## The Day I Didn’t Know a Math Standard I Taught

Two weeks ago it happened again. The dreaded moment I realized I didn’t understand the standard as well as I thought. It was demoralizing. I didn’t know the standard I was asked to teach my students. It doesn’t happen often but it does happen. I’ve contemplated making a blog post about this very topic but have always decided not to. I was leery of making myself vulnerable. Until now.

After 15 years of teaching math, I would say I know my content well. I’ve always loved math. I’ve unpacked standards, repacked and unpacked them again. For 10 years I wrote questions, based on standards, for our state test for every 7th and 8th grader in the state. The questions were quality and went through a battery of tests to make sure they were valid. They passed.

The most recent standard I thought I was teaching to my 8th graders:

CCSS.MATH.CONTENT.HSG.SRT.D.9

Derive the formula *A* = 1/2 *ab* sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

The key word here was, “derive.” My students have always used the formula when finding area that involved trig ratios but never derived it. I looked at the standard and thought, “how does one derive this?” I honestly didn’t know how to derive it. I found a video online and, after quickly watching it, I quickly remembered how. The guilt then set in. How could I have *not *known how to derive the formula? My instruction and assessment both changed. Last week I gave my students the assessment. The question simply stated, “Derive the formula *A* = 1/2 *ab* sin(C) for the area of a triangle.” All my students demonstrated proficiency.

If there is one thing Standards Based Learning (SBL) has done, it has made me a far better teacher. I started SBL last school year. All of my assessments were now reported to standards. I made detailed rubrics that would guide students to proficiency. Prior to SBL, I had used standards in my teaching. For many years I would occasionally look at the common core standards either at a math meeting or on my own while planning. I went on with my teaching. To give myself some credit, I was teaching nearly all of the standards. I just wasn’t teaching them as in-depth as I needed to. I thought I was but when I started making rubrics, it was eye-opening. I had to make 4-point rubrics that went into detail about how students could demonstrate proficiency on each level in each standard. *This alone* is what has made me a far better teacher. This was my accountability. When standards drove my instruction, I became a master of the content. When standards didn’t drive instruction, I fooled myself. I taught my content first and then when I occasionally looked at a standard, I would tell myself, “Yup, I taught that.”

How could I ask my students to demonstrate proficiency on standards that I didn’t know well enough? I couldn’t.

Last year was an eye-opening year for me. I not only knew my standards, I lived my standards. Everything in my classroom was based around these standards so I had to get it right. I did. My students made more connections between concepts than ever before. I watched my students not only make connections across concepts, but also across grade levels. For example, instead of students learning Pythagorean Theorem (P.T.) in 6th grade to find missing sides of triangles they now learned that the P.T. and its converse are conditional statements as well as finding missing sides. In 8th grade they make the connection to conditional statements in geometric proofs. They then proved the Pythagorean Theorem from triangle similarity. When students learn about circles they will derive the formula of a circle all because of P.T. It all correlates. It all meshes. *It makes sense.* Students are aligning the concepts vertically across grade levels as well as linearly within the class.

In year two, I continually strengthen my understanding of the standards. SBL has made me keep myself accountable. I am always striving to get better. In my classroom, it’s okay to make mistakes. Failure is a part of learning. I want students to have a growth mindset and use these setbacks as ways to improve. Failure is a beginning, not an end. If I’m going to ask my students to reveal their setbacks, then I have to lead by example. Not knowing my standards in-depth was my setback but I used it to grow. I used it to improve. I will never stop learning.

## The Day a Student Threw Away His Math Work

In my flipped classroom, students work on the practice in class. The practice can vary. Students will sometimes do an activity while other times students work on challenging problems that involve collaboration. The practice is always given to reinforce the concepts students learned from my videos. The practice is done in class while I walk around assessing students. Sometimes I ask questions while other times I sit back and watch them do the work.

