Author Archives: jdaomath

A New Year Awaits = New things to Try!

Another school year awaits. Year #6 here I go!

#mtbos is a wonderful way to keep in touch with the math teacher community.  I always come across amazing ideas from incredible educators and there really are so many great things to try. Fantastic community we have on twitter–math teachers unite! Nonetheless,  I often forget about these great ideas  throughout the year, so to combat this I am compiling a go-to list 😀

Planning on focusing on fostering strong group work with  Fawn Nguyens math talks

  • John O’Malley Recently posted about finding ways to praise students more often, he created Amplifying Awards  after finding inspiration from other awesome teachers.
    • One thing I remember as a student in elementary/middle school is that my teacher always had a “prize bag” or “grab bag” for students by the end of the week. They usually included items that they themselves wanted to get rid of, but to a student, it could make their day. Definitely need to clean out my place and start a Prize bag.
  • Love Kristin Gray’s post about Talking Points Activity
  • Love Sarah Carter’s idea of a puzzle table and her Deliberate Practice Challenge
  • Used Sara Van Der Werf’s 100 Numbers activity last year, and Greta came up with another number activity This will be perfect since I know the 7th graders last year did the same activity…hehe, what a great way to spice things up for 8th grade.
  • Love What is Math? and What do Mathematicians Do opener to the year by Sara Van Der Werf
    • I have been thinking about this all summer in figuring out ways to incorporate identity more in the math classroom. I’ve adopted these ideas into a compilation of activities I want to roll out at the beginning of the year including: Privilege Walk, Numeric Me Infographic, Math Autobiography, and What does a Mathematician Look Like.
  • Genius Hour Mondays
    • If anyone has had success with this, please share. I am wondering if this can be a weekly endeavor for students, but I need something to hold them accountable for their research. I can also mesh this with a warm-up idea that deals with statistics and hot topics that students are interested in, where they can research and develop a solution to whatever they are passionate about. My colleague Sam has implemented this warm-up template that I for sure want to try this year. Students search for current data that is relevant to them and then create a powerpoint to share the data with their classmates. She developed a checklist.
  • Friday Ted Ed Riddles (Fermi Questions)
    • Ted Ed Riddles are the best on Fridays and serve as a way for students to free themselves from the curriculum but put their problem solving skills into place. I definitely need to figure out how to make this more of a collaborative and visible for students when they work in groups. Perhaps give them some silent think time and then bring ideas together.
  • Fawn Nguyen’s Fun Facts and Between 2 Numbers
    • Definitely need to read up on how she uses this, but it would be a great warm-up throughout the week for students.
    • I am also a fan of Fun Facts where a number is presented and students guess in groups what the number can represent. Would be a great opener to some lessons.
  • Daily Set
    • If there is ever time at the end of class, I love giving this to students. Perhaps this could be a brain break for them from the math they need to do.
  • Estimation 180
  • Would you Rather Math

 

Classroom Organization–*For me to take note of*

  1.  Student Center: Absent work, pencils, handouts,  supplies- markers, glue sticks (number by table and get 3 tier organization box or space maker box with group number); Turn in and Pass back Bin: 1 Hall Pass with lanyard attached
  2.  Word Wall- Notecards, students create with 4 quadrants: definition, picture, non-example, example
  3. Vertical Non-Permanent Surfaces: Students post summary on the walls with expo markers–big ideas…* Make a habit of random groups everyday/week.
  4.  Loved maggie’s @hybrid_mobile 3 Trays for students to place exit slips/assessments Labeled:
    1. I felt the problems were simple and I feel confident in my response
    2. I felt it was a mix of simple and difficult problems
    3. I felt the problems were different and I am unsure of my responses
  5. Welcome Banner by Sarah Carter

Yep. That’s it, for now.

Impactful Wonderings

How should students learn mathematics?  This is the million dollar question.

