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Hidden Figures’ Lessons for the Classroom

hf-all-threeEveryone in the theater applauded as the credits rolled at the end of the movie, Hidden Figures, and for good reason. It is an amazing, humorous, educational, inspiring and important movie. It is a film that every educator and math student should see. This true story of the contribution of three black women to NASA’s launching of John Glenn into orbit is full of so many positive messages about math, science, patriotism and social justice that I am compelled to share my perspective as a high school math teacher.  Here are my reflections from this incredible movie.

On Math
Math is More Than Computing.
Yes, a team of nearly twenty African-American women was known as “the computers,” because in the days before calculators, computation was done by hand. However, the movies’ three protagonists, Katherine Johnson, Dorothy Vaughn and Mary Jackson, were all given assignments for which the math went far beyond simple computation. They had to visualize geometrically, draw graphs, generate equations, assign units, assess another’s work, creatively program and, yes, solve lots of problems. Much of the work that was glorified in the movie was the application of mathematics, not calculation with mathematics. In fact, the director the Space Task Group, Al Harrison insisted:

“This isn’t about plugging in numbers, this is about inventing the math.”

Intellectual work is valuable.
Several times in the movie there was reference made to the “work” done by the various NASA personnel.

Dorothy reference the number of people needed to run the new IBM:  “We’re going to need a lot of manpower to program that beast. I can’t do it alone. My gals are ready. They can do the work.” *

Al Harrison in response to a politician’s inquiry: “That’s the math we don’t have yet, gentlemen. We’re working on it.”

Ruth (Katherine’s colleague) on Katherine’s last day on the Space Task Group: “You did good work around here.”

Al Harrison after John Glenn was returned safely to earth: “Nice work, Katherine.”

Dorothy instructing the other women in reference to Katherine re-computing John Glenn’s critical re-entry coordinates: “Alright, give her space. Let her work.”

hf-workThe work referenced here is the kind of work that educators are called to teach in the 21st Century classroom. We math teachers are currently implored to replace meaningless busy work with relevant intellectual work.

Math put humans into space.
Katherine upon being questioned about how she knows that one type of rocket is needed over another:

“What’s there tells the story if you read between the lines. The distance from launch to orbit is known. The Redstone mass is known. The hf-mathMercury Capsule weight is known. And the speeds are there in the data…. The numbers don’t lie.”

That says it all.

The movie got the math and the science right.
Hollywood has a track record for flunking math and science in movies, however, in this one, they earn a stellar score.

Katherine as an 8-year old child prodigy: “If the product of two terms is zero, then common sense says at least one of the two terms has to be zero to start with. So, if you move all the terms over to one side, you can put the quadratics into a form that can be factored, allowing that side of the equation to equal zero. Once you’ve done that, it’s pretty straight-forward from there…”

Stafford: “The Atlas Rocket can push us into orbit. It goes up. Delivers the capsule into an elliptical orbit. Earth’s gravity keeps pulling it, but it’s going so fast that it keeps missing the Earth – that’s how it stays in orbit.”

A+, Hollywood.

On Math Education
All need to be encouraged to check their work.
When Katherine Johnson was asked by her new boss to check the work of the lead engineer, Paul Stafford, Mr. Stafford balked. In response to his objection, Harrison gave a speech about the importance of the task, and that no one is above having his or her work checked.

“Do I need to remind everyone…that we are putting a human on top of a missile and shooting him into space? It’s never been done before. And because it’s never been done … everything we do between now and then is going to matter: it’s going to matter to their wives, their kids, I believe it’s going to matter to the whole damn country. So this Space Task Group will be as advertised. And America’s greatest engineering and scientific minds will not have a problem with having their work checked.”

al-h-2

Yes, those engineers had to check their work because the boss said so, but the boss also gave them the reason why… because getting the answer right is important. If NASA engineers needed to be reminded of this on occasion, then so do our math students.

Much of the math that launched John Glenn into space is taught in high school.
Yes, the characters in the movie mentioned things like the Frenet Frame and the Gram-Schmidt, but many of the terms used and the equations shown in various scenes would be recognized by students in high school math classes across America.

