Tag Archives: Common Core

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.


A “JUST ENOUGH” APPROACH TO INTERVENTION (Session)
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.


KEYNOTE: RACE, MATH AND WHAT WE’RE NOT TALKING ABOUT
Jose Vilson (@TheJLV)JoseV
educolor.org

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.


AudreySTUDENT-CREATED GEOGEBRAS
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


WHAT IS MATHEMATICAL MODELING?
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.


THE SIDE TALKS
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
 (@ddmeyer):
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: 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!

A Call to Substance, First Interview with Dr. William Schmidt

Schmidt BookcaseIn March of 1998, during the inaugural year of The Math Projects Journal, we had the unique opportunity to publish our interview with Dr. William H. Schmidt, of the University of Michigan. At the time, Dr. Schmidt was the National Research Coordinator and Executive Director of the U.S. National Center which oversaw participation of the United States in TIMSS. The results of the TIMSS report directly led to the developement of the Common Core 20 years later, which is why Dr. Schmidt is nicknamed “the Godfather of the Common Core.” He is also widely published in both journals and books on mathematics education.

We had the opportunity to interview Dr. Schmidt again about the rollout of the new curriculum. Before we post the current interview, we thought it would be valuable to reprint what Dr. Schmidt had to say in the early years of the research. He emphasized focusing instruction on conceptually understanding and higher order thinking skills, rather than on methodology. This is an important message now more than ever with so many untested techniques and ideologies being promoted widely on the internet. This message heavily influenced the trajectory of MPJ‘s lessons and my own classroom teaching. I hope it does the same for yours.
*************

MPJ: Can you give an example of a model lesson from one of the top achieving countries, either Germany or Japan, which are the focus of the videos?

Dr. Schmidt: If you look around the world, there just isn’t a single way to teach that is dominate among the top achieving countries. Some of them are very didactic, lecture-oriented classes. Some of them are like the kind that you see in the Japanese tapes. If teachers know their mathematics well, they can be just as engaging through a lecture format, as they can teaching as the Japanese do. It is very clear to me that there isn’t one way to do this. Instead, the more analysis that I do, the more I believe that there are some principles involved here that just might go across countries.

MPJ: What is the common thread?

Dr. Schmidt: I think the common thread that makes for the top-achieving countries is pure, honest-to-goodness mathematical substance. If the teachers really know and understand the mathematics, then they bring that to the students, through whatever means they know best. Also, a large part of this idea is to develop this stuff conceptually and not just algorithmically. I think many people misunderstand the Japanese videos. It is not so much the methodology, as it is the mathematics. You watch those lessons and the instructor really understands the mathematics, engaging those students in more ways than we do in this country.

MPJ: So, if a teacher were to do a dog-n-pony show lecture with drill-n-kill practice, and do it well, would it work?

Dr. Schmidt: The dog-n-pony show lecture, yes; the drill-n-kill, no. That’s what I said about there being some principles. I think the common element is a clear understanding of the subject matter and then going through it much more conceptually than algorithmically.

MPJ: Can you give us a model to how to teach math conceptually rather than algorithmically?

Dr. Schmidt: A U.S. lesson typically starts out with the algorithm. For instance, there is the example in the videos of a guy teaching geometry. He says to the kids, “Here are two supplementary angles, one is thirty, how much is the other?” A student says, “a hundred and fifty.” And the teacher says “Good, now why is it that?” And her response is, “Because they are supplementary.”

Instead, conceptually, you could show them that if they measure a straight line, it’s always one hundred and eighty degrees. Then they realize that if they put a line anywhere its going to cut it into two parts. That’s conceptual; you start with understanding why, so if you forget the stupid name, supplementary, and you see a line with an angle you’ll know what the other one is. That’s the difference.

MPJ: How is a strong conceptual understanding of the mathematics developed among teachers?

Dr. Schmidt: It comes from two sources. In some countries, they must major in these fields. The other thing we don’t think about is that they are products of their own systems. For instance, Japanese teachers don’t necessarily take more mathematics at the university level than we do. But look at what they already know before going to the university. They are already ahead.

MPJ: In regard to the things that our readership is looking at, active learning, projects, manipulatives, do you have any models from these other countries, or that you think could be done here?