Traditionally, mathematics learning has always been dictated by textbooks. In which students raise the question WHY? This meme says it all:

I recently surveyed teachers about how their experiences in math were and what would their ideal classroom look like. mathexperiences-27g5wid

To combat the disconnected nature of textbooks, there are many great innovative educators out there who have transformed mathematics in new ways. My favorite resources include:

  • Fawn Nguyen’s Visual Patterns
  • Dan Meyer’s 3 Acts Task
  • Andrew Stadel’s Estimation 180
  • 101 Questions
  • Which one Doesn’t Belong
  • Open Middle 
  • And I recently stumbled across this super awesome Graph of the Week from #nctmregionals where students analyze data of relevant information. Dr. Steve Wolk would be proud of this one for sure. I plan to give this at least once a week for my students to analyze as daily warm-up/discussion. One point of critique is that the questions for graph of the week can be better and more thought-provoking than just asking students what does x and y represent.

I did not stumble across these resources overnight. Over the years of attending professional development, collaborating with other teachers, and following @viemath’s warmup routine, these resources have become part of who I am as a teacher. The last thing I want students to do in my class is to just find the answer for x. There is literally no meaning behind that. But building skills such as estimating, predicting, questioning,  analyzing, and providing evidence are all skills I want my students to develop. And these resources help open that door for students.

I had the privilege to attend National Council of Teachers of Mathematics NCTM’s Regional Conference this year in Chicago. At the conference,  Karim Ani, Mathilicious founder could not have said it any better: “*Math is a tool to talk about interesting things; but math is also a tool to talk about important things.”

I agree with Ani 100%. His website provides teachers with resources of more important and interesting questions to give for students. Nevertheless, teachers must pay $360 a year to have access to these questions.

This is where my presentation comes in: Culture and Identity: Humanizing Mathematics, in which I argue, that teachers at the end of the day are the experts. We are experts in our field and we know how to come up with thought provoking questions for our students. We may even know how to set up systems to help our students generate these questions themselves. The main thing against us is time to plan meaningful lessons. But perhaps, less is more. Perhaps all we need to present to our students is an open ended task with an Impactful Wondering, and let them figure out the mathematical evidence to support their wonderings.

In my presentation, I shared how a group of 4-5 teachers sitting in the Complex Instruction Consortium professional development day, thought of an open question: Who has the best access to resources in our community? and transformed it into a project for students to figure out what are the important resources in their community, and how do they calculate the exact distances among those resources.

After sharing, I gave teachers the opportunity to brainstorm thought provoking questions that would require mathematical evidence. This is what they came up with, and I am in awe of the power that we have as educators to make meaningful tasks for our students.

The task kind of reminds me of Fermi Questions. But as math educators, if we are given a list of skills to have students master, we can easily embed important mathematical concepts where we believe would fit well.

True learning requires experimentation, trial and error, and exploring real world data to make sense of it. The question at large is, should educators have to pay for this type of information to teach students, or can they position themselves as the experts and create meaningful tasks for students? And when will they be given the time for this type of work? We must rethink what mathematics learning is: a series of rote steps through memorization and lectures or problem solving.

Teaching the Future

Our 8th grade students spent a great day at the Museum of Science and Industry, thanks to the incredible planning of our science teacher. Students got a chance to see the robotics exhibit and also watch a dome film about engineering. I am really impressed by this museum as it really inspires students for the future.

My principal who went on the field trip, asked me, “how do we bring this (robots, programming, etc)  to our classrooms? This is their (our students) world, and this will help engage them. How do we make our classes, for instance Algebra Excite, exciting for our students?” I full heartedly agree with him, but am stuck in figuring out how we can make it happen. It is important to note that principals really do want awesome things to happen in their schools, and to spark innovation. I am so grateful that my principal is a visionary and wants what is best for students at the end of the day. The question now is how do we make it happen?

Our students should be tinkering and problem solving; not learning skills that they are tested on three times a year. Nevertheless we are constrained by data points and teaching to the test. And when do teachers receive planning time for interdisciplinary units with common prep time with their grade level teams? Never, unless we volunteer our time outside of the school schedule. We must rethink how we do school. Our students are creative, they want to see the relevance in learning, without a doubt but the systems in place and our countless meetings do not support these opportunities. That is the reality.