Paul Stafford: “We need to move from an elliptical orbit to a parabolic path.”hf-paul

Katherine: “On any given day, I analyze the manometer levels for air displacement, friction and velocity and compute over 10,000 calculations by cosine, square root and lately Analytic Geometry.”

Our math students should know that they are actually learning rocket science!

There is opportunity for everyone in STEM fields. (Science, Technology, Engineering and Mathematics)
The three women portrayed in Hidden Figures were specialists in three different STEM fields: Mathematics, Engineering, and Programming. These are all fields in which we have a shortage of American citizens earning a degree, to the point that much of the classified work in this country is being done by people who have citizenship from other countries. The STEM community sees this as an issue and would very much like to see more Americans pursuing careers in these fields. With the typical STEM job offering twice the annual earning of a non-STEM job, there is a huge opportunity for economic advancement for low-income students entering these vocations.  If they are not choosing this on their own, then we educators should be doing more to encourage and support their election of these endeavors.

On Equity
The oppressed are not victims.
Hidden Figures is very much a story about victory over oppression, not victims of oppression. The victory was achieved by the heroines changing themselves, changing others, and changing the system…

In order to adapt to economic change, we must improve ourselves.
When Dorothy Vaughn finds out that the new IBM computing machine means that the human computers will be obsolete, she not only makes moves to position herself well in the new age of computers, she encourages her friends to do the same.

“It’s not going to matter soon. This IBM’s going to put us all out of work… Only one thing to do: learn all we can. Make ourselves valuable. Somewhere down the line a human being’s going to have to hit the buttons… We have to know how to program it. Unless you’d rather be out of a job?”

hf-women-computers

Dorothy then goes to the public library and checks out a book on Fortran (one of the original programming languages). She even reads it aloud to her sons on the bus, as a mother’s lesson in overcoming adversity.

This message is extremely relevant in the political climate today. Many jobs are being lost to automation and changes in the global economy. The promise of today’s politicians to “bring those jobs back,” is equivalent to thinking that the emergence of the information age, represented in the film by the IBM machine, could have been prevented in order to maintain the human computing jobs. It is equally as silly to think that anyone today can stop the evolution of the job market. Instead, we educators should be teaching students, and ourselves, to do as Dorothy did, and adapt to the new 21st Century economic environment.

They were strong women not just smart women.
These three women were more than simply a mathematician, engineer and programmer; they were wives, mothers and daughters. Katherine Johnson was a single, widowed mother who had to raise and support three children. Mary Jackson was a married mother who held down a job and attended night school. It takes internal strength to balance that kind of life.

hf-true-women

They were brave women not just strong, smart women.
The three heroines each had a moment in the story in which they spoke truth to power.  In the engineering lab, the courtroom, and the office.  In each case, their courage effected change.

Black men are not thugs.
The two primary black male roles in the movie, the husbands of Katherine and Mary, were a gangsta and a drug-addict that is too often the portrait of black men in movies. Jim Johnson and Levi Jackson were both strong, family-oriented men of solid character.

hf-mary-husband

Prejudice and Discouragement are sometimes found in your backyard.
The women of Hidden Figures were not only dealing with racial bigotry, but they faced sexism as well, even from their own friends. At the first meeting with her future husband, Katherine’s suitor puts a huge foot in his own mouth:

Jim Johnson: “Aeronautics. Pretty heady stuff. They let women handle that kind of- … I was just surprised something so taxing…”

hf-stroll

video clip

Levi Jackson (Mary’s Husband commenting on her desire to become a NASA engineer): “All I’m saying, don’t play a fool. I don’t want to see you get hurt. NASA’s never given you gals your due, having another degree won’t change that. Civil rights ain’t always civil.”

Both men came around to offer full support of their ladies’ dreams, after their wives stood strong to their convictions. Sometimes the battles for equity must be fought in our homes and communities, not only against “them.”