Dr. Schmidt: You don’t find very much of that anywhere else. They seem to be uniquely American inventions, especially the cooperative learning. We asked teachers how much they use groups, and it’s pretty much nonexistent. We are too much into the methodology in this country, and we miss the substance. We start talking about small groups and manipulatives and it just becomes process. Therefore, the substance behind it gets lost in the shuffle. And for a lot of these ill-prepared teachers, that’s what they grab onto because that’s what they understand.

MPJ: We hear that the US teachers assign more homework and spend more class time dealing with homework than the top achieving countries.

Dr. Schmidt: The dominate activities in the U.S. lessons were reviewing homework and doing seat work. One thing that was startling is that the typical American lesson had only 10 minutes or less of instruction.

MPJ: What role does homework play in other countries?

Dr. Schmidt: It varies a lot. Japan doesn’t give a lot of homework, but the kids study for the next lesson. There’s a difference, of course. Studying is what you do at the university, and homework is what you do in grade school. But Japan is unique. Worldwide, homework and seat work are still the dominate activities. I think if you do that and you do it well, and develop the topics conceptually, it can work.

MPJ: Is this a curriculum issue instead?

Dr. Schmidt: It is the core issue, but just putting that in place by itself wouldn’t work. You have to help teachers teach in ways that engage kids.

MPJ: So, that is something that teachers could start doing today. We could focus on engaging students and developing topics conceptually?

Dr. Schmidt: That is my point. We must start paying much more attention to the subject matter and teach it more conceptually and less algorithmically. And that is why we are in a catch-22. The Japanese teachers grew up in their system seeing math developed conceptually, no matter what they learned at the university level. For our teachers it is a lot more difficult; they have to break out of a mold that they’ve been put into. But I think that is something that teachers can do — Get off the algorithmic side. Don’t just give an equation and when a kid asks why say, “Because that’s the equation.” Try to get them to understand what lies underneath some of this stuff.

MPJ: It seems that, chronologically, you are suggesting a lesson should move from concept to algorithm to application.

Dr. Schmidt: A lot of the lessons that we’ve seen, like in France and such, start out with an application as a motivator. An example is a science one about transformers. They started out by looking at a map of the city and looking how electricity would flow. This got them hooked on the issue, then they hit them with some good hard science about the transformer. That’s very often how it happens: hook them with some kind of application, then take them into it conceptually, let them flounder — that’s where I think what the Japanese do is a good idea — let them talk about some of their ideas, then give them an algorithm, a formula and a few examples. Whereas we typically start with the formula with a few sentences about it, and then have them do worksheets.

MPJ: The report states that American textbooks cover too many topics, yet they typically have only fifteen chapters.

Dr. Schmidt: That is mistaking the notion of what a topic is. The definition of topic has to do with the substance of the mathematics, and when we defined it that way, the measurement across all these topics is not how many chapters are in each book.

MPJ: Can you give us an example of four or five topics?

Dr. Schmidt: Congruence and similarity, three-dimensional geometry, linear equations, and fractions. We actually tested 44 topics and determined how many of these topics were in any given textbook. Our 700 page books address about 35 topics. The Japanese, on the other hand, spend half of the eighth grade year on congruence and similarity alone, and their gain in that year is higher than in any other country. The dilemma I have in telling you what to do is that the teacher shouldn’t decide which five to ten topics should be studied in a year. It only works if somebody coherently lays this thing out as to what needs to be done.

MPJ: Do you have any last things to add?

Dr. Schmidt: People still think that there are general things a teacher should do, like cooperative learning. That’s what people push. We push all the things that have nothing to do with subject matter. I’d like to challenge the notion that there is a single way to do things. If you listen to the ideological left, they say that there is only one way to teach. And the data just do not support that. Among the top achieving countries you cannot find one dominate way of teaching. On the other hand, the ideological right are calling for “the basics.” Yet, the latest analysis shows that the United States, through 8th grade, does average or above average in all the standard arithmetic skills. This is not the place were we are hurting the most. That is all we teach. That is what’s wrong, we never go beyond the basics.

If I wanted to become rich and be an advisor to schools to jack their scores up, I know how to do it. We have certain areas of math that we have the international comparisons on. I can tell you the seven items that we are the weakest on, and if schools just did something in those areas, we’d go up in the international rankings. None of those areas is anything that we would consider the basics.

