Author: MaryAnn Moore Last weekend was the annual UCTM Conference. I had a great experience and left feeling pumped! Steve Leinwand was amazing! At the beginning of his presentation, my friend turned to me and said, "I feel like this man is a math education evangelist. Like someone should be shouting out 'Amen' and 'Halelujah'." Well, I may not have shouted them, but I did give a few Amen's and Halelujah's during his presentation. I'm very excited to try his 2-4-2 homework strategy (2 problems covering new content, 4 problems of mixed review, and 2 problems which require students to explain their reasoning). For me, another highlight of the conference was getting the opportunity to present. I actually presented twice - first a 5 minute Ignite talk on the Math Twitter Blogosphere (#MTBoS) and the power of community, and second a 50 minute presentation on Standards Based Grading. My co-presenter, Desirae Calkins, and I were both surprised at the level of interest and enthusiasm regarding our presentation on Standards Based Grading. Of course, I guess we shouldn't have been too surprised given that we both love it so much and could talk about it all day long. In case you missed it, or in case you came and are looking for the resources that I promised to share, I'm writing this blog post to describe how we do Standards Based Grading. What we do might not be quite right for you or your setting but we encourage you to take the general principle and adapt it to fit your needs. The Problem with Traditional Grading Methods;The purpose of grading is to give students and parents feedback that helps them to identify their individual strengths and weaknesses. Imagine that you are teaching a course about aviation. One of the important standards in aviation is packing a parachute. You teach your students how to pack the parachute and then give them an assessment on this skill. Student A and B nail it right off the bat. Student C really struggles. As the course continues and you other topics in aviation, you continue to occasionally assess your students on their parachute-packing skills. Using traditional grading methods, each of these assessments would be averaged together, resulting in a final grade of 60%, or a D for all three students. However, if you look closer, the data seems to tell a different story. Student A struggles to retain this skill and seems to be progressively getting worse. Student B is very hit-and-miss. In contrast, Student C, who really struggled at the beginning, is showing consistent improvement and by the end of the course seems to have mastered the skill of packing the parachute. So the question is, who do you want to pack your parachute? How Standards Based Grading HelpsHere's a quick overview of how the assessment/grading cycle works in my classroom. 1. Identify content standards 2. Teach the standards (using informal assessments to guide instructional decisions) 3. Formal assessment (quizzes/tests) 4. Grade the student - giving a separate score for each standard assessed 5. Provide feedback that moves the learner forward Any given test or quiz may cover four or five different learning objectives. In the past, after correcting a test or a quiz, I gave students one overall score at the top of the paper. The problem with this system is that it fails to identify in which area(s) each student needs to improve. Two students who received the same score may have completely different areas of strength and weakness. In order to give improved feedback to students, I now use Standards Based Grading. The content I teach and even the quizzes and tests I give students are essentially the same as in the past. What is different is that after taking a quiz, students receive multiple scores - one for each learning goal (standard). Students receive a score based on a 0-10 scale. Students must score two 9's in a row on a particular learning goal to earn a 10. I do this in order to make sure every student is continuing to pursue learning and to make sure that the concept is retained in long-term memory. The first time the student is assessed, the standard is entered into the online grade book as a score out of 9. The second time the student is assessed, it is changed to a score out of 10. Each time a student is assessed on a standard, the new score replaces the previous score. Update: I found that changing two 9's into a 10 became a lot of work for me to keep track of in my gradebook. My coworker, Mrs. Calkins, still follows this same plan. However, I have just started giving students a 10 for a proficient score. Since each standard is assessed multiple times and the new score replaces the old, I don't feel like this does basically the same thing with less work and record keeping on my end. Re-QuizzingIf you are going to use Standards Based Grading, you need to have a way for students to show growth. Each standard ought to be assessed in class at least twice. I usually will give one quiz each week. Sometimes the quizzes are very short and sometimes they take a whole class period. Occasionally I will give students a grade print-out and I will let them vote on which standards they would like to be on that week's quiz. Of course, I get to make the final call, but I love it when arguments break out in my class over whether the quiz should contain problems on 'Solving Systems by Graphing' or problems on 'Placing Rational and Irrational Numbers on a Number Line.' Once the quiz topics have been decided upon, I plan my classes for the week so that I spend a few minutes