Prejudice is sometimes harder to see now.
We no longer have colored bathrooms, colored bus seats, colored drinking fountains or colored coffee pots, but we do have colored schools and even colored classrooms. We know that schools are just as segregated now, as before Brown vs. Board of Education. The inequity in funding and support for the black schools means segregation by opportunity, which is more criminal than segregation by race. The roster of my own class of “at-risk” students is 90% populated by students of color, while those same groups of students make up only 54% of the school population. When I brought this to the attention of the administration, they were genuinely unaware, but instantly concerned. Statistics like this, which exist on paper, are harder to see and less humiliating, but actually more dangerous than a “coloreds only” sign. Therefore, we educators need to be more vigilant in exposing these numbers and in changing the practices and policies that they represent.

The Powers That Be must be part of the change process.
hf-john-glenn
As much as the three heroines are rightfully credited with impacting change in NASA’s practices regarding women and blacks, we need to also recognize those members of power structure that aided them in their cause: Space Task Force Director Al Harrison who gave Katherine access to classified data and high level meetings, Astronaut John Glenn who went out of way to greet the black female computers and insisted that Katherine do the calculations on his re-entry, Polish engineer Karl Zielinski who encouraged Mary to seek her engineering degree, IBM Technician Bill Calhoun who gave Dorothy the opportunity to program the new technology and her boss, Vivian Michael, who promoted her to Supervisor.

People of all ethnicity and gender can contribute.
This story was about more than whites and blacks sharing the same bathroom. It was about the talents and contributions of people of all backgrounds. Katherine makes this very point in the first meeting of her and her future husband.

Katherine: “So, yes…they let women do some things over at NASA, Mr. Johnson. But it’s not because we wear skirts…it’s because we wear glasses.”

hf-kathernine-hand-up

Racial equality is pragmatic as well as moral.
This important story of Johnson, Jackson and Vaughn is about more than women or blacks receiving a fair shake. It is about how one of the crowning achievements of America may not have been accomplished without them.

Vivian Mitchell (Dorothy’s Supervisor):  “Seems like they’re gonna need a permanent team to feed that IBM.”

I don’t want to question Al Harrison’s sense of social justice, but his tearing down of the “Coloreds Only” bathroom sign was as much an action of practicality as it was a display of righteousness.

Harrison “Go wherever you damn well please. Preferably closer to your desk.”

al-sign

His primary purpose was to get an American into orbit, not to get a black woman to urinate next a white one, but he saw that the path into space traveled through an integrated restroom. Katherine knew it also traveled through an integrated boardroom. She was being kept out of key meetings, because of her gender and race, when she knew that her work was being hindered by the locked door. She stated her case for inclusion to her boss, not on a basic of equality, but on a basis of practicality.

Katherine: “I cannot do my work effectively without having all of the data and all of the information as soon as it’s available. Indeed to be in that room, hearing what you hear.”

When Harrison has to stand for her presence in the meeting, he did not say, ‘We need more black women in these meetings.’ Instead, he claimed,

“This is Katherine Goble with our Trajectory and Launch Window Division. Her work is pertinent to today’s proceedings.”

hf-meetingOne of the strongest points of the movie is that prejudice not only harms the oppressed, but it hinders all of us. Equity does not only make America more fair, it makes America better.

On American Patriotism
Black history is American history.
The story of Hidden Figures is not the only story of African-American mathematicians and scientist who have made terrific contributions to our nation. In fact, those lists are long and distinguished:

America always struggles to live up its ideals, but those ideals are America.
hf-friendship
The names of the two spacecraft highlighted in the film are named Freedom and Friendship. These names seem a bit ironic when contrasted to the social controversies of the time. Many blacks and women in the ‘60’s would not have considered America to be friendly or free, however, gender and racial equity made huge strides towards these American values during that time period.

Mary: “I’m a Negro woman. I’m not going to entertain the impossible.”

Zielinski (engineering colleague): “And I’m a Polish Jew whose parents died in a Nazi prison camp. Now I’m standing beneath a space ship that’s going to carry an astronaut to the stars. I think we can say, we’re living the impossible.”

Mary would be happy to know that over 50 years later, not only are women of all ethnicities being allowed to become engineers, they are being actively recruited for such a career, and we in the public school system are being charged with raising them up. Again, this is not a matter of equality; it is a matter of practicality. America needs more engineers, and any antiquated systems of injustice will keep us from achieving our technological potential, and from reaching our highest ideals of Friendship and Freedom.

hf-women-nasa


* All Quotes from Hidden Figures Screenplay by Allison Schroeder and Theodore Melfi, May 12, 2015 (Based on the book Hidden Figures by Margot Shetterly).