MPJ: What are those area of weakness?

Dr. Schmidt: Measurement, error analysis, geometric shapes, perimeter, area and volume, congruence, similarity, vectors, geometric transformations, and three-dimensional geometry. These are not the basics.

MPJ: Tomorrow, our readers will not be able to change the textbooks or create national standards. What can a teacher do in the classroom today that will model the type of change that you and the TIMSS report call for?

Dr. Schmidt: That’s a tough question, because most of what I have argued is, based on the data, these really are systemic issues. However, the data also shows that how we teach is as important as what we teach. Teachers should challenge students with more mathematical substance and develop the ideas more conceptually rather than algorithmically.

Get to the Core of The Core

apple coreThe Common Core curriculum can basically be summed up in the following sentence:

Teach your students to THINK and COMMUNICATE their thinking.

Thinking and communicating are the 21st Century skills. Many people believe that the skills of the future involve the competent use of technology. While it is true that using digital tools in school and the work place is the new reality, it is actually the proliferation of technology that makes thinking and communicating imperative in the information age. When all the knowledge of humankind is available at anyone’s fingertips, memorizing information becomes far less important than being able to construct, evaluate and apply it. You can Google information; you cannot Google thinking.

So the core of the Core truly is Thinking & Communicating.

To make my case for this, I would like to pose that the following equation

6 + 4 + 4 + 8 = 22

be adjusted to

6 + 4 + 4 + 8 = 21

Before you start shouting that everything you have read on Facebook about the Common Core is true, let me declare that I am using this equation simply as a teaching device, not a true mathematical statement. You will understand what I mean after I present my evidence.

6 Shifts

Let me start my case that the core of the Core is Thinking & Communicating with the 6 Shifts, which are best represented by the following document found at Engage NY.

6 Shifts

In essence, these shifts are redefining rigor. Old school rigor was defined as sitting quietly taking notes, and completing long homework assignments in isolation. The new school definition of rigor envelops the last 4 shifts on the list: Fluency, Deep Understanding, Applications, and Dual Intensity. The rigor is now placed on the students’ minds instead of on their behinds.

The shifts are also calling for balance. Dual Intensity insists on both procedural fluency AND critical thinking by the students at a high level. It is not about dual mediocrity or about throwing the old out for the new, but a rich coupling of both mechanics and problem solving.

Therefore, I make the case that:
                     6 Shifts = 21st Century Skills,
which are to
                     Think & Communicate.

4 C’s

Another list that is framing much of the Common Core dialoge is the 4 C’s. Resources for this list can be found at Partnership for 21st Century Learning (p21.org).

4 C'sThese C’s redefine school…

The old school definition: A place where young people go to watch old people work.

The new school definition: A place where old people go to teach young people to think.

… and they redefine learning.

The difference of old school vs new school learning can best be contrasted by the following images of the brain.

Brain Chillin   Brain Build

The image on the left shows a passive brain that just hangs out as we stuff it with esoteric trivia. The image on the right shows a brain being built, symbolizing its plasticity. We now know that when the brain learns, its neurons make new connection with each other. In other words, learning literally builds the brain. The 4 C’s  claim that this building involves the capacity of the students’ brains to Critically Think, Communicate, Create and Collaborate.

Therefore, I make the case that:
                     4 C’s = 21st Century Skills
which are to
                     Think & Communicate.

4 Claims

Smarter Balance creates it’s assessments based on 4 Claims. (I teach in California. PARCC has 4 Claims that closely align to those of SBAC.)

SBAC

4 Claims

Notice that Claims #2 & 3 are explicitly stated as Thinking & Communicating, which also overlaps with two of the 4 C’s. Mathematical modeling is #4, which will be discussed later. I want to point out here that Claim #1 reinforces our idea of Dual Intensity from the 6 shifts.

There are two important notes for teachers about this first claim. 1) It says Concepts and Procedures, not just procedures. The students need to know the why not just the how. 2) The Procedures alone account for about 30% of the new state tests, so if we continue to teach as has been traditionally done in America, we will fail to prepare our students for the other 70% of the exam which will assess their conceptual understanding as well as their abilities in problem solving, communicating and modeling.