during class each day that week reviewing those topics. Additionally, I allow students to come after school to re-quiz on any standard. If a student isn't able to demonstrate mastery on the standard when they re-quiz, I spend some time explaining the concept to them and give them some extra practice until it seems that the student understands. Then I ask them to come in on another day to re-quiz again. I do not allow students to get help from me and re-quiz on the standard on the same day because I want to make sure they can retain the learning. Catching the Mistakes that Traditionally Get Swept Under the CarpetAs teachers, we all have our pet peeves. My middle school students aren't yet advanced enough to commit the mathematical sins that inspired the Dead Puppy Theorem and its corollaries, but fear not! They are quite capable of committing other mistakes that are just as annoying - the most obnoxious of which is their tendency to use an unequally spaced scale on graphs. This grievous error gets under my skin so much that it inspired me to create this poster and write this blog post. In the past, I when I saw this happen on a quiz, I would dock them a few points from their total score, get really annoyed, and then move on. And the problem was never fixed!! The same kids kept making the same mistake all year long. However, when I switched to Standards Based Grading, I created a standard called "Create a Graph with an Appropriate and Evenly Spaced Scale and Label the Axes". When they started getting 0's and 5's on their graph score, my students quickly stopped making that mistake. Victory! I don't grade them on this all year long, but as soon as I start seeing the mistakes pop up, I add it to my standards again. Sometimes I don't weight it as much as I do the other standards, but just having it in there helps the students with the low score identify this as an area that needs improvement. Grading vs Giving FeedbackI think it is important to recognize what grades do and what they don't do. Grading is evaluating student work and putting a number on it. It tells the student where they are. Grading is not the same as giving feedback. Feedback is giving students information that helps move them forward from that point. This could be another blog post in and of itself, but I just wanted to put that out there. If you are expecting students to make improvements, just giving them a grade is not going to be enough no matter what kind of fancy-schmancy grading system you use. You are going to need to find a way to remediate and re-teach, all of which takes time. I have found ways to do this during class time, during the flex period that my school uses, and after school. How you give feedback, how you remediate will look different for you depending on your style and your setting. Standards Based grading will help you identify which students need help, but you've got to figure out how to give them the help that they need to move forward or nothing will really change in the end. TimeI could go on and on about the reasons why I love standards based grading (more productive collaboration, more effective parent-teacher conferences, more student buy-in into learning, greater integrity of grades, etc), but I think it's worth mentioning the greatest enemy to Standards Based Grading - time. Time is the enemy of all teachers. We don't have enough prep time, we don't have enough instruction time. You can't change that. I spent several years thinking about Standards Based Grading and reading all about it and the thing that kept me from implementing it was the amount of time it would take. And then I had an 'Aha!'. I realized that I was grading my students 20% on their practice and 80% on their tests, but I was spending 80% of my precious prep time grading their homework (entering homework daily, entering late work, absent work, etc). Somehow I needed this to stop. I still wanted them to do all of the practice and be held accountable for it, but I needed to simplify this process if I wanted to start using standards based grading. Here is the system I came up with: Students get a sheet like this every week. At the beginning of each class, I look for a student who has completed the practice and showed their thinking. I stamp their homework and I stamp the record sheet using a date stamper that I picked up from Office Depot. I then hand the date stamper over to that student and he or she stamps the rest of the students in the class who have the assignment completed. If a student completed the assignment and showed an appropriate amount of thinking, they get full credit. Once everyone's papers are stamped, we go over the assignment. As I answer questions, I encourage them to correct any mistakes (this is practice after all). If students have late or absent work, these require a teacher signature for credit. At the end of the week, students turn in the record sheet and I enter one score for the entire week of practice. I keep the record sheets in a file cabinet until the end of the term just in case there is any confusion later in the term about who completed which practice tasks. I love that it's called a Practice Record! It makes it feel like band or orchestra - which it should be. Do students cheat on their math practice? Probably. They were probably cheating before, too. That's just the nature of the game. But just like in a band or orchestra class, once assessment time rolls around, it doesn't take a lot of detective work to figure out who has been doing the practice and who hasn't.