The Election Pollsters Still Got It Right

election-forecastThere has been a great deal of Monday morning quarterbacking about how the 2016 Presidential election polls “got it all wrong.” Radio pundits like KFI’s John and Ken have been claiming that pollsters obviously don’t know what they are doing. There are three points to consider here.

1) Did the polls get it wrong?
2) Did the pollsters do something wrong?
3) What good math activity can we generate from all this fuss?

Here are some direct answers with, hopefully, simple, clarifying mathematical (not political) explanations.

The Polls Got It Right
The poll results were within the expected margin of error. In fact, four days before the election, Harry Enten of FiveThirtyEight wrote “Clinton’s lead is small enough that it wouldn’t take more than a normal amount of polling error to wipe the lead out and leave Trump the winner of the national popular vote.” In the end, Clinton still won the popular vote, by approximately 1.5% compared to the 3.3% predicated the day before the election, well within the normal margin of error. Gallup shows that, historically, the polls have been within 2%, on average, of the actual results, and within 1% half of the time, with the victories of Reagan in 1980 and Truman in 1948 being the most notable anomalies.

In fact, Nate Silver of FiveThirtyEight noted the day after the election that a 1% swing in Clinton’s favor across all states would have flipped the Electoral College tally.

Further support that the polls got it right comes from the understanding of probability. Clinton was given a 71% chance of winning on the eve of the election. That means that Trump had a slighter better chance of winning the election than he had of flipping heads on two consecutive tosses of a coin. When heads occurs twice when tossing a coin, should we all protest that statistics and polling are unreliable? This is why Nate Silver claims that the polls missed, but he did not say that they failed.

The Pollsters Did It Right
People have been willing to give more grace to the mathematics than to the mathematicians. Pollsters (those creating the polls, not the folks on the phone) have taken a great deal of heat for poor sampling, but these pollsters have been vindicated voter turnout numbers, because the pollsters surveyed registered voters, not guaranteed voters.

PBS‘s Michael Reagan writes that the data on actual casted votes reveals that Clinton had 2 million fewer voters than Obama did in 2012, while Trump had a slight uptick over Mitt Romney. Had voter participation been similar to the 2012 election, America would have had a different 2016 result.

Liberal filmmaker Michael Moore was extremely concerned just before the election about the lack of enthusiasm for Clinton versus the overwhelming passionate support for Trump. His concern turned out to be warranted.

A Good Math Activity: Secretary Clinton Attempts A Field Goal Kick
Given the information below from FiveThirtyEight, at what distance (in yards) would a field goal kicker in 2014 have the same chance of success as Secretary Clinton in the election of 2016.

election-percentage

Election Kickers.png

Spoiler alert: Approximately 48 yards.

Fortunately, if an NFL kicker misses a field goal attempt from just inside the 50 yard line, I still have faith in statistics and statisticians… and America.

Is Talent a Wall or Launching Pad?

In the quest for delineating the difference between fixed and growth mindsets, educators have created a plethora of lists for contrasting habits, beliefs and statements.

 

With my students, I summarize all of these lists and graphics with two simple pictures that pose a simple question: “Do you see talent as a wall or as a launching pad?”

Talent Wall

Carole Dweck‘s mindset research shows that self-perception of talent as a limit or as a starting point has a tremendous influence on student learning. The mindset is really about how people perceive their natural abilities and view the potential of their efforts, not just their level of effort.

In fact, this double-pronged image of wall vs launching pad helped me make sense of two things that Dr. Dweck has said regrading effort and growth mindset. The first is that “the most common misconception is simply equating the growth mindset with effort.” (Education Weekly, September 2015).  I didn’t fully grasp the issue that troubled her until I heard her say that it isn’t just the struggling math students who have a fixed mindset, but that even some of the more “successful students” have one as well. An example of an advanced student who possesses a fixed mindset is the one who believes that they cannot learn math (remember mindset is about self-perception), so they must compensate by studying and memorizing in order to pass the tests and get good grades.