Before my flipped classroom started 5 years ago, students would do homework. I would expect students to keep this homework in their neatly kept 3-ring math binder. I wanted students to have access to all of their homework in case they needed to pull it out to look at it. I would often do surprise checks to check how organized their binder was and, consequently, would give them a grade on it. I wanted to make sure students were learning math…by keeping all of their homework organized in their math binder. Sigh. To give myself some credit, I did the best thing I thought would work at the time. I’ve definitely come a long way in my ways to check for learning.

Fast forward to today. I no longer grade or collect any formative work. I constantly check this work daily while giving feedback, asking questions and leading students to revise their work. Students receive no score for anything other than summative work. While I no longer collect practice, the expectation is that students still are checking their work and answers with the answers I provide them. Students have answers always readily available to them. I strongly feel students need instant feedback at anytime while they are doing practice. This way students can revise in real-time not having to wait for me to come around.

Recently at the end of class I watched as an 8th grade student (we will call him Bob) finish his practice after he got a difficult problem correct. He exclaimed, “YES! Finally, I got it!” He had worked on this problem for about 15 minutes. I looked over at him with a smile. I then proceeded to watch as he got up, crumpled up his 2 pages of neatly written math practice that he had persevered in solving for an hour, and toss it in the air into the recycling bin. I was shocked. Appalled is probably a better word. How can someone who worked so hard on something *throw it away*!? I still thought students kept everything in a binder so they could pull it out when they study for an assessment if they needed to.

I sauntered over to Bob and asked him why in the world would he throw his work away? He responded, “Why would I want to keep it? Isn’t the purpose of the practice to help us understand the material better? I now know the material” It was a good point. Actually, it was a very good point.

I thought about what Bob said at lunch. I walked into my colleague’s office. Garnet Hillman, an awesome instructional coach, is my go to person when I have questions. I told her what happened. The replay of him crumpling up the paper and tossing it into the recycling bin replayed in my head all afternoon. Then, it hit me. Bob was right.

Why would I care if he threw the paper away? For so long, my students always did things out of compliance. Bob throwing the paper away, right before my very eyes, proved to me one thing. *Bob cared more about learning than compliance*. He did the practice and persevered through the work to learn. He reflected on his work throughout class through my feedback and by checking his answers. The learning happened! Once the learning happened, there was no reason to keep the practice. It wasn’t about compliance, it was about learning. There was no grade attached to the work, therefore, the primary focus of completing the work was to LEARN it, not to earn a grade.

Two years ago I stopped grading and collecting work as it was eating up so much of my valuable time. I honestly thought students would no longer do it since I wasn’t giving a grade for it. Just the opposite happened. They kept producing quality work. Fast forward to a day last month when I watched Bob throw away his work. Little did I know at the time but Bob just solidified everything I was hoping would happen. Students were now doing the work because of the learning, not because of compliance for a grade. There was no need to keep the work. The practice was used to learn the concept. Thank you Bob!

## Getting Rid of Time Limits on Math Assessments

In my journey to make my assessments better, my most recent change has been to eliminate the time restrictions I have imposed on my assessments. Looking back over the last couple of years I now see that I was slowly shifting away from giving students time limits as my classroom became more student-centered.

For a little over 13 years, I gave one class period to take an assessment. At the end of class, it was typical that I would collect and grade the assessments. I expected students to be done by the end of class. I wasn’t consciously or purposely causing kids to have anxiety over my tests but it was what I’ve always done and what I thought worked. At the time, I did what I thought was best but was it best for my students’ learning?

A little over two years ago, I put a lot more emphasis in creating tests that were not only aligned to my math standards but also assessed students on in-depth learning of content. As always, I created tests that I thought students would be able to finish in a class period. However, what I found out was that as I improved the quality of questions I asked of students, the tests that I created were too long and students needed more than one day to complete them. I remember how I felt on these days. I would hand out the test and as the end of class neared, no one was turning them in. I panicked. How can they possibly take this long? How can I start the next unit tomorrow if they aren’t done with the test? The rational side of me kicked in and I remember saying to myself, “Who cares?” I collected the tests at the end of class and gave them one more day. The day went on everything was fine. I made notes to myself to make the tests shorter for the next year.

