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Brainy Apples: January 2015
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Improving Math Fluency Using Backward Timing

Math fact fluency........something that has been a struggle for so many of my students in the past. I am not one of those who believes that math fact fluency is the most important math skill and spends countless hours using flashcards with my students (I do ask them to practice their math facts at home using either archaic flashcards or a fun app). I prefer to spend our time together problem solving and applying mathematics in real wold situations. However, I do realize that students need to be able to compute math facts fairly quickly because, to some degree, fluency does interfere with problem solving.

In the past I have done what many teachers do: give my students timed practice tests. This works great for most of my students. Their math fact fluency improves. However, for a handful of my other students, their math fact fluency never improves. Those kids who get stressed out by a timer, who begin sweating the moment you give them their test, whose hearts are racing by the time you say, "Flip your paper over and begin", who are defeated when they see a page full of problems, and who get more and more jammed up with every completed paper they hear flipping over, this simply I have even had some students whose scores decreased over time. This doesn't mean they knew fewer facts, it meant that they could not handle the anxiety of timed math tests. For adults, we probably think of a timed math test as no big deal. But to a child, a timed math test could be the fine line between having a great day at school or feeling like a complete failure.

I have also given timed math facts because usually it is a skill that is included on a grading rubric for the report card. "Students will correctly solve 30 addition facts in 3 minutes." Or something like that. How else can you assess this skill without giving a timed math test?

With all that said, I still give my anxiety-ridden students timed math tests, but who says the timer has to be counting down? Not even does the grading rubric state that the time has to be winding down on the student. I don't remember who gave me this idea, but the moment I heard it I was like, "How ingenious! This is perfect!"

Backward timing. Instead of the timer counting down to a buzzer (which may be the most dreaded sound in the world to some kids...or whatever sound you like to use to signal time's up. I used my ActivBoard to count down and at the end it would play "Rocky Top" instead of a buzzer...teaching in Georgia this probably WAS the SINGLE worst noise some of my students could have heard!), the timer begins at "0" and counts up until students are done. Once my students figured out there would be no "BUZZZZZZZZZZZ!" or, in my case, "Oh, Rocky Top, you'll always be.....", their shoulders relaxed, sweat beads disappeared, and over time they began improving. So how does it work?
**Let me preface by saying that I only use backward timing with my students who are stressed out by the traditional timed test and those who are not showing improvement because I like to use this as a strategy for those kids.**

First, you have to decide how many correct facts they need to get correct. I had it easy because it was on the grading rubric. Then you need to discuss this with the student and set a SMART goal with the student. Students need to be let in on goal setting, especially since it involves them! In case you aren't sure what a SMART goal is, it is a goal that is Specific, Measurable, Attainable, Realistic, and Timely. You could set the goal to be what is expected for the end of the grading period, but for some kids this is so far off from their current performance, you need to lower it so they feel accomplished by reaching smaller goals and gain confidence.If you aren't sure what a reasonable goal would be, talk to other teachers first to see what they think a reasonable goal BEFORE you meet with the students.

So, as an example, let's say the expectation for the end of the quarter is that students will answer 30 addition facts correctly in 3 minutes. Let's say the student currently answers 7 correct in 3 minutes because you will need to do a traditional timed-test to get that baseline. It is the beginning of the quarter. Setting a goal of 30 correct in 3 minutes by the end of the quarter is specific, but is certainly isn't timely. That is 9 weeks away. A better goal might be, "Johnny will answer 15 addition facts correctly in 3 minutes" with a goal date of 3 weeks away. Then in 3 weeks, or before if he has met this goal, you can increase the goal to, "Johnny will answer 25 addition facts correctly in 3 minutes" with another goal date of 3 weeks away. If Johnny did not answer 15 correctly in 3 minutes at the end of 3 weeks, you will need to see how far away he is from that goal. If he is at 12, 13, or 14, clearly he is improving and you may want to extend the date by a week.

Second, once you have your baseline and goal set, you need to decide how many problems are you going to put on one page. If your goal is for students to get 15 problems correct in 3 minutes, then you don't want to slap 50 problems on a page. Remember, some kids get overwhelmed at the sheer sight of a page full of problems because they know they struggle and this makes them feel defeated before they even begin. I would put about 20 problems on that page for them. Or you can always put the goal on the page, and in this case it would be 15 problems on the page. The problem with this, though, is if they miss just 1, they will never meet their goal. Accuracy is important (which is why I record how many they got correct out of how many they attempted), but even we as adults will make errors every now and again. We can't expect our students to be perfect every time. You may ask, "Well, what if they are taking 3 minutes and 15 seconds to solve all 20 correctly? How am I supposed to know if they can solve 15 correctly in 3 minutes?" You may want to tell students to stop for a moment while you stop the timer at 3 minutes, and ask them to circle the last problem they completed, then resume the timer and let students finish. This way you can see where they were at at the 3 minute mark, and they are able to complete the page.