Therefore, I make the case that:
                     4 Claims = 21st Century Skills
which are to
                     Think & Communicate.

8 Practices

If you open the Common Core Standards for Mathematics, the first two pages of the beastly document contain a detailed description of the Standards of Mathematical Practice. Then at the beginning of each of the grade level sections for the Standards of Content you will find 8 Practices summarized in the grey box shown below.
8 practicesWhat do you notice about the list? Indeed, these habits of mind all involve Thinking & Communicating. While the content standards change with each new grade level, the practice standards do not. With each year of school the students are expected to get better at these 8 Practices. Notice that the first half of the list has already been included in the ones discussed previously: Problem Solving, Communicating Reasoning, Constructing Viable Arguments and Modeling. A case is often made that the other four are embedded in these first four. However one might interpret the list, “Memorize and Regurgitate” is not on there.

Therefore, I make the case that:
                     8 Practices = 21st Century Skills
which are to
                     Think & Communicate.

The Sum of the Numbers

So, as you can now see, the 6 Shifts, the 4 C’s, the 4 Claims and the 8 Practices are all focused on the 21st Century Skills of Thinking & Communicating. Therefore, I can finally, explain my new equation …

Since,

    6 Shifts
    4 C’s
    4 Claims
+  8 Practices
= 21st Century Skills

then 6 + 4 + 4 + 8 = 21!

None of these numbers represents a list of content, because the content changes brought on by the Common Core, while significant, are actually no big deal in the long run. A few years from now we won’t remember all the fuss regarding Statistics and Transformations, but we will all spend the rest of our careers learning how to teach kids to Think & Communicate.

I rest my case.

SMP Posters by MPJ

SMP Posters Pic 2_Page_8I created my own posters for the Common Core Standards of Mathematical Practices. I combined the best from what I found from others and added my own structure. Necessity dictated my doing this for two reasons: 1) I wanted to respect others’ copyrights, and 2) I couldn’t find any that were appealing to secondary students.

With that said, I offer MPJ’s SMP Posters for use in the classroom. (For JPEGs, click images below.) Each poster here has the following features:

The summary of the Practice straight from the Common Core documents, as listed in that famous grey box

SMP Posters Pic 1

The verbage of the Practice written in kid-friendly, first person language

SMP Posters Pic 2

A single word that embodies the particular practice

SMP Posters Pic 3

A diagram that displays an application of the practice, using Algebra as an example so as to span both middle and high school

SMP Posters Pic 4

A group of words that relate

SMP Posters Pic 5

A list of questions that pertain

SMP Posters Pic 6

A clip art image of a high school student to drive home the point that the practices are for them and not the teacher

SMP Posters Pic 7

An instructive statement that includes the word “Think”

SMP Posters Pic 8

A special shout out goes to the Jordan School District’s SMP posters for elementary schools which were the initial inspiration for this set. Other sources include: Eastern Bristol High School and Carroll County.

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.

Graph of the Week (New Site)

Kelly teensI am getting the word out on this awesome site: Turner’s Graph of the Week. My friend Kelly Turner did a presentation at the Great San Diego Math Conference last spring and I loved her idea of having students analyze graphs from magazines and newspapers. These are mostly one-quadrant graphs with a natural context. This ties in directly to the Common Core’s call for applications and for reading non-fictional text. I was so impressed that I encouraged her to go public with the idea. I am serving as her megaphone.

Kelly does this activity once a week with her students, thus the name. The site offers several features:

    • Graphs. You don’t have to find your own. Kelly has already posted 12, and will post more on the GOWS page of the site as the school year progresses.
    • Submissions. If you like the activity and have graphs of your own that would serve others, email them to turner_k@auhsd.us. Kelly will screen the submissions and build the online collection.
    • Templates.  There is a generic worksheet template with writing prompts to guide students in reading, interpreting and analyzing the graphs.
    • Samples. On the home page Kelly will offer the graph that she is currently using for the week. Directly below that will be a student sample of the previous week’s graph.

Try it. If you like it, share with your colleagues. The same graph can be used at multiple course levels, with the level of questioning being adjusted to the level of students.

Kelly thanks for all the work on this. You have made teachers’ work easier and students’ education better.