Sometimes as a teacher I really feel stuck given my constraints.  I am given a curriculum and timeline and know that by the end of the year my students need to master the given standards. But some days, it takes just one kid to make your day. Just yesterday I had a student tell me, “I love math class! It goes by too fast and I don’t even hear the second period bell ring” with the biggest smile on her face. I am happy to hear that I am keeping the majority of them engaged and they are finding meaning out of their class, especially at the end of the day. Nevertheless, it makes me wonder, why are you looking at the clock in your other classes? What opportunities are helping students and what are hindering our students? There is no easy answer but it all begins with the question: What is the purpose?

There are other students who are not as engaged, and I know for a fact that if I give them opportunities to tinker with robots and to learn through play and design that they would buy into education more. However, I do not have the necessary resources to make this happen. Perhaps a gofundme or donors choose account would help start a great mission, but I do not want to ask for money unless I have a clear plan and mission.

I truly believe that the purpose of education is to prepare our students for the 21st century and this is to prepare them for our global society and to help them recognize that they are part of a bigger system than just America. It was great finally getting to discuss with our 8th grade science and social studies teacher about his beliefs in education. I think we see eye to eye when it comes to helping students develop skills to analyze current events and to reflect on the past, problem solving for a better future. We both agree that teachers must help students connect the past to the present and to analyze and to think critically about current events. We also agreed that our time constraints restrict us from planning opportunities for students together on interdisciplinary units, but it would be so cool if we had the opportunity to.

On a positive note, it only takes a few like minds to begin a revolution. I am hopeful for the future. I think instilling change takes time, but it begins with small steps together. Answers are never easy, but as teachers we must always try, reflect, and try again. That is the beauty of teaching. Below are some video clips of our field trip in building robots. Today’s field trip was reinvigorating for me and reminded me why I chose the teaching profession. I love working with students, and I want to help them make an impact and to make an impact on their lives. My goal is to help them see their potential and their potential of helping the world be a better place.

 

 

My thoughts on Rethinking Giftedness Film by Jo Boaler

Just watched this video from my twitter feed from @joboaler and I had to share my thoughts as a student growing up from the gifted program from 6-12th grade.

 

I went to school in Rockford, IL RPS 205.  From K-5th grade I was placed in traditional classes that had a very diverse student body. At the time I didn’t realize that some of my peers had difficult home lives and experienced homelessness and other hardships. My parents very early wanted me to test into the gifted program because they believed that it would bring me more opportunities and I would be around peers that “cared about school.”

Unfortunately, I was not a good test taker. English was not my first language as I learned Vietnamese at home and that was what my parents mainly spoke at home even though I was born in Rockford. I remember testing in 1st grade to try to get placed into the Gifted program, and it was basically an IQ test we took that had all of these arbitrary questions–questions that I could not relate culturally or from experience.  I did not place. But my younger siblings did score well and were placed in 1st grade into the Gifted Program at King Elementary School. I remember feeling that I always had to work harder than my siblings to prove to myself that I was capable and just as smart as them. Those five years, I felt like I wasn’t good enough.

Transitioning to middle school, my parents had me test again and that was when I was placed in the gifted program in 6th grade at West Middle School. I remember the rush of excitement when I learned I was able to join. I felt a sense of achievement for finally being labeled as gifted. From then on, I learned how to play the game of school. The student demographics in the gifted program was not as diverse as it mainly comprised of White and Asian students with a few Black students that did not stay in the gifted program throughout high school. The gifted program was under the facade that it was teaching the best and the brightest. In addition it promoted the idea that students would be challenged; but in actuality from my reflection it was a way to place the “good students” from the “bad students.” What do I mean by this?

A “good student” was a student who experienced privilege in some way. These students learned how to play the game and were very compliant. These classrooms did not have classroom management issues because we all had responsive parents. In the same school, the non-gifted classrooms experienced more management issues as many of these students were the outcasts of our system of schooling. I argue that labeling students as “gifted” perpetuates an outdated system of education and sets unfair opportunities within the classrooms.