Practice is a means to an end. I've heard a lot of English teachers talk about how for students to be making significant improvements in writing, they should be writing so much that it would be humanly impossible for one teacher to read every single word of it. So they get creative about ways to get students to self-evaluate their work, peer review each other's work, etc. I think the same principle should hold true for math. We ought to be able to come up with creative ways to motivate students to practice and hold them accountable without grading every single problem they attempt as though it were a test question. If you have other good ideas on how to do this, please let me know. Just Do It!I worry you are starting to feel overwhelmed as you read through all the details of how I've made Standards Based Grading work for me. Here's the key though: I didn't start out with anything organized. I just knew I wanted to do it so I started. It was messy. I changed a lot even within one school year, but it didn't take long for me to feel comfortable and start seeing the benefits. The logistics of how my classroom works didn't come together overnight. You've got to try something and be willing to make mistakes before you will find the solutions that work best for you. We expect our students to make mistakes. It's part of the learning process. As teachers, I hope that we are professional enough to allow ourselves the same grace that we give so freely to our students. You Don't Have to Take My Word For ItThere are a lot of different ideas about Standards Based Grading and I studied a lot of them before I tried it out on my own. If you are wanting to read more, here are a few good places to start: Global Math Department: This site offers free weekly webinar PDs - another great collaborative product of the Math Twitter Blogosphere (#MTBoS). On July 8, 2014, Jessica Bogie and Matt Owen presented on Global Math Department about Standards Based Grading. You can view the recording here. Dylan Kane: Dylan's blog is one of my favorites. It is incredibly insightful and introspective and is usually right on the money with what current research says. He has recently written several great posts about assessment in general (here, here, and here) and a couple specifically about Standards Based Grading (here and here). Dan Meyer: This post and this post had a huge impact on how I think about grading Dane Ehlert: This page of Dane's blog, When Math Happens, gives a great overview of how he uses SBG and is loaded with lots of links to more resources on standards based grading Robert J. Marzano: His book Formative Assesment and Standards Based Grading is research based and the seminal work about Standards Based Grading Dylan Wiliam: One of my heroes. Though not directly tied to Standards Based Grading, no discussion of assessment would be complete without mentioning Wiliam's book Embedded Formative Assessment.
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When I first learned about math teacher blogs, Dan Meyer's blog was one of the first that I stumbled onto. I spent about half the day reading his posts, watching videos on his blog, and browsing through his 3-Act Tasks. I was hooked. In one afternoon, I'd gotten more good quality professional development from Dan Meyer than I'd gotten from years of state and district sponsored classes. And it was completely free! I'm still learning from him and still working on implementing some of the great ideas I've gleaned from him. Recently, Dan Meyer posted a video of a presentation he gave at the 2014 NCTM annual conference. It's about an hour long but entertaining, thought-provoking, and well worth the time.
Here's what Dan Meyer has to say about this presentation:
"Students generally prefer video games to our math classes and I wanted to know why. So I played a lot of video games and read a bit about video games and drew some conclusions. I also asked my in-laws to play two video games in front of a camera so we could watch their learning process and draw comparisons to our students. These are the six lessons I learned: - Video games get to the point.
- The real world is overrated.
- Video games have an open middle.
- The middle grows more challenging and more interesting at the same time.
- Instruction is visual, embedded in practice, and only as needed.
- Video games lower the cost of failure."