This thought leads me to another of my favorite image comparing fixed and growth mindset… the scans of the brain of someone with a fixed mindset versus one with a growth mindset.

Brain Mindsets

brain-coldWhen faced with a challenge, the fixed mindset brain “goes cold.” It literally shuts down.

brain-on-fireHowever, when faced with the same challenge, the growth mindset brain “fires up.” It knows that more is being asked of it, so it kicks into high gear to meet the challenge, rather than duck it.

Some frozen brains walk away from learning by checking out or acting out. Other frozen brains circumvent the learning by grinding through the course with a hyper-powered work ethic. If good grades is the ultimate goal, then one of these fixed mindset responses is valued more than the other. If learning is the true prize of an education, though, then neither response is sufficient; instead, Dweck claims that students need to implement a “repertoire of approaches—not just sheer effort—to learn and improve.” After all, it is how one reveals to setbacks that reveals their true mindset.

To see some of my novice attempts at teaching growth mindset in math class, see the following posts: Nicki the Neuron, Neuron Stickers, Brain Surgeons & Wrinkle Sprinkles, and Neuron Problems and Classroom Norms, or click Growth Mindset in the tag cloud.

Ready, Set, Launch!

 

Nicki the Neuron

NickyAfter I gave a presentation about my use of Neuron Stickers, Brain Surgeon & Wrinkle Sprinkles at Twitter Math Camp 15, Julie Wright (@julierwright) sent me a tweet that directed me to a stuffed Neuron with eyes. So Bitchen!

I took her suggestion and hung it at the front of the classroom as a class mascot, naming it Nicki the Neuron, since Nicki is a name that is gender and ethnic neutral.

Julie Wright Tweet

 

Nicki was  a bigger hit than I expected. One of my students insisted on holding our new mascot during class.

Nicky n Fan

This inspired me. I thought to give Nicki temporarily to the group to which the most recent Neuron Sticker was awarded. I was concerned the boys wouldn’t receive this too well, but Nicki quickly became of badge of honor for the groups.

Nicky n Girl

Nicki is now part of the responsibilities of the Brain Surgeon and is generating a great deal of focus on the Process Reward System that I am implementing. Thank you Julie!

Neuron Stickers, Brain Surgeons and Wrinkle Sprinkles

Brain-SurgeonI was inspired at a Growth Mindset workshop by Jo Boaler and Carol Dweck. I knew I was going to be teaching a class of at-risk students, qualified by being on the socio-economic disadvantaged list and having struggled in 8th grade math. Rather than repeating in high school the math course that they failed in middle school, these students would taking Algebra 1 with me. If there is a group of students that need help shifting from a fixed mindset to a growth mindset, it is a group of at-risk students who have struggled in math. However, I did not want to just put a bunch of Power Point slides saying how they should believe in themselves.

So, I came up with three vehicles to develop growth mindsets in my students:

Neuron Stickers

Dr. Boaler emphasizes the plasticity of the brain. This means that the brain actual rewires itself when it learns, by forming new or strengthening current connects between brain cells. We also know now that the outer later of the brain thickens as we learn, much like muscles get bigger from exercise. These facts create a contemporary view of the brain that is in direct opposition to the conventional view in education in which the brain is a passive vessel to be filled with knowledge. These two views are best contrasted by the following images of the brain.

Brain Pair

The image on the left implies that we are building a brain. I love that idea so much that I enlarged the graphic to poster size and put it up on the classroom wall. I tell my students that is exactly what they are here to do … build their brains. We then publicly discuss the actions that help us build our brains in class, like…

  • Sharing mistakes publicly
  • Offering unique solutions
  • Asking clarifying questions
  • Making connections
  • Having an “Aha!” moment
  • Helping others

To encourage these and other behaviors that contribute to learning, I created Neuron stickers. This was easy, I pulled a drawing of a neuron from the internet and created a sheet that I could print onto a sheet of mailing labels.

neuron color

Neuron Sheet

Each time a student demonstrated action that promoted learning, the student receives a neuron sticker which they get to place on the Brain Poster. Once the poster is filled, I put up a new one and we continue honoring growth mindset throughout the year.