TMC13 Session Recaps

TMC DrexelIn my last post, I summarized the overall experience of Twitter Math Camp 2013 at Drexel University. Following is my recap of the sessions that I attended. This conference was unique in that I learned something significant in each session.

Geometry Break-Out #1, Megan Hayes-Golding @mgolding, GA & Tina Cardone @crstn85, MA

After the opening greeting, the first morning session was a choice of break-outs according to course (Algebra 1, Geometry, Stats etc). These were intended to be open-ended discussion/work sessions. In the Geometry session, there was an overwhelming need by the group to wrap their heads around the Common Core Geometry Standards. Megan & Tina wisely went with the flow, and had us jigsaw the standards in pairs and share out. It was enormously helpful for everyone. I was already very familiar with the standards, but I still learned something about the CC standards on constructions. Specifically, the standards not only call for the four basic constructions plus those involving parallel and perpendicular lines, but the students are expected to construct a square, equilateral triangle, and hexagon as well. This was time well spent, with the bonus of getting to know Edmund Harriss @Gelada, Jessica @algebrainiac1 and StephReilly @reilly1041.

Edmund ArtThrough out the weekend, I had extended conversations with Edmund from which I learned a great deal. Mostly because Edmund is a math professor and as he spoke of his work with the mathematics of tiling patterns, I felt my IQ rise just by listening to him. Much of our discussions centered around the American education, though. Edmund had an interesting perspective, because while he teaches at the University of Arkansas and also leads special math programs for gifted children, Edmund is British. From that experience, he had a great deal to share about “how to run standards based education correctly.” I hope he blogs about that soon.

“I Notice & I Wonder,” Max Ray @maxmathforum, PA

Max Ray is the “Professional Collaboration Facilitator” at the Math Forum at Drexel. In essence, he teaches teachers how to teach problem-solving. I had heard before of starting lessons with “What do you notice? What do you wonder?” This phrase, which was originated by Annie Fetter @MFAnnie, is intended to initiate student thinking on a rich and robust task. That seemed pretty simple, so I wasn’t anticipating much new learning here … Boy, was I wrong! Max started with a picture of 3 glasses and the phrase “What do you notice? What do you wonder?”

TMC glasses      TMC graphs

We were asked to ponder for a moment, then share our thoughts with our neighbors. (Think-Pair-Share).  “I notice they have different shapes. I wonder if they have the same volume. What kind of drinks go in each one?” Then he posted the picture of 4 graphs, and again posed the same questions: “What do you notice? What do you wonder?” The ensuing discussion resulted in everything from “I notice the graphs are different colors” to “I wonder if the graphs correlate with the filling of the glasses.” The thing that I noticed about this whole activity is that Max let us mull this over without offering a single number or formula. Nor did he offer a single answer to any of our wonderings. Two pictures and two questions occupied us for 15 minutes. In the era of rushing through content it was wonderful to be reminded that mathematics starts with an observation and a question. Speaking of questions, my group wondered what glass shape would correlate to the fourth graph… while Max stood at the front of room silently smiling.

“Practicing the 5 Practices,” Christopher Danielson @Trianglemancsd, MN

Christopher Danielson is a professor of mathematics at Normandale Community College and also teaches methods courses for elementary school teachers. He shared the research published in Five Practices for Orchestrating Productive Mathematics Discussions. In summary, the 5 Practices are:

5 Practices PicAnticipating, during planning, student responses to the lesson prompt
Monitoring students repsonses during the lesson activity
Selecting which student responses are to be discussed publicly
Sequencing those student responses chosen
Connecting the responses to each other and to the mathematical ideas

Chris emphasized that the first and last of these are the two most troublesome for teachers. Chris modeled all these principles by conducting a math lesson on fractions. He knew what the issues would be with the context. He called us specifically by name to present our responses in an order that allowed the discussion to develop from simple ideas to more complex. I was particularly impressed on how he asked us to compare and contrast the various strategies. This is where I personally saw that I needed to bolster my own efforts on connecting ideas in own my class discussions. I walked away with the understanding that while any class discussion is better than none, there truly is an art form to doing class discussion right.