About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email MaryAnn at mmoore@dsdmail.net if you are interested in contributing to the UCTM blog.Speed Dating is one of my favorite structures for incorporating review in a collaborative, non-kill-and-drill manner. If you've never heard of Speed Dating in math, I suggest that you stop reading this right now and read this post by Kate Novak right now. She explains it much better than I could. Here's what I did to make it work in my 8th grade math class: Since we've been working on graphing linear equations, I made my cards by printing out some problems from the Chapter 3 Student Workbook from UtahMiddleSchoolMath.org (pgs 10-14). After cutting out the cards, I wrote the equation of the line on the back. Students had already done these problems as an assignment, but they did so poorly on the quiz that I knew they needed to revisit them. Ideally, every student has their own card. However, when you've got 36 students in a class like I do, that's a lot of problems to come up with. When I did the graphing speed dating, I made 3 sets of 12 identical cards. I then have 3 separate groups of speed daters, which works well since my room is arranged like this: This also works out well for me time-wise because I only have 45-minute class periods. If you're going to use 3 identical sets of cards, I highly recommend that you number/letter each card in the set so that they are easy to sort out when they get mixed up or lost. I learned this lesson the hard way. Each student gets their own card, turns it to the graph side, writes the equation of that graph and then checks the answer on the back. The student then is the 'expert' on that problem. Students then trade with their partner across from them and write the equation for that card. If they struggle, they ask the person sitting across from them for help. I set my online bomb timer for 1-2 minutes, depending on the class. When the timer goes off everyone switches cards back so that they are holding their original problem. The students on the window side of the classroom remain seated while the students on the wall side of the classroom move one space toward to the right. Students switch again and begin working. I found that some of my speed dating groups had an odd number of students. This is quite simple to fix. Just place a card on the empty desk (make sure it is on the non-rotating side) and have students work on that problem when they rotate to the desk without a partner. After students wrote the equations for all 7 problems (their own problem plus their 6 partners), I had students swap their cards diagonally and turn it to the equation side. I gave each student a set of coordinate grids kind of like this. Students then had to graph the equation that was written and we repeated the whole speed dating process with the same set of cards, but this time going from the equation to the graph. The results? After a day of practice, when I re-quizzed my students on these topics, they did much better! A few hang-ups still: students forgetting to write a negative for equation of lines with negative slope; students who can't differentiate between y = 2x and y = 2. Any suggestions for dealing with these two issues? About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email her at mmoore@dsdmail.net if you are interested in contributing to the UCTM blog.In my last post I discussed some of the things I learned about mathematical modeling at a recent Math for America professional development. At that same professional development, I had a conversation with a few people about modeling and developing great tasks. I mentioned that I have to practice looking for great questions, but until I'm able to come up with all of them on my own, I steal (borrow) a lot of great content that people share online. Over the next few weeks, I will write blog posts to share with you some of my very favorite modeling and number sense resources. Let's get this party started by discussing my all-time favorite number sense resource: Estimation 180Website url: http://www.estimation180.com/Author: Andrew Stadel @mr_stadelDescription: "Each day of the school year I present my students with an estimation challenge. I love helping students improve both their number sense and problem solving skills. I'd like to share the estimation challenges with you and your students. Michael Fenton and I have collaborated on this handout for your students. Happy Estimating!Enjoy, Andrew Stadel" Why I Love It: Honestly, I first started using Estimation 180 because I was looking for an easy time-filler/warm-up for a class of students that was way below grade level. I needed something that I knew everyone could do no matter their mathematical skill, that would keep them busy for a few minutes at the beginning of class while I took attendance. I'd heard some buzz about Estimation 180 on Twitter and on some blogs, so I decided to try it out. I got a whole lot more than I bargained for! Here's a few reasons why this site is so awesome: 1. Low-ThresholdEveryone can estimate. Everyone! That kid who says, "I don't know how to do this," every time you call on him? Yep, he can estimate too. I have 100% student participation when we do an estimation challenge. On some days, it might be the only 5 minutes of class that everyone is participating, but at least everybody was thinking mathematically for at least 5 minutes. 