Brain Color Brain Pic Final

Brain Surgeon

Each day we designate a “Brain Surgeon,” who serves as a class leader for the day. I purchased this model of the brain to be given to the day’s Brain Surgeon.

Brain Surgeon Model

The role of the Brain Surgeon comes at the beginning and end of each class.

Opening Class Duties

  • Supervise preparation for class (getting materials ready)
  • Lead Drum Roll (Class Opener)
  • Reading of Instructional Objective
  • Placing Nicki The Neuron with the group who had it last during prior lesson

Closing Class Duties

  • Supervise clean up and storing of materials
  • Return Nicki The Neuron and the Brain
  • Lead Wrinkle Sprinkle 

Wrinkle Sprinkle

Each class concludes with a debrief titled “Wrinkle Sprinkle,” implying that learning adds a new wrinkle to the brain. (Note: Anatomically we know this is not accurate, though we know that the neurons make new connections and the outer layer of the brain thickens.) The brain surgeon calls on students who raise a hand to offer something that they learned that day. These Wrinkle Sprinkles are recorded on the 180Blogs on this site. Wrinkle

 

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.

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.

Roatan: Math in Honduras

RoatanIn June of 2015, I was privileged to join my wife and several other swim school owners on a service trip to the island of Roatan, in Honduras. The purpose of the trip was to provide much-needed toys & supplies to some of the public schools there, and to raise physical fitness awareness.

Of the nearly fifty swim school owners, instructors and family members that made up our group, I was the only school teacher, therefore, I viewed the experience through a different lens than the others. I also made several connections with the teachers and was able to observe one do an outstanding job of teaching 1-digit subtraction. Watch the video below and you will be as equally impressed. The surprise for me was learning later that the class was 4th grade (in the U.S. this topic is taught in 2nd).

Video Link

Video Still Roatan

My Guest Lesson

I also had a unique opportunity to teach a brief high school math lesson. I could see on the board that the lesson was about the surface area of a sphere. The teacher had written the formula A = 4πr² and there was an example showing how to calculate the area given the radius. I saw the students doing guided practice in their notebooks. The teacher learned that I also taught math and offered to have me show something on the board. From her limited English, the teacher translated for me. I kept it simple, checking for understanding via head nods after each step… I drew a sphere, then a hemisphere, then the Great Circle. I asked how many of these circles would it take to cover the surface of the sphere. We took a finger vote. Most of the class claimed “2.” I claimed that the teacher already showed them… in the formula … 4 circles (πr²). I then applauded the teacher for knowing that. (You can see me building her up to her students, in the picture below. They all applauded her.)

Shore Teaching2

Half Moon Bay

 

Schools in Roatan

25% of all Roatan children do not have the means to attend to school. Of those that do, 30% do not continue beyond the 6th grade. This will change as the economy improves. Thirty years ago, there was no electricity and no paved roads on the island. Progress on Roatan has a strong upward trajectory that can be accelerated with a little bit of help.

Kids on roofFlowers Baycrawfish orck

Our 2015 Visit

We visited six schools:

  • Victor Stanley West End School
  • Froylan Turcios School
  • Escuela Juan Lindo
  • Garby Nelson
  • Thomas McField
  • Isidro Sabio

We provided donations from the swim school owners and from the clients of the schools.The outpouring of generousity was amazing. The supplies ranged from desks to soccer balls to toothbrushes to backpacks.

Chair donation

Table stuff

BDay Girl

Another intention of the trip was to provide physical fitness awareness. The kids had a great deal of fun with both the new exercises and the activities.

Race

Push ups

Many of the students greeted us warmly. We learned that many kids had not seen pictures of themselves, so they got a kick out of us showing them their images on our phones.

Cute Kids

Casie n Girls

 

The trip ended with the Swim Celebration on the beach at Half Moon Bay in the West End. I was surprised on an island how children didn’t know how to float. The lessons were readily accepted, as was the swimming gear (swim suits, intertubes and goggles). As you can see, my wife fell in love with the Honduran children.

Water Baby crop

Our group will be returning to the amazing land and people of Roatan in the summer of 2017.