“5 Ways to Boost Engagement,” John Berray, @johnberray, CA

I have to say that the number one way to boost engagement is to teach like John Berray. The joy that he has for the material and for his students was just bursting out of him. With that said, John had 5 other ideas on increasing engagement:

1) Turn the Mundane on its ear
2) Jump on the timely
3) Bring in the outside world
4) Unlikely objects arouse wonder
5) Spill some paint

Translation: 1) Make it fun, 2)Tie math to current events, 3) Use the internet, particularly video, 4) Be goofy, 5) Connect the material to kid’s lives.

The highlight of the session was John showing how to make a textbook problem more exciting (a textbook makeover). The sample problem asked how many ways are there to take a 10-question true-false test (assuming all 10 question are answered). John asked us, “Who wants a shot at the glory?” and offered $5 to anyone who can match his answer key exactly. We were all prompted to number our papers #1-10 and choose T or F randomly for each. Once we all had our answers to this hypothetical 10-question True-False quiz, we were all asked to stand up. He began to display 10 questions, one at a time, about the participants at the conference. This offered humor and another level of engagement, as we were all trying to guess correctly, even though we had predetermined answers. After the first answer was revealed, all those who answered wrong on the paper had to sit down. We were asked to notice how many were still standing. This routine continued as we went through the entire list. Nobody won. The obvious question is, “How many people would we have to do this with in order to expect a winner?” He had just turned the mundane on its ear.

Geometry Break-Out #2

Our group reconvened with a few new people joining in. It was especially nice to See Peg Cagle @pegcagle after so many years. While the first day was a working session, this day was all about discussion. The group really wanted to talk about how to teach all the standards we listed in the previous sessions, while instilling the CCSS Practices. Teachers shared their various ideas, experiences and techniques. There was also a question on grading practices that revealed the dark side of the MathTwitterBlogosphere … We can be a very opinionated bunch. The hot topic for us was standards based grading. This turned out to be a benefit to the new teachers in the room or to old teachers with open minds, because quite a variety of ideas and positions were shared. It was an engrossing conversation, because no matter the positions taken, they were all shared with a passion for teaching students rich mathematics. The end of session came way to soon.

“Still Keeping it Real,” Karim Kai Ani & Team Mathalicious, @Mathalicious, VA

Mathalicious offers engaging, innovative math lessons with a focus on “real-world” applications. Karim @karimkai led us through two Mathalicious lessons that were solidly based in mathematics and loads of fun. The first, Datelines, tied the age of potential dates to systems of inequalities. The age gap on a date becomes less of an issue as people get older. For example, a 24-year old dating a 20-year old is less awkward than the 20-year old dating a 16-year old. This is an engaging topic for teenagers that Mathalicious sets to a graph and poses critical questions according to a given rule on dating ages. Like I said … solid. The second lesson, Prisn, used Venn diagrams to analyze the probability of being wrongfully flagged by the governments PRISM program for mining data. This lesson was about as relevant as any can get. It allowed for rich non-partisan conversation on how much error the public will accept. As I told Karim, these lessons are sexy, but have a lot of substance. At the conclusion, he generously gave the TMC participants a free trial subscription to Mathalicious. I intend on checking out more of their work.

“Getting Students to Think Mathematically in Cooperative Groups,” Lani horn, @tchmathculture, TN

Ilani BookThis one was very special for me, because Dr. Ilana Horn was such an influence on the teacher collaboration model that we have implemented at my high school for the last 9 years. Back in 2004, I was about to be the Math Department Chair for a new high school and was speaking with Jo Boaler about collab models for teachers. She told me that the person to contact was Lani Horn at the University of Washington (She is now at Vanderbilt in Tennessee). A week later, I happened to be vacationing in Seattle, and Lani was kind enough to give up time to a stranger and talk about her doctoral research. She was gracious as well as knowledgeable.

So I was excited to see her again and share how her information helped lead my crew back home to be one of the highest performing schools in the county. She was pleased to hear the news. Her session this time was on student rather than teacher collaboration. The specific model she shared is known as Complex Instruction (CI), in which students are grouped heterogeneously, with intentional methods to have all students participate. The focus of Lani’s session was on how academic status affects student engagement during group work. She was very intentional in telling us that participation is hindered by this perceived status about smartness, which is too often defined in math class as “quick and accurate.” To help make it safe for everyone to participate, the teacher needs to redefine smartness by acknowledging and rewarding “good questions, making connections, representing ideas clearly, explaining logically, or extending an idea.” Lani shared a video of a group of students working on a math problem, and asked us our thoughts regarding each students level of participation. She also asked us to analyze the teachers interaction and prompted us for alternative responses. This analysis of the work done by each student debunked the conventional wisdom that non-participatory children are lazy, stupid or shy. I had learned as much from Lani Horn on this day as I did in our first encounter.