2. High CeilingNot only can every kid DO the Estimation Challenges, but every kid can LEARN from the estimation challenges. I find that the best learning often happens when I ask kids the 'why' behind their estimates. Other good teaching moments come from having students calculate their error. For example, I had no idea how difficult it would be for my students to calculate their errors of estimating Mr. Stadel's height and the height(s) of his family and friends. First we had a discussion about all the different ways to correctly write out his height (6 feet 4 inches) and why it couldn't just be written as 6.4. Then we had some interesting discussions on how to calculate error if someone had estimated that Mr Stadel was 5 ft 9 in. Why can't we just do 6.4 minus 5.9? Students brainstormed several strategies to determine the error, including counting up and regrouping to write his height as 5 feet 16 inches. Was this part of my lesson plan? No way! Is it in the eighth grade core that I teach? Not exactly. Do my students need it and does it help them improve their number sense? Absolutely! I consider it to be time very well spent. 3. Kids Love ItI wish I could record for you that moment that I 'reveal' the correct answer! There is often shouting, occasionally there are fist pumps. There are sometimes exclamations of disbelief! "What?! There's no way that is only eighteen napkins!" When a student's estimate is perfect, it's as though he or she had just won The Price Is Right? I usually try to take a moment to acknowledge the person with the smallest error. That's all they get - no candy, no extra credit - just a moment of verbal praise, and the knowledge that for that moment they had been more successful than every other person in the room. You wouldn't believe how motivating that is.4. Estimating and Problem SolvingAs a math student and, until fairly recently, as a math teacher, I always thought that teaching estimating was a waste of time. You know what I'm talking about - those worksheets that teachers gave kids where they had to use rounding to find their answers before they learned the actual algorithm. Students' answers are invariably different from those in the textbook because they'd rounded to a different place value than the textbook had used. In all honesty, I still don't see any value in the 'kill-and-drill' form of teaching estimating. However, I see a lot of value in teaching the Estimation 180 form of estimating. When I give my students a task like Noah's Ark or Styrofoam Cups, I now begin the task by asking my students to tell me something that is too high, something too low, and then an estimate. This starts them thinking about what the answer should be. For my students, choosing the appropriate mathematical operation is often the most difficult part of a problem. If they already have a good estimate in their head before they start to problem solve, the students are able to figure out much more quickly if their strategy is leading them down a wrong path. About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email MaryAnn at mmoore@dsdmail.net if you are interested in contributing to the UCTM blog.Last weekend I attended the Math for America Utah Fall Conference. The topic of the conference was Mathematical Modeling and the presenter was Kara Imm, Co-Director of Math in the City. My mind is still spinning a little from some of the ideas I received, but I wanted to share one or two in particular that have already had an impact on my teaching practice. Less is MoreDan Meyer has been talking recently about how "You can always add. You can't subtract." Usually a mediocre math task or even a good math task can be made much better by removing some of the information. For example, in this task called Styrofoam Cups by Andrew Stadel, rather than presenting students will all of the information they need to solve the problem (how many cups will stack to reach the height of the door), Andrew Stadel asks students "What information would be useful to know here and how would you get it?" Since we're not in Andrew's classroom and can't actually measure the height of the door and the height of the cup, he provides us with links to pictures of that information which can be given to students when they request it. By leaving that information off to begin with, students are given the opportunity to think about the problem and why that information would be useful. I find that sometimes when students are given a problem that gives them every piece of information they need, they have a hard time then knowing how to process the information. In contrast, when I allow students to think about and request information, they have a much better idea of what to do with it because they've thought about why the information would be important and how it relates to the situation. Processing the InformationAs students ask me for information, I ask them "Why do you think that would be important to know?" After that student gives their reasoning, I like to ask a few other students if there is any other reason they would want to know that information. I don't tell them how to use the information they request. They tell me! Choosing the Model