Last school year, I tweaked my assessments while also changing the way I assessed students. None of the assessments I gave last year had time limits. Some students would be finished in 30 minutes while some make take 3 days. I began to let students choose when they were ready to assess and in doing so, also gave them the choice in how long it took them to complete the assessment. What happened was remarkable. The stress that was put on students to complete the test in a certain time limit was gone. The anxiety had subsided and students spent way more time and energy in producing amazing work to show their learning rather than how fast they can do it in. I wasn’t without my doubts. There was always a part of me that thought if a student wasn’t done with a test, they could go home, look up an answer and study some more. I worried that they would use this time to cheat. What would be the point of studying for an assessment if you could just get the assessment, then go home and study what was on the test? Let’s be honest though. If my students could go home after viewing my test to look up an answer or method to only write it on the test the next day the problem isn’t with the student. The problem is with the quality of tests I am writing. If I do write a quality test and my students go home to study and prepare more after they’ve seen the test, why is this a bad thing? Don’t we want them to study? Don’t we want them to problem solve? Isn’t this what we do as adults on a daily basis? We use the resources around us to make us better at what we do.

I have given unlimited time on assessments for over a year. The quality of work has improved. Students now check their work making sure their answers are reasonable. A lot of students now use multiple ways to solve a problem. Some students make their own examples to prove or disprove items. Students are making fewer and fewer math errors that would be considered minor errors. At the end of the year, my students took a final exam that align to the high school standards. This final is identical to the final given at our local high school as my students are taking the same course in junior high. There was a time limit. I informed them of this time limit early on. I told them to not worry about the time limit and to focus on the content. Even though I told them not to worry, I was worried about it. I hoped they would have enough time. In hindsight, what did I do? I sparked the fuel of anxiety once again.

Research has shown that anxiety actually causes a brain to almost shut down when doing math. Jo Boaler, a mathematics professor at Stanford University, has done significant brain research on what anxiety does to a math brain. Take a moment to watch this video on research on the brain in relation to math. One of Jo Boaler’s four math points is, “Speed is not important.”Boosting Math is a great video highlighting four points with teaching math.

While students were taking the final, it was apparent that they wouldn’t finish with the given time limit and it wouldn’t even be close. ** I made the decision that knowing the content and proving to me their learning was far more important than deciding how fast they should do it in**. I interrupted them and told them the time limit was gone. The sighs of relief could be heard and for the rest of the class period and a whole other class period the work students produced for their final was some of the best work I have ever seen in 15 years of teaching. Students were producing arguments, proofs, reasons, counterexamples and pages upon pages of extra work that

**.**

*showed their learning*For more information on Jo Boaler, the growth mindset and her work on Inspiring all math learners check out YouCubed through Stanford University.

## Math tests – Why I was failing my students and how I changed.

Why do most math tests look the same?

For 12 years I gave math tests that looked like this:

This test was created and given in 2012 to 8th grade Algebra students. I never intended to make tests that showed nothing more than doing rote memorization of skills. At the time, I honestly thought this was a great test. For 12 years I created tests where a majority of the problems were just like the problems we did in class. I then would put one or two challenging problems and the last question would be a bonus problem. It was the typical way I had always been taught and it was the way all of my tests looked when I was a student. It wasn’t a bad test. It just wasn’t enough.

I never was assessing what the kids were truly learning. Rather, I was assessing whether or not they could mimic the problems in class. Had I given my students a completely different, more challenging problem that required multiple steps and thorough understanding, they would have struggled. The bottom line.. I wasn’t assessing the standard.

In December of 2014 I remember deciding to scrap an assessment for my 7th grade students who were learning how to solve systems of equations. In my mission to give students more choice, I remember throwing out the copies of the paper test and sending them this shared document:

I asked my students to, “prove they have mastered the standard.”