Nevertheless, I am so grateful for my education and the opportunities I received. I had excellent teachers that helped prepare me for college, and I truly felt that I was at an advantage from my college peers when it came to writing and heavy workloads because I experienced the stress and countless nights writing Ms. Longhenry’s infamous Word Paper for my AP English Literature class, incorporating research and ideas of philosophers. I learned sentence structures and how to write a paragraph that modeled a pyramid and I am able to write literature reviews at the graduate level without much struggle. My freshman world history class taught me to think about world issues as my teacher, Mr. Sabathne scratched the textbook and had us work on inquiry projects, answer questions such as What are the causes of war? We had to select a focus and research, finding primary and secondary sources, writing a research paper and presenting our research.

But all of these experiences come at a cost. It comes at a cost from the students who were not placed into these opportunities because they did not tested into the gifted program. One may argue that they could have been labeled as gifted if they tried hard enough or cared, but I think that is a hasty generalization. If we are truly modeling an education system that provides opportunities for all of our students, we are doing a terrible job at it. And it all begins with the labeling of students. We easily label and categorize students as early as pre-school and kindergarten instead of recognizing and fostering their potential.

Jo Boaler’s video epitomizes the dangers of labeling students early on. We must start a new narrative as a society especially in our education system. There are hidden structures within our education system that perpetuates the labels among our students and they can easily see and read between the lines. One great example is math tracking. At my school, we used to have an Algebra 1 and Algebra 8 class that used the same curriculum and pacing, yet the students with higher MAP scores were placed in Algebra 1 “to be challenged” and the Algebra 8 class “needed more supports” because students did not score as high, but in actuality the only difference between the two classes was that the classroom demographics did not accurately reflect the school demographics.

 

Nepantla: The Space of Tensions in Teaching

When teachers say:  “I am a master, I’ve gotten teaching down, or I do an amazing job and don’t need any input,” it sends a red flag. Why? Because teaching–in all seriousness–is hard. And it is an under appreciated profession in our country.

Some of the best teachers I know, admit after teaching 20 to 30 years, they are still trying to figure out what is best for their students and are constantly open to new ideas and collaboration. These teachers are my idols. And I look up to them because in my mind as a young teacher, I am thinking: wow they have taught for so long yet they are still learning. These are working professionals who model life-long learning. As the student body in our classrooms are growing more and more diverse, we must be cognizant of the material we are presenting to them and the different learning opportunities we are providing for our students.

One of my current colleagues epitomizes the critical thinker and reflective practitioner as she constantly strives to figure out how to engage her students through replacing units with project based learning in the math classroom.

During my undergraduate years, my professor Dr. Rochelle Gutierrez presented the term: Nepantla. What does Nepantla mean? My colleague, Esther Song defines this term on our teacher community webpage of Nepantla Teachers Community:

“It is the the space of the middle.  In other words, it is the space of uncertainty, tension between truths, and “grey area”.  As mathematics teachers, we strive to learn in this space by reexamining our beliefs and questioning current models.  We assert that growing in Nepantla help us form critical perspectives to better prepare our students.”

What does Nepantla mean for teachers? Well this is the space of tensions when it comes to grading, teaching styles (indirect or direct instruction), student choice, real world application, content, globlal citizenship, 21st century learning ideas, collaboration, group work, the hidden curriculum, null curriculum, and in essence: teaching beyond the curriculum.

How should we grade and assess students? Right now the current buzzword is standards based grading, and through my experiences at the end of the day, grading in itself is subjective. But why do we grade students? Hopefully to provide feedback for them to help them improve, and not to document the days they complied in class aka work completion points. I am a firm believer that grades should reflect growth and understanding; not compliance–unless someone can convince me otherwise.

As a middle school mathematics teacher in her 5th year, I am constantly in a space of Nepantla when I am trying to help build the whole child–making sure my students learn how to communicate and collaborate effectively in groups and to advocate for themselves in addition to building executive functioning skills and learning content. I get my students for 80 minutes everyday, and I am know having them for a double block period has its pros and cons. On the one hand I have the luxury of time; on the other hand I know a 13-14 kid cannot sit still in a chair being lectured to for an entire duration of 80 minutes.

