2.08.2014

DO PD right: do it YOUR way

2014 has been the year of the professional development binge. My weekends and winter break have been filled with summits, workshops, edcamps, and trainings. I can't remember the last time I slept in or had a full day to switch out of teacher mode. My colleagues think I am crazy, tell me I'm going to burn out, and that I am over-invested in my profession.

Thing is, the job is hard enough 5 days a week. And when you take into account teachers ALWAYS bring their work home, even if it is just mentally hashing out lesson plans if they are disciplined enough to not physically take it home, it is very much a FULL TIME GIG. So why add more to the workload?

Most teachers don't realize the power of good PD because they have never experienced it. Good PD takes away from the workload, even if it means giving more time out of your schedule. It connects you with people who have the same vision of student success. These people affirm your frustrations and show you how you can be bigger than your hurdles. You walk away with tools and resources to make your job easier. They make you feel like you are a rockstar teacher. You leave knowing your potential for greatness and the ambition to realize it. Good PD PUMPS YOU UP.

Why is it that most teachers don't have positive associations with PD? There are two types of PD: the PD you choose and the PD you are sent to. All teachers have been sent to bad PD. They have their prep times wasted on poorly run PD meant to indoctrinate or satisfy an administrator's checklist. Not maliciously, of course. Administrators (most) authentically want to help teachers and see PD opportunities as a way they can give the classroom teacher a hand while also fulling their district level responsibilities. Unfortunately, these PD session often lack a place for teacher voice, questions are not heard, and teacher concerns are not honored. Administrators don't realize the PD is really being built for them, not the people they are trying to help. Because these broken models are not built for teachers, they create a sense in the teacher attendees that PD isn't for good teaching, it's for good compliance. No one wants that. My most frustrating PD (and least useful) is typically that which I am sent to, not that I choose for myself.

Trainings are part of the job. Compliance is real and serves a purpose. We often can't escape bad PD, but we don't have to let it be the ONLY PD we ever experience. As teachers, we need to actively seek out good PD. Our practice and professional happiness depends upon it.

Good PD is the only reason I am still in the classroom. It helps me cope with the challenges of an imperfect system that sometimes makes my classroom a mathematics dumping ground. It connects me with people who understand good teaching is always in beta mode and NO ONE ever has it ALL figured out. It's not about certifications or resume building. It is about relationships. Relationships that remind you that kids matter. That the hard work is worth it. Most importantly, that it's OK to care that much. In fact, it's more than OK. It's critical to the advancement of the profession.



What was the last good PD you attended? As soon as you are feeling drug under by the current of reform and change, passive aggressive peers or communication frustrations with administrators, sign up for some good PD. Find something you love, or just something you are curious about. Find a group of people and run with that PD pack. There is a TON of low cost/no cost PD out there. Go to an edcamp (free), a Saturday seminar put on by your local university's school of education, a workshop offered by a professional organization or museum of science (cheap). Do an edchat (free). Get on twitter (free). Read blogs (FREE!!!!). Splurge on a regional conference, write grants or push admin to send you to a national conference. Get out and talk to people. IT WILL CHANGE YOUR TEACHING LIFE.

No one is going to send you to good PD. You have to get out and do it yourself. I go because I feel unstoppable when I am with my people. My peers build me up, celebrate my victories, and connect me with resources that help me be even greater. They see potential in you that people at your site might be overlooking and encourage you to dream big. I started by attending a Google Apps for Education summit because I was interested in making a Google site.  Now I am hooked. I get to share my experiences by presenting at conferences. I swap lesson plans on twitter at crazy hours. I finally applied to grad school after working with a presenter who pushed me to take the plunge. Good PD has connected me with a network of professionals just waiting to hoist me up on their shoulders when I finally figure out how to do something right. I wouldn't be as successful in my classroom without it.

1.06.2014

From a different angle

My dental hygienist, grocer, and local waitstaff will all tell you how awesome my job is because I have all this time off. Just like they clean teeth, pack bags, and serve tables for the pure joy of it when they are "off", I have spent most of today trying to figure out how to pack approximately 100 days of learning into what is left of the less than 90 days of instructional minutes this school year. Am I am overwhelmed. I am terrified my students aren't going to learn. And I have no idea what to do about it.

