Attempt #1 of Being Less Afraid in 2019

Public comments given at tonight’s school board meeting:

Hi. I would like to make some comments regarding the push for equity in WJCC. I will preface by saying I definitely don’t know all of the solutions to every problem, but it is striking to me that in a division where 40% of our students are not white and nearly as many qualify for the free and reduced meal program the public conversations about equity I have witnessed or been a part of are continually held by middle-to-upper-class white people like the majority of this room, myself included.

As someone who received 12 college credits from the AP classes I took in high school, I fully understand the opportunity those classes can give students. But if we want more students succeeding in AP courses, don’t they need better foundations? How are we doing that when some AP courses have 4-5 students and other teachers have over 30 students or new collaborators each year that are unfamiliar with the courses? We also have multiple AP classes that take place in one semester due to the demands of block scheduling, meaning students finish their material in January and have to keep it fresh until May or students have significantly less time to prepare for the AP exam than they should in the spring. And while there are students signing up for AP exams, many AP students do not take the exam that qualifies them for potential college credit. One reason that I’ve heard from many of my students is that they aren’t confident they can do well in May when they’re done in January, but they stayed in the class for the GPA boost.

WJCC also increased the amount of leveling of our math classes with the re-introduction of teaching Algebra 1 in parts. There are tons of divisions across the country that get just as good, if not better, math scores on standardized tests, especially in the subgroups WJCC is concerned about, with 50-75% of the instructional time we use. Slower versions of our math courses tend to consist of more black and brown students than the regularly paced versions of the same courses. San Fransisco Unified School District, obviously more economically and racially diverse than WJCC, requires all students to take Algebra 1 as freshmen. In the first few years of implementing this, they have cut the percentage of students who need to repeat Algebra 1 to fewer than 10%.

A 2015 report from the CDC states that the average start time for middle and high school students in the state of Virginia was 8:04 AM with only 10% of divisions having an average start time before 8 AM. WJCC’s average start time for middle schools and high schools is 7:39 AM, nearly half an hour earlier than the vast majority of other divisions in the state. This group we are in is going to continue decreasing as large districts such as Chesterfield and Virginia Beach are planning on starting later in upcoming school years. Is start time a measure in which we want to lead the state?

There is much more that I’d be happy to discuss but I’ll end here. I do believe that the division’s communication is improving, I appreciate that teacher opinions are being solicited, and I am super excited to be building another Commonwealth Innovations course to be offered at all three high schools.

Thank you.

Following the meeting, a board member walked out to my car with me. During our 2 minute walk they told me:

  • my age (26) explains a lot,
  • Virginia is a “Right to Work” state,
  • they don’t generally like unions but think teacher unions are important and I should be more involved in ours, and
  • to remember that people can’t choose their color. 


I got in bed at 9:47. It’s now 1:18. I’ve been so close to falling asleep 3 times but it hasn’t stuck yet. My best friend went to Beyonce in Cleveland tonight. My sister and I are leaving for a 12-day-long road trip Sunday. My brother just got cheesecake out of the fridge. My boyfriend takes his final exam of medical school tomorrow. Seems like as good a time as any to blog about TMC.

Let’s start a few months ago. Cue me, having already grabbed a quick bite by myself the night before prior to the National Council of Mathematics Teachers (NCTM – proper APA for Bob) Annual Meeting and Exposition Opening Keynote session.

I knew there were people from MTBoS (math-twitter-blog-o-sphere) at NCTM. I had even met a few of them already and they were all super nice. But there were 4,000 people here, and even if I was checking my phone, my service and WiFi were questionable. So I happened to run into my student teacher and some people from her college cohort and ran to get lunch with them.

I spent some time at the MTBoS booth that afternoon between sessions. Later that night I dipped out on ShadowCon early (it is SO HARD to be an active listener at 7 PM after a full day of active listening, y’all) and made my way to Desmos Happy Hour. After a couple of laps around the room, I was really hoping the person I thought was Megan was actually Megan… so I went up to her and asked “hi, are you @veganmathbeagle?” It was, and she kindly invited me to join their trivia team.