My students opened this document and instantly panic set in. The students started to react:

“What do you want me to do?”

“Tell me exactly what you want”

“How long should the this be?”

“How do I get an A?”

“Where’s the test?”

It became very clear that after all of these years, I had failed my students. They weren’t concerned about the in-depth understanding of the concepts. They wanted to comply. They wanted to play the game of school they were so comfortable with. They wanted to take this test and earn the grade.

I honestly had no clue if this would work. Would my idea crash and burn? Would it take 2 days? 5 days? Did I actually teach them well enough to do what I am now asking from them? To prove understanding.

Students worked for 3 days in class on this. I gave them no direction as to what to actually do. I gave them feedback…quality feedback. One child was working through his presentation to which he said he was finished. The work he had done was superb but I looked over it and noticed he had forgotten an aspect of what it looks like when solving a system would yield an answer other than 1 or 0 solutions. I posed the question to him, “Can you have more than 1 or 0 solutions?” He looked up and said, “Wow, I can’t believe I forgot many solutions.” Back to work he went.

After 3 days, I received presentations, movies, paper tests and a plethora of explanations. It was clear to me. The work I had received was far better than any paper test I could have given. *They were proud of what they turned in because it was theirs. They had ownership of the product they produced. *I was shocked at the quality of work I saw.

Here are some examples:

In addition to collecting their projects, they would answer the questions I asked verbally. From that point on, I started to ask my students to prove understanding much more.

Let me state that I still believe in paper and pencil tests but the quality of questions I ask has dramatically increased. Questions that ask students to prove to me understanding and allow them choice in how they prove it. That’s the quality I want.

This year when testing students over quadratics, I still gave them a written test in which they had to solve challenging, in-depth problems that asked them to prove understanding. But that wasn’t the end. We went further than a test. I sent them this:

Off to work they went. I gave them no direction into how to determine the “best drinking fountain” except it had to involve quadratics. This is what I saw as I walked around the hallways:

In addition to the paper work and their verbal explanations, this is what my 7th graders turned in:

Then we went further. They built catapults to further than understanding of quadratics:

I now look at assessments differently. They are an opportunity to give students autonomy over how they prove to me understanding. I still give many paper and pencil tests but the questions asked always ask for them to prove or explain. I believe that if students truly understand the material, then they are able to explain the concept to someone else.

My challenge to you is to do something different. Step outside your comfort zone even if on the inside you are saying, “my kids could never do this.” On your next assessment simply write on the board, “Prove to me mastery over…” and see what happens. You might, too, be incredibly surprised.

## Recap! The newest tool that’s changed my classroom.

It isn’t often I come across a new tool that is so profound and unique it changes how I do something in class. If that tool doesn’t help my students for the better * and *isn’t something that is easily integrated then it’s not something I’m going to use. It must serve a purpose and make things easier for me. It is even less often that I am so excited about a new tool that I want to publicize it to everyone I know to show them how phenomenal it is. Yesterday, I found that new tool and it is called, “Recap” found at letsrecap.com. Simply put, this formative assessment tool is amazing.

Simply put…it’s amazing.

**So what is it? **Recap is a way for students to submit a video response to a question that a teacher asks through Recap. As teacher I can pose questions in video or written format to students. I set the video time limit and the due date and I’m done. Students then use their webcam or phone to submit their response. It’s that simple.

**Why do I like it so much?**

*It’s free.

*It’s so easy to use. I don’t have to input all of the names of my students. I simply give them a class code to sign up and log in and bam! They are all added.

*The videos are all gathered in a single location. I am able to click, “play all” and quickly watch each one without having to continually open each video. It really takes about 5-10 minutes to watch a class set of videos. The picture below is what I see with all of my student video responses. I’ve disguised the students and their names.