Earlier this week I was excited to get back into school mode: great causal professional development conversations, the upcoming Google Apps For Education 1:1 summit this week and an EdCamp this weekend all have inspired me to go out, be great, and change the world. But then I sat down and tried to pace my first unit of the semester and I was hit with an overwhelming flood of anxiety. The kids aren't going to get what they need, and I have no idea how to fix it.

What do these kids need? Exposure to mathematical ideas or an meaningful experience in mathematics? What I am told I need to do for students and what my students tell me I need to do for them conflict completely. I need to step back and rethink my options before I let this imbalance negatively influence my attitude this semester. I could be angry with my administration for all the changes they are throwing at us, even after promising they wouldn't let this happen. I could resign to just teaching what I'm told so I make sure the kids are exposed to all the materials they need to make the curriculum shift next year. I could get angry with my colleagues for not working together to develop a plan to combat this. I surely felt all of these things today when I took a blank pacing calendar and started filing in all the instructional minutes I lose to testing, PLC meetings, the new Response to Intervention Pilot, and professional development pull outs. Then taking into account the standards I didn't teach last semester because the kids needed more time to gain mastery. Then trying to make sure my pacing would allow me to collaborate with my PLC (required) for the Intervention schedule. Then keeping in mind that many of my students need additional time to gain understanding and I promised them we wouldn't move on until everyone who is trying gets it, so we will likely get behind again. And then I have to teach the extra standards that were left out before we switched to Common Core, big units like Statistics, Probability, and Conic Sections that the kids wont get when we switch to integrated next year unless I find time to teach them.

You see, I don't want to be the angry teacher that is always bad mouthing the system, but it's hard not to let that impulse take control when you feel like the world is conspiring against your students' learning. I'm trying so hard to incorporate mastery learning, literacy in mathematics, problem based learning, collaboration, and technology, but my instructional minutes just keep disappearing. All of this obsessing and freaking out done in isolation because we are not given adequate planning days to prep for the upcoming year. I want to scream for help at the top of my lungs, but I am terrified that it will be heard as weakness, whining  or just ignored all together. I don't want to feel like this. I just want to be a good teacher. Anger and resignation have gotten me nowhere so far, so I want to try a different approach. Maybe things can be better if I can approach this challenges from a different angle.

I need help finding that new angle. I don't know where to go from here. I had planned a solid triangle congruence unit that incorporated exploration, writing, collaboration, and multiple approaches to a problem. I wanted to the kids to try to write proofs of the same concept using different perspectives so they could capitalize on their strengths to fortify their weaknesses. But when I integrated it all into the big picture, I realized that I would barely have time to teach Area and Volume (traditionally the last unit) before the year is over, and would completely miss all the backfill standards I am am being asked to teach as part of the common core transition. When I scaled the unit back, I realized it didn't make much of a difference, there still isn't time in the year to teach what I am expected to teach. Not even close.

What happens to my students if I teach for mastery and we don't cover the materials? How will impact their success next year? In college? Will they feel betrayed because other teachers will expect them to have knowledge I was trusted with imparting? Will they feel cheated when they realize the math class they actually started to understand didn't even cover what they were supposed to learn? Will it damage their ability to see themselves successful in mathematics?

I worry obsessively about failing my students. I think most teachers do. We resist change not because we are lazy or believe we have it all figured out. Mostly, I think teachers push back because we are not convinced that the risk to our students is worth it. We are protecting our students, not ourselves,  because no one has shown us enough evidence to believe in an idea's success. I can't remember the last time I was asked to try something new in my classroom, and that proposal was accompanied by measurable evidence of success and training to ensure success could be replicated in my own classroom. I have tenure. I don't need to protect myself. But my students, they need advocacy, because no one else is looking out for their mathematical education.

Certainly, my situation is not unique. How are other teachers responding to the pressures of change? How do I gain a different perspective? How do I calm my anxiety and confidently go forth and teach those kids? It's days like this I wish I had a mentor I could call up, vent, and find a solution with. It's days like this I curse the isolation that can come with the profession.