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 …

 

Recap: CA Mathematics Network Forum, 2015

Logo CAMNThe 2015 California Mathematics Network is a community of math education leaders from twelve regions in the State. This Conference focused on the NCTM publication Principles to Actions. The book is an amazing resource that discusses what needs to be done in math classes, and what actions need to be taken by teachers and administrators alike to make that happen. It should be read by anyone who has an investment in math education. A good primer is p 5, 10, & 109-116, or check out the Executive Summary. Following are some terrific ideas from the conference speakers on how to implement these Principles.


The Best of the Common Core Closes the Achievement Gap — Dr. Lee Stiff, former NCTM President

  • Lee StiffThe Achievement Gap can best be narrowed through Effective Teaching of the CCSSM Practices.
  • Where do these effective teachers come from? … “from our good work!” (as instructional leaders)
  • The primary purpose of Principles to Actions is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards.
  • NCTM Guiding Principles
    (from Principles to Action)
    Teaching and Learning
    Access and Equity
    Curriculum
    Tools and Technology
    Assessment
    Professionalism
  • NCTM Teaching Practices
    (from Principles to Action)
    1. Establish mathematics goals to focus learning.
    2. Implement tasks that promote reasoning and problem solving.
    3. Use and connect mathematical representations.
    4. Facilitate meaningful mathematical discourse.
    5. Pose purposeful questions.
    6. Build procedural fluency from conceptual understanding.

    7. Support productive struggle in learning mathematics.
    8. Elicit and use evidence of student thinking.
  • Student placement and support should be based on DATA not DEMOGRAPHICS.
  • We create the gap!!
    Screen Shot 2015-05-21 at 10.50.39 PM

Teaching Practices that Support Student Learning of Mathematics — Peg Smith, University of Pittsburgh

Peg Smith PicDr. Smith had us read through a well-known task, the Hexagon Train, and then analyzed it through the lens of each of the Teaching & Learning Principles in Principles to Actions (Summarized Below):

Hexgon Train

 

 

1. goals
2. tasks
3. representations
4. discourse
5. purposeful questions
6. procedural fluency

7. productive struggle
8. evidence of student thinking

  • It’s all about the task. Choosing the task really matters.
  • “What you put in front of the students frames their opportunity to learn the mathematics.”
  • Have your questions “locked and loaded,” and your responses “in your back pocket.”
  • It’s time to break out of the “postage stamp” lesson plan, (the homework, & examples fit in a little box), and write analytical, anticipatory lesson plans. (This one needs a cute name, too)
  • It’s difficult for teachers to use a high level task. It’s even more difficult for them to use it well.
  • Decrease the complexity of language without decreasing the cognitive demand of the task.
  • “Never Say Anything That a Kid Can Say.” (Article)
  • Writing “SWBT” objectives limit what students learn. Is the goal really to be able to find the length of the hypotenuse or to understand the relationship of the areas of the squares formed by the three sides of a right triangle?
  • Dr. Smith is the co-author of 5 Practices for Orchestrating Productive Discourse in Mathematics Class.
  • Dr. Smith shared this Principles to Action Tool Kit:

Dr. Smith then asked us to restructure a standard series of textbook questions into a more robust task. The conversation at my table was very rich. It was a briefer version of a lesson makeover, and would be an awesome PD activity.


Smarter Balance Update — Mary Tribbey & Jane Liang

This slide makes two BIG statements:

  1. The Red Dot () is along a timeline from the start of the assessment initiative to full implementation. We are still in the early stages of perfecting it.
  2. There do exist Interim Assessments that few schools (including mine) are using to check for student readiness.

Screen Shot 2015-05-19 at 9.52.34 AM

This day was the first I heard of the scaled score for the reporting of the test. It appears that there will now be some reporting on the standards as well as the claims, after all.