I worked at the booth a few times. I met a few more people. I went to some really great sessions (and a few snoozers). I felt energized for the end of the year. I was happy with my experience.

Cut to last week. Thanks to a Google Sheet, I was able to volunteer to pick someone up at the airport on my way into Cleveland. I met my roommate, who I originally “met” via Padlet. I took a quick trip to Cuyahoga Valley National Park with two random people that saw my tweet/Google Sheet post. All on Wednesday, before Twitter Math Camp even technically began.

Over the course of these four days I learned. I learned how much manipulatives and color-coding can help students see different algebraic relationships in the same pattern. I learned how other schools do a variety of interventions for their students with “math gaps”. I learned the ways teachers verbally and non-verbally appreciate, congratulate, and redirect students.

Over the course of these four days I was challenged. Mattie and Chris challenged me each morning to keep my mouth shut and let my students/peers do the talking, which is often easier said than done. Marian challenged me to put my students of color at the center. Julie challenged me to believe in myself as a #teacherleader. Kent challenged me to deeply appreciate and understand base 10 operations (and other bases, which I’ll get to eventually).

During these four days I just felt good. I got to play games and talk about fun things with cool people.

I got to post really great ideas that were immediately built upon both on Twitter and in real life.

I got to meet five other math teachers from my state, one of which lives twelve minutes away from me.

And on top of all of this, I got complimented? I really don’t mean to toot my own horn here, but when people like Sam Shah say that they appreciate your tweets… it makes ya feel good, y’know?

I also had the pleasure of meeting Robert Berry, NCTM’s new president and UVA professor. He might be the most genuine person I met at TMC. He spoke, listened, asked questions, pushed back, listened more, and participated in this little grassroots conference. He invited me to tailgate with his family at a William and Mary soccer game. Presidents of big organizations don’t do things like this, do they? This isn’t normal, is it???

I honestly have enjoyed both NCTM experiences I’ve had so far. I learned something new from each. But neither one holds a candle to TMC. Thank you to everyone there (and everyone following along online) for just being you, and helping (and pushing) me to be the best me. I probably won’t be able to make it to TMC19 but that’s okay. I know I have people across the country I can turn to daily for ideas and support. Maybe another first timer can take my spot next year and feel the same.

It’s now 2:20. Goodnight, Meeple.


Curriculum with a Message word-vomit: VA Algebra 1

In April I went to Jonathan’s NCTM session titled “Curriculum with a Message”. I had been fascinated by his ideas on Algebra 2 for a while but wasn’t fully understanding what the year looked like. I left the session really itching to do this with my next Algebra 1 or Algebra 2 course. I still don’t know what I’m teaching for the upcoming school year, but today I started to look into what this might look like for a Virginia Algebra 1 course (NOTE: we are not a CCSS state).

Before getting started, two of our standards include translating verbal expressions algebraically and representing linear and quadratic functions using multiple representations (verbal, tables, equations, graphs). I plan on doing both of those regularly throughout the course, and including concrete and other pictoral/symbolic representations as needed.

Big Idea #1: Equivalence

Our students are expected to do the following:

  • evaluate expressions given replacement sets using absolute value, square roots, and cube roots
  • use the laws of exponents
  • add, subtract, multiply, and divide polynomials
  • factor 1st/2nd degree bi/trinomials in 1 variable
  • simplify square roots of whole numbers and monomial expressions
  • simplify cube roots of integers
  • add, subtract, and multiply 2 monomial radical expressions with numerical radicands

I would add into this part of the year solving multistep equations and inequalities (and literal equations) since we have to teach them to use properties to justify their steps. I don’t know what this big idea would look like but I’m imagining lots of open middle problems. I’m imagining this big idea taking from the beginning of school (day after Labor Day) to around Thanksgiving.