Moving Along the Modeling ContinuumEach of these ideas about mathematical modeling (Collecting and Selecting Information, Processing the Information, and Selecting the Model) can be represented along continuum. Some tasks are high in one area and low in another. Sometimes all a task needs is a small tweak to make it fall a little higher on the modeling continuum. A Final ThoughtIn the four classes that have done the Styrofoam Cups task, my students were able to determine the information that they needed rather quickly. However, all of those classes were honors classes. This has me wondering if I perhaps ought to make some changes before I run this with my regular ed classes next week. One thing that really got me thinking was this blog post by Joe Schwartz from Exit10A. Joe talks about working on his own to solve this swingwraps task, also written by Andrew Stadel. What fascinated me most about Joe's thinking was this image that he shared: To help him think about how many times a swing would wrap around a pole, he grabbed a poster tube and a chain, and wrapped the chain around the tube. What a beautifully simple model! I would have never thought of doing that! At our MfA conference, Kara Imm suggested providing students with a Tool Table. For the task we did at the conference, the tool table held paper (lined and graph), rulers, string, markers, tape, scissors. There were also pieces of tape on the wall to use as 'measuring stations'. We had each been instructed to bring a graphing calculator to the conference. Kara later told us that she wished this hadn't happened, because it limited the types of models that we constructed. She mentioned that she sometimes puts a limited number of graphing calculators on the tool table - but not enough for all students/groups to have one. Students are given full access to all the tools at the tool table, but are not told how to use them. My students have tool baskets at their tables, in which I vary the tools that are available depending on the activity. When I run the Styrofoam Cups lesson with my regular ed math classes in a week or two, I'm going to include some cups of varying sizes. If students struggle to identify the information that they need to solve the problem, I will give them some time to experiment with stacking the cups in their tool baskets, if they choose to do so. Just another testament to the power of online collaboration and the #MTBoS! Thanks Mr. Schwartz! I would have never thought of that without you! About the author: MaryAnn Moore (@missnarymm) teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email MaryAnn at mmoore@dsdmail.net if you are interested in contributing to the UCTM blog.In my last post, I mentioned that I read a ton of math teaching blogs and am constantly collecting ideas from them. Great math tasks are just one of the many things I glean from reading math blogs. Since I'm attending a conference this weekend and have been asked to bring one of my favorite tasks, I thought I'd take this opportunity to tell you about it too. Noah's Ark by Fawn Nguyen (click on the link above to check out Fawn's original post about this task and download a Word Doc of the task) Mr. Noah wants his Ark to sail along on an even keel. The ark is divided down the middle, and on each deck the animals on the left exactly balance those on the right — all but the third deck. Can you figure out how many seals are needed in place of the question mark so that they (and the bear) will exactly balance the six zebras?This task is pure gold. It's problem solving; it's balancing equations; it's systems of equations. And there are no numbers. A sixth grader could do this task (it was written by a 6th grade teacher), but it is engaging enough for a calculus student. Here are a few snippets of dialogue from my students as they were working on this task last year. "So one bear equals three zebras." "How many seals does the elephant equal?" "Can you have half a kangaroo?" "Get a smaller kangaroo!" Student: So there are 6 zebras on that side, so then we take zebra out. Me: Wait, you can't just take a zebra off one side. Your ark isn't balanced any more. Student: Well, we're not really taking it off. We're just saying 'Sit down, Zebra. Wait for us to catch up.' This all sounds completely crazy, but believe me, it's very fun. Last year, I gave the task right before Thanksgiving. Many of my students figured it out in class, but for those who didn't, I informed them that it was NOT homework and they didn't have to do it over the break. The following Monday, a few of those students complained to me that I had ruined their holiday. They spent hours working on that task because they just had to figure it out. Actually, Noah's Ark sort of took over my own family Thanksgiving last year too. My oldest nephew, Max, was in eighth grade at the time, so I printed out a copy of Noah's Ark and handed it to him before dinner. Intrigued by Max's intense frustration/determination, one by one, each of the adults in my family found a copy of the puzzle and started working on it. In case you think this sort of thing is a regular occurrence in my family, believe me when I tell you that I'm the mathy oddball in my family. We don't sit down and do math together. Ever. It was one of the most strangely awesome holidays I've ever spent with my family. About the author: MaryAnn Moore teaches 8th grade math in Davis School District. She coordinates the UCTM teacher blog and is also a regular contributor to the UCTM teacher blog. Please email MaryAnn at mmoore@dsdmail.net if you are interested in contributing to the UCTM blog. |