*It gives me a very quick and accurate snapshot of how well students understand the concepts. Students are able to rate themselves on how well they understand the question(s) asked. The graphic below shows what I see as a teacher.

*I can share the videos with the parents of the students by either entering a parent email or sharing a unique and private weblink.

*I can give feedback to each student. By clicking the “Leave feedback” link I can quickly give each student quality feedback on their response.

*It’s fun. Really! It is, I swear.

Here’s what I see when all students submit their responses:

**So how do I use it?** In my flipped classroom, I have students watch my video lectures at home. To check for understanding I submit a question to them about the concepts covered in the video. Students must explain the concept(s) to me from the video. Sometimes I will only ask, “Explain how to….” and sometimes I give a specific example. This gives me instant feedback on how well students know the concepts by how well they can explain it to me in a precise manner on video.

Thank you Recap for creating a tool that is so awesome!

## 7 things that happened after I implemented Standards Based Grading

It has been 8th months since I’ve fully implementing Standards Based Grading (SBG) in my math classroom and, while skeptical at first, I’ve come to realize that my students are achieving more then before. I’ve noticed quite a few changes in not only my thinking but in the overall aspects of my class. The 7 things I have noticed:

**The quality of work has increased.**Make no doubt, I still give classwork. So what’s changed? I don’t grade or collect a single piece of it. I do give valuable feedback to students as I walk around the class checking on their work but I have noticed something profound. When you take grades out of the equation of classwork, the quality of work increases. I know it’s hard to believe but it follows the theory in Daniel Pink’s book on motivation, “Drive.” He states that when you make a person’s salary high enough where it no longer becomes a factor in their job, the quality of work increased because the employee never worries about doing work for pay. They do work because they are intrinsically motivated. I find the same to be true with my students. Now that grades are no longer a factor, students don’t fret over earning that grade on each piece of work. They work because they know it’s important. It’s a profound discovery I have seen first hand and one I never would have believed had I not seen it within my own classroom. Here’s an example: (Remember again that I don’t grade this or even collect it.)**Students have changed their language.**Students no longer strive for the grade. They are never saying, “What can I do to get an, ‘A’?” I now here students tell me, “I need to reassess on the standard 7.G.4 because I need help finding the circumference of a circle.” Students know the concepts in which they need to improve upon.**I was held accountable for knowing my standards.**I am a math nerd. I know math quite well and I have always worked with standards. I thought I knew my standards well…and I did but not to the extent I needed to. When writing assessments I had to be flawless in writing questions that met the standards. It helped me to delve into my standards even farther to truly understand them.**Grading was less subjective.**With nothing factored into a grade other than content, I was no longer falsifying the grades I gave. The grade was a reflection of what the student(s) know. I grade all of my summative assessments based solely on the standards and whether or not students have mastered those standards.**Students look at the feedback.**When I put a grade at the top of the paper, students never looked at the feedback I wrote on their work as much as I had hoped. They were fixated on the grade. Once that percent and grade disappeared they started to read the feedback I gave.**The busy work is gone.**I actually feel at times like I have cheated the system that we call, “the game of school” but I no longer have hours upon hours of busy work. No longer do I have homework to grade, collect, record and pass back. It simply has disappeared. I now spend the time I used to spend grading endless amounts of work creating more meaningful lessons, videos and assessments.**The grades now have meaning.**The grades students earn are now a true reflection of what they knew. Simply put… they are now valid.

## How SBG has changed my conversations with parents.

I have always valued parental engagement in student learning. A strength of mine has been routinely emailing parents to let parents know how their child is doing in class. It isn’t uncommon that I would email every parent after an assessment and let them know how their child has done.

This school year I implemented Standards-Based Grading (SBG) and while writing my most recent round of emails to parents I noticed something. My emails looked different. They felt different. Lets take a look at an actual email I sent last year. I have blocked out the information to identify anyone.

It’s a positive email talking about how a child has done well on a test and their current grade. This is when I knew nothing about SBG. Now lets take a look at an email I sent last month.