Big Idea #2: Graphically Representing and Understanding Linear and Quadratic Relationships

That’s a long big idea title but it gets the point across. I’m choosing to start with graphs first because I believe that when students have the ability to visually represent things it’s much easier to connect to the algebraic, more abstract versions.

Standards that would belong in this part are:

  • slope
  • graphing two-variable linear equations and inequalities
  • graphing two-variable quadratic equations
  • systems of two linear equations or inequalities
  • characteristics of relations
    • domain/range
    • zeros/roots/solutions
    • intercepts
  • direct variation
  • parallel and perpendicular lines

I think mostly with this big idea my goal would be to do a lot of word problems and get those words into a variety of visual representations; drawing, making tables (that then turn into graphs), etc. Those characteristics would be used to help us determine the reasonableness of our problem set-ups and solutions, as well as visually provide answers for word problems (like when the water will run out, when the ball is the highest, etc.). Depending on snow days, this would take until Presidents’ Day-ish.

Big Idea #3: Algebraic Representations of Linear and Quadratic Relationships

The idea here is that we would move from “nice, easy” numbers to realistic numbers, which is why graphs and other representations wouldn’t be our best option anymore.

Topics include all of the exact same things as Big Idea #2, but now we would focus on equations. Two things that would need to be included are:

  • parent function transformations of y = x with m and b
  • linear and quadratic regression

This would take until a week or so before the standardized test so there would be some time for test prep. The only standard that isn’t included is inverse variation. Such an annoying one to include when you don’t do rational functions. So I’d be sure to touch on that during test prep and then maybe do a mini-unit on inverse, joint, and combined variation after the test?

So basically this course would be three trimesters and each trimester would have a different theme… I’m not going to flesh it out any more until I know I’m teaching Algebra 1 next year, but if anyone has comments/questions/suggestions, I’m all ears!

#mtbosblog18: Snow Days

I’ve now taught 6/13 scheduled days this month. Our exams were supposed to be next week but they just got cancelled, except about half of the classes with state tests still have to take them. I’m not sure if snow days are worse at the beginning or end of a semester.

All of the snow days made me lose track of the date so I’m starting the 2018 blogging challenge off a day late. Here’s a quick recap of the fall:

  • I taught all entirely new-to-me classes, including two sections of the same brand new course.
    • ProbStats was great. My kids were really talkative and sometimes argumentative. I didn’t create the best climate and wasn’t the greatest at managing the classroom. But they learned enough and we made it through with me telling them the wrong thing only a handful of times.
    • Man vs. Earth is also great. It’s stressful and there have been lots of mistakes, but it’s great. The students have learned about data collection and analysis and did a propaganda survey on environmental issues. They learned about probability and discrete probability distributions and will be using discrete/binomial distributions to compare population pyramids of countries in The Americas.
  • I have my first student teacher. Her name is Nicole and I’m going to try convincing her to either start her own blog or at least do a few guest posts on here. She starts full time in a month.
  • I’ve been volunteered as the Pathways curriculum lead, which is fine. I like logistics. Organizing and planning is soothing.
  • Personally, I bought a house and have been spending time painting and decorating. I’ve also been looking at cars and planning summer vacations.

So it’s been a very busy last few months. 2017 was a busy year in general! It was good though.

I need some help finishing up the year though:

  • I really want to incorporate more geography topics into my lessons this semester. We’re going to be doing continuous probability distributions, confidence intervals, and hypothesis testing. I’ve already started pulling ideas and worksheets from The Stats Medic and am thinking about how I can adapt them but if anyone has ideas I’d love them.
  • My other courses will be blended Algebra 1 and Algebra 2. These are on alternating days and have been taught by other teachers since the beginning of the year. It will be my first time taking over a class in the middle of the year so if anyone has advice on that too I’d appreciate it. I think it will be good for everyone though. Due to changeover in our admin team this summer two of our new math teachers ended up with 4 preps each and this will get them down to 2 and 3. Bless them.