1.01.2014

Believe in the Best

I'm still trying to figure out the whole online professional learning network culture thing. I have these ideas of how I want things to be, or how I believe they should be, and become quickly frustrated when 1) Reality proves otherwise; and 2) I can't figure out how to adjust one or the other to make it work. For instance, Twitter is a tough love for me: I don't have much patience to filter through pictures of people's lunch or kids to find gems for my classroom. But I keeping reading and hearing about how powerful a PLN tool it can be, so I am trying to keep an open mind. 

This is where Sergio at Call Me Coach V really drives me nuts because not only does he regularly post pictures of his admittedly adorable son on his twitter, but he also tagged me in one of those pass it on questionaries from my adolescences. Doesn't he get it? My blog is supposed to be professional! How am I supposed to be the vision of a game changing educator I have for myself when he is asking me "Michael Jackson or Madonna?". This is the guy who is supposed to be bringing me into a PLN, not destroying it! And then it hit me: this guy is trying to bring me into a PLN. Maybe I need a different perspective on PLN culture...

My mantra for 2014 is to "Believe in the Best". Believe in the best for myself, believe in the best for the people around me. It is going to be the first thing I tell myself when I wake up, the last thing tell myself before I go to bed, and something I am going to try to reframe my perspectives in this new & exciting year. So in the spirit of believing the best, I'm going to give this a try. After all, you do silly things in the classroom to build relationships. Why not in a blog as well? I won't be hurt if you stop reading here :) If not, read on see my silly responses to his Sunshine Post:

11 Random facts about myself:
  1. I don't like raspberries. Blackberries, blueberries, strawberries are all good. Raspberries are awful. In all forms. Even though I love to eat, and eat a lot, raspberries are a non-starter.
  2. I have a bucket list and I try to accomplish at least one a year. In 2013 I ran a sub 2hr half marathon. In 2014 I hope to learn to surf, and maybe get 6 pack abs. In 2015 I hope to run Boston Qualifying time  (3hr 30 min) for a full marathon. 
  3. I haven't been athletic or fit my whole life. I came into running 6 years ago to manage depression and get ready for a wedding (not mine), and I've been doing it ever since. Now I'm kinda crazy about it.
  4. I ran the Boston Marathon in 2011, but not because I qualified with a fast time. I won an essay contest on a blog and had my entry sponsored. The Boston Marathon had been the one of the top 3 biggest influences on my life.
  5. I majored in Religious Studies at Chico State. Most people who know me as a math teacher are really surprised and sometimes intrigued to learn this.
  6. Although I was baptized Free  Methodist, I most closely identify with Zen Buddhism and practice regularly but independently.
  7. I have no tolerance for violence and I find graphic violence and excessively crude programs deeply upsetting. Because of this, I rarely watch TV. I only have internet, no TV programming at home so I control what I am exposed to. 
  8. My mom is my best friend. She is the most impressive woman I will ever know and I strive to possess even a fraction of the strength and grace she has modeled throughout her life. She is truly incredible.
  9. For a long time, I wasn't sure I wanted children of my own. Now I know I really would love to have a daughter. That really makes the whole kids thing complicated...
  10. My parents save the Sudoku and Kakuro puzzles from the paper for me every day, even though they only see me a couple times a year. I love them so much (My parents, but I really like the puzzles too).
  11. People come up to me often and believe I am someone else. I get called Jennifer a lot, but also Lauren or Stacy. I've even recently been asked if I have been on TV or if I am a celebrity. I must have a pretty convincing doppelganger out there, or maybe I am more warm & inviting than I perceive myself to me. Or maybe I am just too WASPy.
Sergio's Questions:



  1. Best moment of 2013? When it became 2014? 2013 was a horrid year. The best moment was finishing the Rock n Roll San Jose Half Marathon in under 2 hours. I felt like a real runner, even though I'd been running for 6 years.
  2. Michael Jackson or Madonna...why? No, seriously, why? I pick neither. I've been told this is an essential question, so I have revised my answer to Prince. 
  3. Why did you get into education and what keeps you there? I knew I loved helping people learn early on and I wanted to do something that made a significant positive difference in the lives of others. I wanted to make up for all the teachers that failed my brother while he was in school, and that is a big part of what keeps me there. I know teachers make a difference.
  4. What is something you have done/made/accomplished, that you are most proud of? I am the first person in my family to earn a Master's Degree. I'm also really proud to have completed 4 marathons. Both have changed who I am as a person.
  5. If you were not in education, what would you be doing instead? Counseling & Psychology? I can barely remember life before my career switch.
  6. Best "moment" in your career as a teacher/leader? Notes from low and middle achieving students telling me they like math for the first time ever. When kid who is barely passing tells me they like proofs. It's teacher crack.
  7. Best gift you ever gave someone? Taking my mom to Pt Reyes for her birthday. One of the best weekends i've ever had in my life. I love her!
  8. Share something charming/weird about your family: We like to scare each other. We hide scary masks in weird places and hide in dark places to jump out and terrify one another. I once hid in a coffee table so I could pop out and scare my mom. She returned the gift with a scary clown mask in my closet.
  9.  What is your best personal gift/quality/strength? Perseverance and determination. When I set my mind to something, I do it and I do it well. It's all or nothing.
  10. #bestdayever? Running the Boston Marathon with a qualifying time , then celebrating after with my family and my boston peeps, chocolate milk and beer. Everything I love in one place!
  11. What are you most excited for when you think of 2014? Changing the way I play the education game. I'm ready to rub shoulders and make make a splash with the movers and shakers of math education. I'm ready to love what I do, believe I am good at it, and not let anyone convince me otherwise.


11 bloggers I'd like to know more about:

Sarah Rubin (I want to be meet her!)

(OK, it's only 3 because I'm still figuring this all out. But at least it is 3!)

Questions/Statements for my bloggers:

  1. If you could teach in a different subject area, what would it be?
  2. Public education or private education?
  3. If you had to make a New Year's resolution for your classroom, what would it be?
  4. Share someone/something that allowed you to view yourself differently.
  5. Funniest slip up you've ever made in front of your students?
  6. Eat out or eat in?
  7. Favorite blog you've been reading and why.
  8. What's the best professional development experience you've had an what made it so great?
  9. Where do you see yourself in 10 years?
  10. What song best describes you, as a teacher?
  11. Favorite book of all time.

Here is your Task
  1. Acknowledge the nominating blogger.
  2. Share 11 random facts about yourself.
  3. Answer the 11 questions the nominating blogger has created for you (see below).
  4. List 11 bloggers ( I don't know 11 bloggers so I tried my best)
  5. Post 11 questions for the bloggers you nominate to answer, and let all the bloggers know they have been nominated. Don’t nominate a blogger who has nominated you

12.31.2013

Interactive Notebooks

What is an Interactive Notebook?
Student interactive notebooks

Interactive notebooks are traditionally built into blank composition books or constructed using loose leaf paper in a three ring binder. It aids students in organizing input (lectures, notes, group activities) and output activities (homework, reflection activities, other practice), making materials organized, accessible, and easy to use. They typically contain a table of contents in the front to organize topics and assignments. Although many of the mathematics teachers use the traditional composition book, I have adapted the idea to construct individual notebooks for every unit. I've found my students do better breaking the year into smaller chunks, and the new unit allows time for reflection, revision of habits, and new goals. If they have a bad 3 weeks, they can start over in their next notebook. My TAs build them and I provide them free of charge at the start of each unit. My notebooks contain a page of reflective questions in the front, a table of contents, section to complete the daily warm-up, a page for each day of instruction with a blank sheet opposite (this means no double sided printing for instruction days), and a grading rubric on the last page. Some units have all the graphic organizers pre-printed, but now that we have switched to the Common Core standards, I haven't had time to create all the handouts before the unit, so pretty much all the pages are blank. I make some student books with graph paper to accommodate students with disabilities or severe organizational/penmanship challenges. Other students have a sheet of lined paper they slide behind the page to help provide structure on the black paper (their idea, and it is genius!).