Yet another positive email but lets compare. In the first email, the focus was solely on the grade and the percent. No where in the email was any content, any focus for improvement or anything to do with the actual *learning.* In the second email, the focus is clear. No where did I mention a grade or score. It was all about the *learning*, the content and what this child could do to further her understanding on a concept.

It’s important to note that I never once consciously made the effort to change my emails. It just happened. ** When I subconsciously changed my own focus on the content rather than the grade through SBG, that comes through in the things I do inside my class.** I no longer am putting effort in a subjective grade but rather than in the understanding of the concepts. My emails contain much more informative information about what students can do to improve. What can a parent really gain from an email saying their kid received an 87% on a test?

“Change the focus. Change the learning.”

## What do my kids do in class? – Vlog #2

As my journey of my flipped classroom continues, here is the second part of my blog series to show you what happens within my flipped classroom. This time you will see what happens during class.

## 8 Things that happened when I gave my students choice

Giving students choice. It’s a scary idea. As a teacher, it was one of my biggest fears. I found myself always making excuses as to why I couldn’t let my students have more control in my class. It all started a little over 4 years ago when a student asked if he could wear headphones and listen to music while working. My first thought was, “ABSOLUTELY NOT. That goes against everything I’ve been taught about keeping classroom control.” Ultimately I bit my tongue and let him wear headphones. I let him wear the headphones and you know what? The world didn’t end. He was on task and no longer was a discipline problem. That was the first decision to start giving my students choice in my class. Over the last 4 years, I have been giving students much more choice from when they assess to when they do the work and how they do it.

*Here are the 8 things that happened when I gave my students choice. *

1. **They choose their own seating.** I let students use the space however they see fit. They can sit on the floor, go out in the hall, stand the whole period, etc. They can also move the furniture without asking me.

2. **They learn at their own pace.** Students are now given the date at which I want mastery of the content and how they pace themselves is up to them. I now let them decide when to take their assessments as well. Some students work far ahead and some don’t (and that’s okay).

3. **They decide when, and if, to turn in classwork.** At the start of this year, I decided to no longer grade or collect classwork. It was something I always thought I had to do and if I didn’t, my kids would somehow fail. Students now only turn in the work if they need extra feedback in addition to what I have given to them in class. I still give classwork and activities and kids still do it. The quality of work is actually better than when I collected it and I am no longer spending endless amounts of time doing busy work.

4. **They perform better on assessments.** When students get to decide when to assess, they reduce the anxiety they have to cram for a test. By giving them autonomy, you let them decide much more in their own education. Class and district benchmarks have improved.

5. **They decide when to reassess.** Students get to choose when they come in and reassess a particular standard to improve. Students will now tell me specifically what standard they need to improve on and which ones they want to redo. Students now know the exact content they need to improve on.

6. **They choose what concepts to learn.** I now give students the same project each year, having them pick a math concept they know nothing about but want to learn more about. They can make any sort of presentation they would like on it but they can learn anything. I recently had a student tell me his project will be to see how Fitbit uses math to calculate the relationships between steps, calories and how it all works with technology. Awesome! I can’t wait to see the end result.

7. **They choose how to present their content.** I no longer tell students that they have to make a poster, a Prezi, a movie or any other way to present. All of these are acceptable ways to present material but let students decide. They will think of ways that you haven’t. Why should you restrict them?

8. **They teach each other.** Each evening, they get the instruction from me through flipped videos. In class, they now work collaboratively with each other. They teach each other which gives kids a second exposure to instruction. When kids can teach each other, it strengthens their understanding of the material. Nothing is more fun than sitting back and watching kids take charge! The goal of myself as teacher is to enable my students to get along without me.

## What does my class look like? – Vlog #1

As the journey of my flipped classroom continues, what better way to explain what happens than to show you. In this blog series, I am going to break apart my class and show you what happens. In this blog, I am showing you what happens as students begin class.