Moreover, teaching the Algebra curriculum, I find myself in a place where I am trying to find creative and meaningful opportunities for my students to learn while making sure they understand the Pythagorean Theorem and Quadratic Formula.

I admit, some days I feel that the lesson went along beautifully until I receive student exit slips. So what do I do with these exit slips? Reflect and figure out how it can inform the following lesson. I could use the exit slip as a warmup and have students try and fix their errors and discuss, I can use exit slips to figure out partners or targeted groupings.

All in all, being an educator means to be a reflective practitioner. Someone who is always trying and someone who is always learning new ideas. My heart goes out to all teachers. We have hard jobs. Sometimes we go home and think that we are failures, and that is okay. I feel like the best teachers are the hardest on themselves and if we are not critical of our own practices, what impact does it have on our students? Perpetuating an outdated school system through teaching practices and curriculum is within our control, so how can we begin redefining the norms?

Whose story should we teach?

 

In all honesty, how many teachers have the time to answer this question? Nevertheless, I am one of the lucky few to ponder this question after work on Mondays when attending grad school. I have the privilege to be a student in the Master in Science in Teaching and Inquiry (MSTI) Program led by Dr. Steven Wolk at Northeastern Illinois University. I began this journey a year ago during Fall 2016.

Let me explain my journey.

Although my days start and 6am and end at 10pm every Mondays, I must admit, I always leave class fired up and enlightened by the highly rich discussions we have about education. Today, we read an article titled “Decolonizing Curriculum” by Christine Sleeter and discussed about about what it meant based off the current histories we teach in schools. Reflecting on my school education, I remember learning how Abraham Lincoln was a revolutionary leader who abolished slavery; after watching a Ted Ed talk by Aaron Huey, I realized I never learned how he had the opposite impact on the  Lakota tribe-a group of indigenous people from our country.

Moreover, I believe that so many times and based off of my school experiences as a student, history has always been presented as an event that happened in the past. Textbooks rarely or even never relate on how history influences the present let alone include current events that impact students today. Moreover, textbooks are often carry Eurocentric ideologies and nationalistic views–a student asked me today in school: “How come we learn only about history in the U.S in social studies this year?” True statement, as all of our students are required to take U.S. History in 8th grade.

Wolk @stevewolk_ presented two awesome Ted Ed videos that I recommend every educator should watch. This allows us to reflect on our current teaching practices, curriculum, and decide what histories are missing and what needs to be incorporated in our classroom. Dr. Rochelle Gutierrez, one of my undergraduate professors at UIUC wrote it beautifully in one of her research papers by asking: what windows are we providing for our students to see? Right now, I think we are just presenting one window for our students: The White American Window. And some awesome teachers are reinventing this norm recognizing that textbooks only present one window for students. I recall my World History teacher freshman year in high school scratching the textbook and presented inquiry based questions such as: What is the Cause of War? How does religion influence culture?  in which students selected topics that they were interested to answer the focus question and presented their findings after researching primary and secondary sources. The entire year we had about 5-8 big questions that we brainstormed as a class and selected for our Inquiry Based Project.  I thank James Sabathne for teaching me how to be a researcher, writer, and critical thinker which makes researching a natural endeavor when I was a 14 year old who had no idea that she would be writing a literature review on Culturally Relevant Pedagogy in the Mathematics Classroom as a graduate student.

 

 

What does this mean for educators?  As a mathematics teacher, I find myself stuck in Nepantla- this messy space of tensions between tensions. Not black; not white, but a grey area where I am trying to decide what to do that is best for my students. The messy space is a place I know that I have a curriculum and standards to teach based off of a timeline. But I recognize that my students are human beings/thinkers, and my job is to help them critically analyze the world to make it a better place. However, the mathematical goal at the end of today was to apply the Pythagorean Theorem. How do I begin to reinvent the norms to make sure my students learn the math skills to score well statistically but at the same time help them become thinkers and not robots? I not only want them to learn math, but want them to use math to critically analyze the world and use mathematical evidence to support their ideas. I understand that it is not always easy to incorporate mathematics into bigger ideas, but if I am truly an expert in my field, I know that it is possible. Today after I taught students how to apply Pythagorean Theorem to a baseball diamond, they started on their Access Project in which they are answering the inquiry based question: Which ward in your community has the best access to resources? After they answer that, they are going to explore which community is lacking resources and how can we help that community? If you are interested in this project see my previous post to get the directions page and also stay posted for my reflection on how the second year of implementing the project goes.