Why Interactive Notebooks?

Fact: the prefrontal cortex, or executive functioning center of the brain, is not fully developed until the mid-twenties. So why do we expect high school students to have the whole organization & planning thing all figured out? I spent my first year of teaching agonizing over lost and missing notes & assignments. If they did manage not to lose it, it went straight into the trash can as soon as it was handed back.

Luckily, our science department is filled with rockstar teachers. A physics teacher and chemistry teacher had been using interactive notebooks with great success, and I immediately knew they had to be adapted for the mathematics classroom. Midway through my second year, I dove right in and it is by far the best decision I have made in my entire teaching career. I'm in my 3rd year of implementation and have used them for both Algebra 1 and Geometry. 

Being an unexpected math teacher, I was shocked when I started teaching high school and my students didn't do homework. SHOCKED. This doesn't happen at these proportions in elementary school, so I naturally I took it very personally. Am I so bad a teacher they didn't understand the lesson? Am I so boring they don't care? Do they hate me so much they are trying to get me fired by failing to learn the materials? Finally I stumbled upon the correct question: How can I motivate and engage my students to learn both inside and outside the classroom? Interactive notebooks were the answer.

The interactive notebook accomplishes three BIG things that increases student likelihood for success: Increases engagement in classroom and homework activities, facilitates reflection on the macro and micro levels, and helps students organize their work in way that empowers them to their best. On Back to School Night & at parent conferences I introduce them as an accountability, encouragement, and support tool. Tutors and support teachers around campus rely on their structure to help my students. No exaggeration, interactive notebooks were a game changer for me (and my students).

Creating an Environment for Interactive Notebooks

A surprising number of my students arrive to school with NOTHING. No backpack, no notebook, not even a pencil. The likelihood of this student taking useful notes and engaging in classroom activities? Pretty small. Now, put a pencil box on this student's desk with scissors, highlighters, erasers, glue sticks, protractors, and compasses. That box makes a powerful statement: you want EVERYONE to learn, and at HIGH LEVELS. People will tell you that you are denying kids the valuable lesson of responsibility, that giving them everything enables them to be lazy and apathetic. Remember that prefrontal cortex? Before it is fully developed, it requires a lot more energy to do little things, like remember a calculator, highlighters, and color pencils (not to mention the problem solving that comes with math). I view my room as a learning lab, not just for math, but for school skills as well. I encourage them to try the methods we use in their other classes. I show them that there is payoff for being prepared and organized. Pretty soon, they start bringing highlighters for their other classes. Former students stop by to make interactive notebooks for their new math classes that don't use them.

 The supplies can get expensive. We were told by our principal that we can no longer offer extra credit for donating supplies (despite the fact it was nominal and never really changed a grade), and my department chair told me there is no money in the budget to restock the boxes for second semester. I spend a lot of time begging family to donate basics (my mother is our angel), and parents of students I've had multiple years usually send in supplies here and there. I make sure to go to any supply give-a-ways and hit up the back-to-school sales hard to build up enough to get us through the year. If your school can not financially support this, you will have to get creative. Be careful spending your own money; the kids steal and destroy the supplies (even the good kids have bad days). I notice when my classroom management gets relaxed, the destruction and theft increase as well. 

Notebooks can get messy. Any teacher who has ever done interactive notebooks will tell you the secret is in pre-cutting the handouts as often as possible. Another idea I plan to try next semester is putting a small scrap bucket in the middle of each table group so bits of paper don't go into the pencil boxes or on the floor.

Most of all, students need to see value in maintaining a high quality notebook. Out Geometry team allows students to use notes on assessments, so my students are motivated to work hard on notebooks not just as a study tool, but as a test taking tool as well. When notes are missing, or homework is sloppy or incomplete, they have nothing to fall back on. Being able to use the notebook on the test is a HUGE motivator for my students. Students get attached to their work because for many, it is the first time they have something to be proud of in a math class.