I don’t know how to end this so I’d just like to say thank you to everyone who’s helped me in #mtbos so far and I look forward to reading all of the #mtbosblog18 posts!

ProbStats Assignments: Graph of the Week and Significant Digits

We finally got some tech issues and scheduling issues taken care of and were able to start homework last week. About 1/3 of my students didn’t complete all of it and about 1/4 of them didn’t write well (they were supposed to do a paragraph and multiple students made lists or wrote 2 sentences). BUT the other 5/12 of my students did an awesome job for their first time around.

Their Monday assignment is to respond to Turner’s Graph of the Week. They respond in an online discussion board (we use Canvas for this class) and have to post something on their own but are encouraged to reply to their classmates as well. Last week’s topic was the relationship between fast food sizes and obesity rates among children. Here’s my favorite exchange:

R: The graph(s) show obesity in children since 1971 and show the serving size of fast food in the 1950’s vs now. 1st graph (obesity): The x axis represents the years from 1971 to present and the y axis represents the percent of children who are obese. 2nd graph (fast food): The x axis represents the years since the 1950’s and the y axis represents size of the food. Some observations I can make from these graphs is that fast food and obesity are growing in size through the years. However, children of ages 2-11 are not as obese as they were in 2003 whereas children ages 12-19 are still becoming obese. I foresee obesity and fast food servings continuing to rise in the next 10 years.

J: Very interesting prediction R. I’m not quite sure about the fast food servings sizes increasing as I predict the next marketing tactic used by fast food companies will be healthier eating by reducing sizes.

A: I agree with J to a degree. I do believe that the portions will become smaller, and there will be “healthier” options, I don’t think this will truly change the climbing rate of obesity. Simply because there are better options presented, just opens up an aisle to a new kind of customers. However, that does not prevent or discourage those that simply want to eat unhealthily from doing so as they have for so long.

The other days of the week, students are supposed to select a Significant Digit to discuss. I’ve asked them to summarize what they read, make any connections they can to other things, use this new information to make predictions about the future, and ask questions they still have.

Here are a few good posts from Tuesday:

J: Equifax’s share price has fallen by 35% after the company publicly acknowledged there security breach. Unfortunately, most companies don’t take security seriously until something drastic like this happens. It’s disgusting that such a large company could be so negligent with there security especially considering that hold over 143 million American’s data. This includes social security number, which are supposed to be kept private.

H: The paragraph labeled “$60 Million” talks about how much money the movie “It” made this weekend. The paragraph explained that this would have been the best weekend if it wasn’t for the fact that this was the second weekend the movie was in theaters.The movie achieved a record-breaking $123 million opening the week before. The movie knocked Hotel Transylvania 2 down to third place. Why was the movie so successful? Why was the second Hotel Transylvania more successful than the first? What cinemas played It?

T: Apparently, according to Bloomberg, rich people nowadays are interested in buying submarines. The article focuses around the M7, a submarine that looks like a huge yacht that can go underwater. What fascinates me about it is how much it entices me to want it. Though, what truly baffles me is why anyone would buy it. I mean, unless you’re going to live in it, I doubt anyone smart will drop at least 2.3 billion on it…

These assignments will continue throughout the first semester, which is when we learn about data collection, analysis, and visualization and probability. I began the Graph of the Week in my regular ProbStats class but I don’t think it’s going to create as much thinking and conversation if they just respond on paper. I need to figure out a way to create a space for that.

Building Vocabulary in Math Class

A draft I didn’t realize I had made me #pushsend today! This is from pre-school planning in August!

Math has a lot of vocabulary terms and for the past three years I’ve pretty consistently complained about how my students can’t solve problems because they don’t know what the words mean without really doing anything about it. During planning time today, I asked one of my colleagues (English teacher currently pursuing a master’s in literacy) to help out. Here are some suggestions she gave with what I hope are correct examples… I made them math examples when I could think of one easily!