Math Projects: Art and Social Justice for Looking for Pythagoras Unit

I teach from the Connected Mathematics Program (CMP3) and I just want to say that the second unit: Looking for Pythagoras is my favorite book. Students explore and derive the Pythagorean Theorem on their own and it connects so much to their understanding about finding distances (horizontal, vertical, and diagonal distances). My goal is to share strategies on how I implement each investigation in the near future but right now I want to focus on sharing some of the projects I had students work on throughout each investigation. Hope this is useful!

Social Justice Project: Applying Pythagorean Theorem to Analyze LFP Access Project Dao-1leetmu

  • When to Implement? After Investigation 4
  • What are students focusing on? Which ward has the best access to resources in your community?
    • You may need to select a different local map for your community (This is a map of Evanston)
  • What is the goal? For students to apply the Pythagorean Theorem in their community and use mathematical evidence to analyze their community.

Art Projects:

  • When to Implement? After Investigation 3 and 4
  • What are students focusing on? Applying pythagorean theorem to calculate the exact distances and to calculate area of irregular shapes. Applying pythagorean theorem to calculate the different distances (hypotenuse) on the Wheel of Theodorus.

Wheel of Theodorus Art Project-14nc8jj (2-3 days)

Area and Perimeter Design Project-xt8ie9    (1 week)

Dot Paper-26k28i0

 

A kid asked me today…

“Where are the steps on how to do the problem? I need you to tell me step 1, step 2 step 3 so I can do it…”

Some teachers may provide students with step by step instructions on how to do a mathematical problem. But I want to ask these teachers, are you really helping the student learn or rather helping them learn how to memorize the steps and regurgitate it like a robot? I feel that the best way for students to learn is through productive struggle and exploration. Of course at the end of the lesson I will summarize and help students unpack ideas; nevertheless , so many of my students want the easy way out and wait for the teacher to tell them the answer.

It definitely depends on the students and some need more guidance than others, but if we as educators do not allow room for productive struggle in our classrooms, are students truly learning and thinking about problems deeply?

I can definitely see arguments from both sides. But this is how I have been trying to meet halfway. When students spend some time exploring 10-15 minutes on a problem, I recap as a whole class and ask the class what strategies have worked for them, and show the strategies that students share underneath the document camera. After we see multiple strategies we discuss which ones are the most efficient and the students help me summarize what step 1, step 2 and step 3 should be, etc. That is why I never have pre-typed notes; we create notes together as a class organically.

 

#IstandwithRochelle

My day began when I saw a picture of my professor on a Fox News Article titled:

“White privilege bolstered by teaching math, university professor says”

What a title taken way out of context.

Nevertheless, my twitter feed has been flooded with countless support and educators who recognize the importance of Rochelle’s work. Illana Horn said it beautifully: “Voicing my support for . Her detractors’ venom only proves her point about power, white supremacy, and math ed.

I have worked with Dr. Rochelle Gutierrez since my undergraduate years when I was a pre-service teacher at the University of Illinois at Urbana-Champaign. She has inspired so many teachers throughout her career, and her work is foundational in the movement on mathematics education.  She not only serves as a professor, but also as a mentor and inspirational leader among educators. She continually pushes her students to be creative within and beyond classroom walls.

This is the professor who embraces the beauty of mathematics, strives for equity in mathematics education, and recognizes the politics surrounding the teaching of mathematics. Furthermore, it is so important to recognize that mathematics has been a world contribution, and unfortunately our education system and textbooks do not often recognize this fact. Very recently, when I taught the Pythagorean Theorem, I showed students this amazing Ted Ed Video that shares how mathematics has been a world contribution.