Inside the Interactive Notebook

The input/output model for my interactive notebook is very simple: notes/class activity on the right, daily homework assignment on the left. My classes are composed of many English language Learners at ALL levels, as well as mainstreamed special education students, so the need for scaffolding through graphic organizers is critical. Nearly every day, I create a graphic organizer for my students to paste in. Sometimes it support vocabulary development, other days problem solving or seeing patterns/relationships between ideas. We have a routine, and if I ever miss a detail, the kids are all over it. Our learning objective is always at the top of the page under the title, and we constantly refer back to it through the lesson. I frequently ask the kids if what we have done so far fulfills the objective. We use the objective as we write to predict relationships and solutions, as well as frame the language for our responses. Any time we have a new word, we draw a picture or diagram to support it. Sometimes it even gets silly as we find clever ways to remind ourselves what is important. I remind them that this is not a math skill, everything we do can be done in any other class with any other teacher. I try to train them to be actively engaged with the lesson, no matter who is giving it to them. We end each lesson with a summary statement at the bottom of the page, answer a question related to the objective. I give students an optional word bank or sentence frame on the board to help them put their ideas into words. Students struggling to develop their mathematical language use all the scaffolds. My high achievers use the scaffold as a way to check their work. 

Modeling and language are the two most important features of the notebook. Students tell me they have never written so much in a math class. They also tell me this is the first year they have taken math notes that make sense, that they are proud of their notes, and that they find their notes helpful then completing assignments, studying, and taking tests. I am extremely impressed with how much my students' mathematical literacy grows over the course of the year, and the interactive notebook is a key component of their growth. The input side isn't just vocab or just examples of how to do a problem. It contains explanations of processes and relationships that promote sense-making. This aspect of the notebook is very important.
Class notes: objective, vocab/theorem, modeling, sentence frame, and summary. No graphic organizer provided, but all their notes look just like this. Amazing!
Graphic organizer for reading assignment on writing paragraph proofs. Students read an article, completed the outline in small groups, and reported back to class. Their versions were highlighted better, an they let me know it!
Graphic organizer on left side summarizing process, student practice on right. GO folds down to reveal learning objective, summary (not shown) at bottom of page.
Notes for algebraic process. Objective at top, vocab w/diagram, then step by step example with explanation & justification that we did as a class (they did the steps...they did not copy me doing the steps!)
Lastly, it is important I note that I model EVERYTHING that goes into the notebook under my document projector. They follow along as I write the notes, show them what highlight, and explain why we are organizing and emphasizing. Every students knows what their notes should look like, and because I do this with every class period, each class has it's own copy in the front of the room to reference if they are absent or just want to check their notes against the class set. In the beginning, I do most of the organizational work, but as the year goes on, I ask the kids to predict what should be highlighted, or what goes next in the notes. I also rely on card calls to have students work through every step of a problem; I never "give" them the answers or "tell" them how to do it. This aspect of the notebook keeps them actively engaged the ENTIRE period and it helps them have ownership over the lesson as they play the teacher for a moment. Some teachers feel this sucks the creativity out (it might) and fails to teach them to be independent notetakers (see note of prefrontal cortex development). If I were teaching gifted learners, I would not provide the scaffolds I do. If the language is not accessible, the math becomes mystical instead of magical. The structure and routine is our access point, so by the end of the year we can get creative, think critically, and have fun. Without the notebooks, we were so burnt out and discouraged by the end of the year the magic was gone and math wasn't fun for anyone.

Grading Notebooks
Student reflection inside cover of interactive notebook. Good feedback about tech compatibility, insight about why HW is not getting done & where student needs help.

Inside the cover, there is a reflection/self assessment that students are required to complete before I will grade their notebooks. Students use the rubric in the back to grade their own work and answer questions that give me insight into the quality of their work and the honesty behind the self grading. I collect each notebook after the test and give each student a score out of 10. We do it together for the first 2 notebooks, then I expect them to self assess on their own the night before the test.