Quad(Tri) Text

  1. Introduce math term using pictures or video first.
  2. Read a narrative passage that uses this math term out loud to the students (they can read along with you if you’d like, but she emphasized it’s important for the teacher to read it out loud in context).
  3. Read the math term in informational text passage (textbook, article, etc.).
  4. The fourth step of this would be to read a longer text (like a short story, novel, study,  full article, etc.) but this would most likely be skipped for most secondary math terms.

Word Lines

  1. Determine what you want to be ranking/sorting. Type up and print out.
  2. Create top and bottom spots (usually greatest to least) in a physical location in your classroom.
  3. Pass out cards to students. Have them sort themselves on the word line with guidance from the class.
  4. EXAMPLES: sorting probability words (generally, usually, impossible, guaranteed, etc.) from a probability of 0 to 1; sorting types of polynomials (linear, quartic, etc.) from highest degree to lowest.

Shades of Meaning

  1. Have paint chips of one color varying in shade.
  2. Choose a basic vocabulary word/term. Make this the lightest shade paint chip.
  3. Determine synonyms for the word and rank them on intensity. The darker the shade, the higher the intensity of the word.
  4. EXAMPLE: This is easier to see than read about.

Four Square

  1. This is basically a Frayer model but you can change the titles of each box to suit your needs.
  2. EXAMPLE: If you were teaching about Federalism, you could use “definition, people, events, and beliefs” as your boxes instead of “definition, characteristics, example, and non-example”

Concept Mapping

  1. Choose a broad vocab term. Place this at the top of or in the middle of a piece of paper.
  2. Identify the key concepts that directly relate to that term and branch them out from the original concept.
  3. Repeat step two for each branch as needed.
  4. EXAMPLES: A nice blog post from Tina on concept maps with a few pictures.

Semantic Feature Analysis

  1. Choose a broad vocab term/category.
  2. Determine subgroups. Identify characteristics of each subgroup.
  3. Create a table with subgroups in the far left column and characteristics in the top row. Check off each box that holds an always true statement (could use for A/S/N also!)
  4. EXAMPLES: A partially filled out example on quadrilaterals. I’m imagining you could do this for features of graphs as well.


  1. Select a broad vocab term. Create a list of terms that relate to the vocab term.
  2. Cut out all of the terms, including the broad vocab term, and have enough copies for each group.
  3. Have students group the terms based on similarities, looking for the broad vocab term (label) and creating titles for each group (related to their reasoning for creating the groups).
  4. EXAMPLES: An example of how to do it independently/without cutting out cards.


  1. Choose a vocab term. Identify two examples and one non-example of the term. Write these in a random order in a list.
  2. Students circle the vocab term, cross out the non-example, and leave the two examples as-is.
    1. f(x) = ax² + bx + c
    2. g(s) = |14s – 6|
    3. h(t) = 5
    4. {Polynomial}

General Tips

  1. Have discussions involving the math term.
  2. Take virtual field trips (less possible in math).
  3. Provide context clues.
  4. Teach root words.
  5. Provide examples and non-examples.
  6. Use kid-friendly definitions.
  7. Students need 8 exposures (them actually using the word) to a word before it’s a part of their vocabulary.
  8. DO NOT ask if students know what a term means – an incorrect response sticks as the correct response.
  9. Require students to use correct spelling as often as possible.
  10. Teaching Tier 2 words (academic but content-neutral: characteristics, accurately, illustrates, etc.) has the greatest effect on students’ vocabulary and reading comprehension skills.

This was from a 15ish minute conversation around lunch time on the topic. There are examples of each out there – some ideas are definitely easier to adapt to secondary math than others. I will change this list based on what I find useful in my classroom!

Moral of the story though: USE YOUR RESOURCES – English teachers and reading specialists (and elementary teachers) are a wealth of knowledge when it comes to vocabulary and are almost always willing to help as it’ll make their lives easier too!