So many of my colleagues have been inspired by Dr. Rochelle Gutierrez that they are doing incredible things in the realm of mathematics education–including developing a teacher community striving to teach math meaningfully for all students, especially for our traditionally marginalized youth.

I began my undergraduate studies knowing two things: that I enjoyed mathematics and working with students. Nevertheless, Rochelle inspired me to develop deeper ideas about: What is mathematics?  Who is a mathematician? Was math discovered or invented? What is social justice mathematics? How can we empower our students? During seminar discussions revolving around these questions, my colleagues and I pondered about these ideas, often leaving with more questions than answers. This messy space–Nepantla–allowed us to continuously reflect on teaching strategies and pushed us to question the status quo.

As mathematics transcends mere numbers and arithmetic, Rochelle modeled the beauty of mathematics in puzzles, games and brain teasers, providing undergraduates the opportunity to share this beauty to young students in the community. She initiated and ran a weekly club: iMaths, at the Champaign Public Library with a focus of bringing in marginalized middle school students to participate and run a club centered around mathematics. Undergraduates recruited students who particularly did not view themselves as mathematical. One may imagine a typical mathematics club with students working on math problems on a whiteboard, or quietly working on a worksheet. Contrastingly, iMaths served as a space for students to play with mathematics, including origami, hexaflexagons, card games, investigating the “tricks” behind such card games,  brainteasers, and various strategy games. Students collaborated, shared their strategies, and served as mathematics ambassadors to recruit their friends and peers to join the math community.

I can only count a number of impactful teachers in my education. Dr. Rochelle Gutiérrez was one of the few teachers that transformed, inspired, and supported me in my endeavors. I recall my countless nervous interviews searching for my first job. I would call Rochelle on the way home sharing with her how my interview went and she gave me advice for future interviews.

It saddens me that Fox News took Rochelle’s work out of context. I am so excited to read her new publication. #IstandwithRochelle

Nevertheless, I am hopeful for the future. Professor Matt Felton-Koestler @FeltonKoestler  wrote an amazing blogpost in regards to Privilege and Oppression in Math Ed.

Teaching Philosophy Then and Now Reflection

Right before I graduated from University of Illinois at Urbana Champaign, I was required to write a Teaching Philosophy. This was what I wrote in Spring of 2013: College Teaching Philosophy in 2013 

Reflecting on whether much has changed on my teaching philosophy, I recognize there are foundational beliefs that I feel very strongly about. When I stated “I aspire to create a community of active learners,” I truly meant that. I do not believe that students can learn meaningfully through merely taking notes and listening to a teacher lecture for an extended period of time. I find myself very lucky to be in a supportive school district that coincides with a lot of my beliefs in teaching. We use the Connected Mathematics Program (CMP3) which allows students to explore and to think about mathematics deeply through a Launch, Explore, Summary model. Furthermore, I get to teach students for 80 minutes everyday so that they have time to explore and process new mathematical ideas.

Then: From my education, I experienced a lot of direct instruction.  I remember going home with 20 practice problems to complete every night; skill and drill was the approach. I recall memorizing the Pythagorean Theorem and the Quadratic formula in 8th grade without really understanding what those equations meant. Math was a lot of rote memorization for me as a child, and I sadly, I was good at memorizing. It was not until I was a college student majoring in mathematics when I started making more connections and thought about mathematics more deeply. Struggling through Abstract Algebra and Abstract Linear Algebra and writing proofs, I began to making deeper connections in foundational mathematics at the secondary level. I made a vow to myself that once I understood the concepts that one day when I teach it to my students, I will not ask them to memorize but to help them understand WHY the mathematical concept works.

Now: As we are wrapping up our unit on finding the shortest distances, students had the opportunity to explore how to find the exact distances and formulated the Pythagorean Theorem through their investigations. I did not start the unit telling them to memorize a^2+b^2=c^2 and it is incredible to see how deeply students understand. Below are some student activities that helped them explore the Pythagorean Theorem.

Area and Perimeter Design Project

Students find exact diagonal distances by drawing area of tilted squares and square rooting the area to find the side length.

Students learn that the square root of the area of a square equals the side length of that square.