The kids are pretty accurate in their grading. They are brutally honest about whether they did homework, and after a few rounds, you know who grades too hard and who inflates hoping you aren't paying attention. I use the score to do my own grading, quickly flipping through for completion, organization, and attention to detail. I don't look for correct answers; I mostly look to see if they did the homework, if they graded their homework (shows if they did the HW on time or copied it from someone after the fact), if they went back and fixed mistakes in their HW, if their daily notes are complete and highlighted, and if they included the daily summary at the end of each lesson. It takes me 1-2 minutes per notebook to read, comment, and grade, which I don't find burdensome. I usually grade them in the front of the room while another class is testing, and kids usually get a score +/- 1 point of own assessment. Without the self assessment, notebooks would take forever to grade (hence why I do not accept them if the reflection is not complete). The reflection also requires students to be honest with themselves about the quality of their work and the effort they are putting forth. I get to leave comments, get feedback about what challenged students the most, and leave notes of inspiration specific to each students goals. 

Future Notebooks

I would really like to move back towards standards based grading, and would like to explore how to incorporate that into the notebooks. This would include adding progress monitoring elements, perhaps to the table of contents. I think if there was a running record of how a student was scoring on formative assessments, as well as an added element of self assessment beyond marking correct/incorrect, students would be more motivated to complete assignments, as well as go back to fix their errors. Seeing data could also help students be more precise in their reflection and more accurately predict their score on summative assessments. 

I also want to change my approach to homework overall. Lessons need to be shorter and students need more time in class to practice. Homework needs to be finishing the practice, not starting all over again in isolation outside of the classroom. I really liked how homework sets were differentiated for my Algebra classes, but I am struggling to realize this for geometry, as that course is much more textbook driven due to diagrams and shapes. Ideally, my geometry students would have a choice of the level of challenge they feel prepared for each day (this worked incredibly well in the Algebra classes), but again, the textbook limits this and the workload to create differentiated Geometry problem sets is not within my current ability.

The notebooks are continually adapting to student needs, workload constraints, and my own professional development. I'm excited to see where else they will grow!

12.24.2013

Paragraph proofs


photo credit: http://aardvarkmath.blogspot.com
Being an unexpected math teacher, I learned to teach Geometry from the textbook. This meant subjecting students to the horror that is 2 column proofs. For those of you who blocked proofs from your high school memory, a proof is a logical argument that explains why something is true. This year we only write paragraph proofs, and I will never go back. Yes, my population is nearly half current or reclassified English Language Learners. Yes, a disturbing number of my students come to me scoring basic or below on state tests in mathematics. Yes, I have a fair share of mainstreamed special education students in the mix as well. So, why does it work?

Language is the most powerful tool we give out students. Being able to express yourself is empowering and fulfilling. So much of mathematics is mystical and inaccessible to students. A labyrinth of patterns and algorithms, memorizations of tricks and processes to get the one right answer.  Student lose interest in mathematics not because they don't want to know, but because they tire of not having the language to know what to ask or how to ask it. The mathematics classroom rarely honors what students know if the knowledge is partial. Paragraph proofs help change that. Mathematicians write paragraph proofs. If we want to empower our students to be successful in math, we need to empower them with the language skills that enable them to be successful mathematicians.

I always cringe working with two column proofs because so much is dependent on putting the correct pieces in the correct place. This approach requires the student to have a clear vision of the solution and a precise articulation of that vision. My students live in a math fog perpetuated by years of mediocre mathematics instruction. It is unfair for me to ask them to perform a high level task they haven't been prepared for. Paragraph proofs allow them to tell me what they know. It says "hey, it's ok you don't remember the theorem. It's great you remembered what the theorem tells us, and you deserve credit for that understanding". Here are the biggest changes I have seen in my classroom as a result of teaching paragraph proofs:

1). Hardly any students leave a problem blank.
2). Students are more willing to collaborate in groups to practice writing.
3). Students are more reflective on their work and even REVISE to improve arguments.
4). Students come up with crazy creative ways of thinking about the problem outside of the axiom model.

Most of all, students LIKE proofs. For the first time, many of these students feel comfortable writing about math. Yes, they still complain, because writing about math is hard, but they are open to the process because paragraph proofs give them a voice in the math classroom. This is the first year students have told me they enjoy writing proofs. Nothing in the world of geometry could make me happier! Now to figure out how to transition to proofs in google docs ;)