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.
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 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!
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.
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.”
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.
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.
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.
Recently I was given this phrase and asked what it means. Along with two other colleagues, we were asked to come up with our own blog post with the same title without reading each other’s blog post. I’ve pondered quite a bit about what it means to,
“Be together. Not the same.”
So often in the world of education, we feel the need to mimic what others do in the classroom. We are often encouraged to adopt certain methods of teaching that are used in other classrooms. I remember after a few years in successfully flipping my classroom an administrator whom, after I changed jobs, told the incoming teacher they wanted them to also teaching using the flipped model. After plenty of hard work from the teacher, it was abandoned for the traditional way of teaching through no fault of the teacher. Why didn’t it work? It didn’t work because it wasn’t her style or the methods that worked for her. Trying to mimic someone else will never work and it shouldn’t as it’s not intrinsically motivated. We must have control over our classrooms to create an environment that works best for us and our students.
As teachers, we need to have choice in our own classrooms. We need to have autonomy to develop our own pedagogy that works with our style. We must be encouraged to get better and to explore methods of teaching that we as teachers want to explore. We must also work together towards an end goal. How we get there is up to us as the individual.
When I think of “being together,” I think of a group of individuals working together for the betterment of the students and school culture. I think of a collaborative environment that encourages growth for everyone in the school. Being together does not mean that you have to be the same. Lets look at a classroom math example. As a teacher, I am teaching a unit on solving systems of equations. I have equipped my students to solve systems using a variety of tools. The end result to successfully solve systems of equations is expected of all of my students, but how they get there is completely up to them. They are together is working for the common goal yet none of them have the same pathway.
I must often remember that what works for others in their class may not work for me. More importantly, if it doesn’t work that is okay. We have to develop our own pathway to reach that common goal. It’s always important to be together. Not the same.
The methodology of testing seems to be a timeless tradition in the math classroom. Halfway through the chapter, you would give a quiz and at the end of the chapter, the students would take a test. Until recently, that’s what I did as well. During the last year, I have changed the way I assess students. While changing the way I assess, I have made some observations.
- I no longer differentiate between a test or a quiz. I simply refer to my quizzes and tests as assessments. If the purpose of a quiz or a test is to assess students over material, why do we put a different emphasis on them by calling them something different? Worse yet, I used to assign different point values or percents in the grade book for each test or quiz. By calling them assessments, it doesn’t skew the importance of what we are assessing.
- The assessments I give are now aligned to the standards. With the implementation of Standards Based Grading (SBG), I now put the standards next to each problem. While doing so, it made me take a hard look at the quality of my assessments. I also realized that there were standards that I wasn’t assessing to the extent as what I thought. I also give students the standards so they know what is expected of them. The following picture is what I put on their open-ended assessment I gave them this week:
- Students have choice in their assessment. When you think of an assessment, you often think of using paper and pencil to assess students. While I still give paper and pencil tests for some assessments, I also have been allowing students the opportunity to show their mastery of the content in the ways they choose. I have now given open-ended tests where I will say, “Prove to me you have mastered the following standards.” Students present their mastery by using whatever they see fit. Some students made presentations while other students present it on paper. In the following picture, this is all I gave them for proving 7 high school standards for analyzing lines of fit.
- Students can reassess. If you think about any part of life, we constantly improve ourselves by redoing. However, in education we often give a students an assessment and then never allow them to improve. How does this help the student understand the material? I was one of those educators who had no problem allowing a student to retake my class but never allowed them to retake an assessment. Reassessment is not about giving them the same test again in hopes they memorize the material. It’s a chance to offer students ability to improve from their mistakes and apply it to different problems to master the content. Reassessment just makes sense.
- The quality has improved. By giving students autonomy over assessment paired with better questions that are aligned to standards, the quality of what I am receiving is by far the best I have ever seen in my classroom. Students not only make up their own problems and make sense of it, they can present it to me anyway they see fit. The following pictures, handwritten work and a Prezi, are examples of what students are turning in within my classroom.
- Students perform better. It’s no surprise that with better assessments, student ownership, and reassessment comes a better understanding of content. Students are performing higher on all standardized tests and in the understanding of what they are being asked to do. If a student can explain the concepts to someone else fluently, then they truly understand the content. They understand the why and the how behind the concepts.
- Time limits are gone. No longer do I give students a single class period to finish an assessment. Just this week, I carved out two days to do the line of fit assessment shown above. After two days students weren’t finished so I am giving them another day. I am often presented the question, “Since students already have seen the test, can’t students go home and study some more?” The simple answer, “Yes.” What does it matter if students use the resources available to them to help them with understanding content? In life we have those resources at our finger tips as well. If a teacher is more worried about students looking at the test and then going home to cheat after memorizing the problems so they can get the problems correct the next day, then the teacher should rethink the quality of the assessment. I know that’s what I had to do.
- Every test is an open note test. This changed recently for me. Research shows that students who are allowed to use their own handwritten notes, they perform better. It forces students to prioritize the material to which they need to study. In addition, if given a quality assessment, students will not be able to just look at their notes without studying and be successful on the assessment. In our life and at our own jobs, we are able to look up any resources we need to in order to be successful. We should teach this to students as well.
- I don’t give a grade. All of my assessments no longer have a grade at the top. With SBG, I provide feedback and a level of proficiency for each standard. The student no longer focuses on the subjective grade, but on their own mastery of content. This is an example as to what is stapled to every assessment to show the student’s level of proficiency:
I recently gave my second assessment that I graded using standards based grading (SBG). While the feedback I gave was the same as I’ve always given, what really surprised me was how the traditional way I grade a math test was faulty and how it masked what the kids didn’t know.
Lets take a look at a typical math answer key:
I, like most math teachers, gave point values to each problem. If an equation takes 7 steps to solve I would assign 7 points to the problem. If a student makes an error and then follows through with the correct process, they would miss 1 point. If major computation or conceptual errors were made, more points would be deducted. It was a practice my own math teachers used and was one I learned while student teaching and I thought it worked well up until two weeks ago when all of that came crashing down.
While using SBG, I noticed some students had issues with a few problems on the assessment. I was not used to more than a few students getting a problem incorrect but then it dawned on me. It wasn’t the students. It was the way I had always graded a test or quiz. If I had 7 problems each worth approx. 6 points, that would be a total of 42 points. If 4 of the problems were incorrect with 1 minor error they would maybe miss 1 to 2 points per problem, they’d still earn 38/42 an A- and at the worst a 34/42 B-. The students would look at their A or B, accept that they did well, glance over the ones they missed and file it away in their binder. I always would make note of the problems students struggled with and reteach those concepts as needed.
With SBG, I was able to pinpoint the one standard from which most mistakes stemmed. I identified that concept, retaught and reassessed. The A’s and B’s that students would have received via traditional grading would have masked the concept students struggled with. Currently with SBG, students are in a cycle of consistent improvement. Students go problem by problem looking over what they missed, correct mistakes and then verbalize those corrections to me making sure students understand the why. Each student has to meet with me before reassessment. Having students explain their corrections is a powerful learning experience. They want to understand what they missed, not simply strive for the A or B.
It really opened my eyes to SBG and why it worked. I experienced t first hand the power it had for student achievement. I now could pull apart individual problems and pinpoint the exact reason or standard throughout an assessment that the student was struggling with. This is now how I report achievement to students on an assessment:
No longer does my traditional way in grading a math assessment mask what the students don’t know. It’s a freeing experience to have gotten rid of points.