Due to another engagement, I had to fly home early from the conference so I did not get a chance to attend the last session on Friday or any on Saturday. I heard I missed some great stuff,  which I don’t doubt.

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.

Tiger Woods Gets a C- in Golf

Tiger SsshhMy district is seriously looking into standards-based grading. I have dabbled in it and see both the value and the pitfalls. Interestingly, I wrote the article below in 2002, long before SBG came into vogue and before the Common Core started flirting with Performance Tasks. While Tiger may not be the top golfer in the world anymore, it speaks directly to my hopes and concerns. I invite some push back here from the SBG gurus.

***********************************************************
Earl Woods? Hello sir, thank you for coming to my classroom to speak with me about your son Tiger. Yes sir, I know that he appears to be doing well at home, but Mr. Woods, to be honest with you, Tiger is in danger of failing golf.

Currently his grade is a C-. I can show you the grade breakdown if you like. Certainly. As you know, there are approximately two hundred professional golfers. Each is ranked in various skill categories. Your son, Tiger, ranks as follows.

Driving Distance 2nd
Driving Accuracy 72nd
Greens in Regulation 1st
Putting Avg. 159th
Eagles 132nd
Birdies 2nd
Scoring Avg. 1st
Sand Save Avg. 4th

As you can see, Tiger does very well in most skill categories, but appears to perform poorly in two. Now, failing in two out of the eight leaves him with a score of 75%. There is a third category in which he is only slightly above average; therefore, he only gets partial credit. This diminishes his seventy-five percent to a 70%, and thus, he gets a C-.

My concern is that if Tiger were to falter in any one of these eight categories, he would surely fail golf. However, there is plenty of room for him to improve in these problem areas. He has an excellent work ethic, so I am confident that with a little more effort, Tiger will succeed. Mr. Woods, thank you for your support in this matter.

Can you imagine ever having this conversation regarding Tiger Wood’s ability as a golfer? How does the best golfer in the world get a near failing grade in golf? The answer is in the assessment.

The rankings given in the previous scenario are true. Furthermore, from this list, the All-Around Rankings of each professional golfer is determined by adding the golfer’s relative rank in each category. The lower the score, the better. Adding Tiger’s categorical rankings places him 10th in the “All-Around Rankings.”

In other words, there supposedly are  nine other golfers in the world better skilled than Tiger Woods. Being in the top five percent of all golfers in the overall skill category would certainly raise his grade in golf to at least a B, if not an A. However, he still does not rank as the top All-Around player in the world.

If we change the assessment, though, Tiger fares much better. For instance, Tiger is the richest golfer in the world. He is number on in season earnings and is the all-time career money winner. His is also number one in the World Rankings. The World Rankings are based on how well a golfer finishes in tournament play in comparison with the strength of the field. In other words, how well does the golfer compete?

Tiger Trophy

Tiger wins the most tournaments and wins the most money. In my mind, and that of many others, that makes Tiger the bets golfer n the world. Yet, I am basing my opinion on his performance as a golfer rather than his skill as a golfer. Analyzing two other golfers can show the difference between the value of skill and that of performance. Do the names Cameron Beckman or John Huston ring a bell to you? No? Me, neither, and I am an avid golf fan. The reason that you do not know these names is that these two people are average golfers in the World Rankings. (They don’t win much.)  Yet, they both outrank Tiger in the All-Around (2nd and 9th respectively). According to certain forms of assessment, Beckman and Huston are better than Tiger Woods.

Beckman Q2

We can see this scenario being played out in our classrooms. The Beckmans and Hustons get higher grades than the Tiger Woods, because too much of our assessment is based on individual skill rather than on mathematical ability. The Tigers excel in the performance assessments that we occasionally offer, but these are so out weighed by itemized tests that the All-Around Ranking (skill) wins out over the World Ranking (performance),

A more appropriate balance of skills, testing and performance assessment in our classes may send our most underachieving mathematicians to the head of the class.