Screen Shot 2015-05-19 at 9.53.08 AM

 


Equity-Based Teaching Practices — Karen Mayfield-Ingram, EQUALS Program, UC Berkeley

  1. Mayfield PicGoing Deep with Mathematics
  2. Leveraging Multiple Mathematical Competencies
  3. Affirming Mathematics Learner’s Identity (multiple access points)
  4. Challenging Spaces of Marginality (diminish status within class)
  5. Drawing on Multiple Resources of Knowledge (including culture and experience)

Lesson: “He Was Suspended for Being Mexican” (excerpt from The Impact of Identify in K-8 mathematics Learning and Teaching) This was an anecdote of a teacher who took a students statement, “He was suspended for being Mexican,” and turned into a statistics lesson in which the students had to analyze data to determine if the school policies truly were racist or not. While we can’t tie every topic into a student-oriented context, I think it is a powerful idea that should be done more often.


Technology & Computation — Joe Fielder, Cal State Bakersfield

  • Pic FeidlerAll computation outside the classroom is done by a machine.
  • Machine computation is mostly done with spreadsheets.
  • Hand calculations are only done in math classes. (referenced TED talk by Conrad Wolfram)
  • If we are going to teach students mathematics that is relevant beyond the college entrance exam, we need to give explicit instruction on the tools of computation.
  • TI InspireDr. Fiedler is currently working with the college board to change the SAT to reflect computations done by hand-held graphing calculators.
  • The introduction of the first scientific calculator 1972 was controversial, because teachers were worried that students would no longer be able to use tables.
  • “Students are idle, indifferent, irresponsible in response to absurd work. This is a rational response!”
  • There is no change without a loss. If there is no loss, there is no change. Similarly, literacy diminished the need for memory, but we still teach students to read and write.
  • Yes, part of education’s job is to pass on old knowledge, but it’s not the entire job. It’s time to get with the times.

BREAKOUT: Exploring the Common Core Statistics & Probability Standards — Jim Short, Ventura County Office of Ed

  • Pic Jim Short“Statistics means never having to say your certain.” The irony is that this is what makes math teachers uncomfortable with stats.
  • Teachers are avoiding the teaching of statistics, but the ponderous of the Performance Tasks on State Tests are based on Statistics and Data Analysis.
  • Statistics is more important than Calculus. (referenced TED talk by Benjamin Arnold)
  • From the GAISE Report,
    4 Components of Statistical Problem Solving
    I.   Formulate Questions
    II.  Collect Data
    III. Analyze Data
    IV. Interpret Results
  • You aren’t teaching statistics unless you are teaching modeling.Here are some great tools that we used in the session to generate statistical displays in a spreadsheet:
    g(math) {Google Sheets add-ons}
    Geogebra {box-n-whisker}

    Core Math Tools {NCTM}
    =norminv(rand(), means.d.)” {Excel Macro for generating a set of normalized data}
    Stats vs Prob

BREAKOUT: The Right Answer is Not Enough — Ivan Cheng, Cal State Northridge

  • PIc Ivan ChengWhat the teacher assesses is what the students think that the teacher values.
  • How is “doing math” defined differently under Common Core versus NCLB? How you answer that questions, determines how you teach and assess under the new standards.
  • After a test, if the teacher can’t state what the student misconceptions are, then the teacher needs to do some more digging.
  • Teachers should use assessment questions that intentionally reveal misconceptions.
  • Why “a” student missed a question is as important as which question they missed.
  • Clicking Smarter Balanced ASSESSMENTS (in SBAC navigation bar) will take you to documents that map targets to standards.
  • “Think about getting through to the kids instead of getting through the textbook.”
  • This sample question demonstrated why the students have issues with the new assessments. The students instantly think that the answer is “20,” because x = 20. Since 20 is not a given situation, they often choose “D: Neither.”

Inequality Sample


My Big Take-Aways

  • The achievement gap can be closed by the effective teaching of the Math Practices.
  • It’s all about the task!!
  • Two Big Words kept coming up: Meaningful & Equity. Equity is achieved by giving all students access to meaningful, high-level mathematics.
  • Get with the times, and start using technology in order to move from computation to deeper, higher mathematics.
  • There are some amazing tools available for Statistics tasks. This is a pervasive topic that needs serious attention and support.
  • Our assessments communicate what we value. The assessments are changing, because our goals are changing. Therefore, we teachers must change our values and practices.
  • We should all read Principles to Action.
  • The Region 10 Team is an amazing group of intelligent, passionate people. I look forward to seeing how we will put all these principles into action.

Region 10