic, simplifying and basic solving is mastered in 6th grade. Solving multi-step equations and deeply understanding rates and ratios is the focus of 7th grade. The 8th grade standards focus on linear equations and systems. While Geometry topics like surface area, volume and transformations are spread throughout the middle school grade levels, along with probability & statistics, the key here is to see that the entire first semester of a traditional algebra course is covered by the end of 8th grade. This way, the students can be handed an exponential function when they walk in the door on the first day of their freshman Algebra class. So don’t get it wrong; students under the common core are still learning Algebra in middle school; they are just not finishing it. The Common Core does not delay the Algebra course for students; it simply redefines Algebra.

No More Than 3, Sometimes 4

Tim Kanold once shared with me the pathways created at Stevenson HS in Illinois. He claimed that they had two pathways… one pathway led to Calculus, another to Pre-Calculus. It was actually one pathway: Algebra 1, Geometry, Algebra 2, Pre-Calculus, Calculus. What made this sequence look like two pathways was the course that students enrolled in as freshmen (Algebra 1 vs Geometry). Stevenson HS offered a ride on a single train; the only variation was which boxcar a student boarded when arriving at high school. I ask Tim if every student graduated with a minimum of Pre-Calculus. He said that while 58% of the seniors graduated with Calculus, some only took three years of math. When I pressed for the pathway offered for special education students and the like, he conceded that those rare few were allowed to deviate from the given path. He stated, “Create only 1 path, no more than 2, and sometimes 3.”

My district embraced this idea, but we have one more level of need. My high school has an International Baccalaureate (IB) Program. In order for students to be able to reach its “Higher Level,” we need some students to come into high school taking Algebra 2 as freshmen. Furthermore, while California only requires two years of math, my district requires three, and the state still only requires Algebra 1 to graduate, not Algebra 2. Therefore, students on an IEP may take Middle School math classes through our Special Education Department, and anyone passing Algebra 1 may take Accounting to complete the third year.

With all that, my district adopted a “No more than 3, sometimes 4,” policy. These  3+ pathways are shown below.

The Pathways for Temecula Valley Unified

Pathways Math

Our district decided to stick with our traditional model. The scope and sequence of our “Common Core Pathway” is very similar to what the Dana Center of Texas produced. We also took some inspiration from Montgomery Schools in Maryland (scroll to the bottom of their page, and you will see a graphic very similar to ours) and Tulare County in California which beautifully laid out the scope and sequence for both the traditional and integrated models.

The Traditional Pathway allows students to reach Pre-Calculus or other similar 4-year college options. There are two keys to notice here. One, there is no remedial track. All mainstreamed students will be taking Algebra and Geometry. This is freaking out teachers who are anticipating having a significant number of “those kids” in college prep classes. They have told me that the kids won’t be properly prepared. I pushed back claiming that the kids will be ready, but I am not sure we teachers will be ready. (side note: Professional development training is imperative to make this work.). The second key to notice is that there are two types of Algebra 2 courses. Our Pre AP course was designed with the Common Core plus standards (+) included, for those students who intend to go beyond Calculus AB (Calculus BC or IB). For details on other courses shown in the diagram visit the Math Department at Great Oak High School.

The Accelerated Pathway was an easy adjustment. If we note the definition of Algebra explained above, then in 8th grade we teach a traditional Algebra course, substituting the Geometry and Stats topics for the Pre-Algebra topics. 6th and 7th grade remain untouched. Two years of math is condensed into one.

The Compacted Pathway was a bit trickier to create. In the past, students who wanted to take Geometry as 8th graders, simply skipped 6th grade math and got to Algebra 1 by 7th grade. That’s no so easily done now under the Common Core. So we have to compress 4 years of courses (6th, 7th, Algebra & Geometry) into 3 years as shown.

NOTE: Now that we have implemented these three pathways, I would only recommend the first two. Unfortunately, the Compacted Pathway is too much for both students and teachers. Since our high schools still need a means for students to reach Calculus B/C and beyond, it appears best to have that relatively small and uniquely talented population to accelerate in high school, through summer school, online options or Junior College courses.

Choosing a Pathway

The big question that follows after creating these pathways is “Which students are assigned which pathway?”  Or more to the point “Who gets to Accelerate?” We actually would like to see the majority of students follow the Traditional Pathway. For our upper level high school math programs to thrive, we need at least 20% of the middle school students on the Accelerated Pathway, and a little under 10% for the Compacted. Of course, we shouldn’t fit students to the needs of the school. The students are to be recommended by ability based on assessments and teacher recommendations. Our schools need to be watchful, though, because our community has parents who feel their child won’t be able to compete for a top college if they are in the bottom track. While some vigilance will be necessary, we also have an open access policy… students/parents may take any courses they wish. I am curious how these pathways portion out.

Furthermore on placement, another of Stevenson High’s policies that my district is adopting next year is the practice of moving students onto the next course … even if they flunk. I have also heard this same pitch from Bill Lombard. So, if a student flunks Algebra, the student enrolls in Geometry the following year, and makes up the class in summer school, online remediation or concurrently. Same thing is true when going from Geometry to Algebra 2. However, if a student fails Algebra 2, they may repeat, since these students have multiple options at this level (Trig, Stats, PreCalc, etc.). Needless to say, our teachers have a great deal to get done in terms of Intervention and Standards Based Grading to make this work.

I hope this helps those of you that are planning ahead. My district and its teachers still have a great deal of work ahead of us, so please share here what you learn in the construction of your own pathways.