Third, explain to students how their new timed tests will work. Let them know that they will have as much time as they need to finish the page. If they  need 3 minutes, 4 minutes, or 5 minutes, let them know they will not hear a buzzzzzzzzzzzz. When they are finished, you will stop the timer that is counting up, and you will record that time (or if you have several students who are using backward timing, you may want them to raise their hand when they are finished so you can write the time down, or you may want them to take the test in small groups if you have several to make it more manageable). Let me add, that if students are taking longer than 5 minutes to complete the page, you have too many on the page for them. I would scale back the number on the page. If your goal is 15 and you have 20 on the page, I would probably lower the goal and lower the number of problems on the page. Remember, you want your students to feel successful, so if that means setting a goal that is more easily attained at first, then do that.

Fourth, after students have finished the test and you have graded the tests, fill in a graph  WITH the students. I like to record how many they got correct out of how many they attempted because this helps me see if their accuracy is improving. If you don't have one to use, check out the FREEBIE I made below! Graphing the results allows the students to see their progress. It gives them motivation to do better next time, and students soon realize they are no longer really competing with a timer but with themselves, trying to do better with each test they take. Intrinsic motivation can be a powerful thing!

Here is what the graph might look like. You may want to alternate colors each time so you can more easily see the different days, or you may want to keep the same color.

Repeat, as needed. Decide how often you will give students this timed test. Twice a week? Three times a week? I don't recommend every day, but that's just me. I like 3 times a week. But choose what is best for you and your students. Once students reach their goal, celebrate it with them, then create a new one with them and start a new graph. Repeat the process until they are meeting expectations. And, honestly, when they are meeting expectations, I may not set goals with them anymore because they are where they need to be, but I do continue to use the backward timing test with them. They do well with it, and I am not going to use the traditional timed test anymore.

How can you use the backward timing test for grading purposes? Well, you are writing down the time that the students finish, so if they finish in under 3 minutes (or whatever the given time is), and they correctly answer 30 (or whatever the minimum correct is), you have evidence of them meeting expectations. Let's say they don't finish in under 3 minutes, and the grading rubric says they are "in progress" of meeting expectations if they correctly answer 20-29 in 3 minutes. You are going to have to tell students to stop at the 3 minute mark, you will stop the timer, ask students to circle the last problem they finished, then resume the timer and let students continue working until they are done. You can go back to using the traditional timed test for report card assessments, but I feel as though I would be setting up my students for failure because I know they get anxiety and we haven't been using the traditional method. The grading rubric doesn't say it has to be a countdown timer.

If you want to use the FREEBIE I made click here!

I hope I have given you an alternative way to help increase your students' fact fluency in lieu of using traditional timed tests. Backward timing does take a little more effort because you have to set goals and decide how many to put on a page and keep track of when students finish, but I have seen such great growth out of my most struggling students, that I feel it is worth it.

I would love to hear your thoughts and comments about your experiences with backward timing. Thanks for reading!

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Integrating Writing Into the Content Areas: RAFT Tasks

Who are the writing teachers out there? I know some upper grades teachers departmentalize, so you may be the writing teacher on your team, or you may not teach writing at all. I think (and this is my total personal opinion) that even if you aren’t the designated writing teacher, you can still find creative ways to have your students practice those important writing skills. I want to use my post today to give you some tips on how to incorporate writing into other subject areas.

I have found through my years teaching, that some kiddos seem to have a permanent writer’s block. You can give them a prompt, they can’t think of anything to write on it. You leave it open-ended and they can’t narrow it down. I have found that when I focus my writing time around science, social studies, or math content, my kiddos have an easier time filling their paper with meaningful thoughts. Of course, this only happens if they have learned enough about the content to be able to write about it.

I personally love using RAFT writing tasks (Role, Audience, Format, Task) to accomplish this. RAFT tasks allow students to write for different audiences and take on different roles, and it requires them to apply learned concepts through their writing. I also love how RAFT tasks add an element of novelty for the kiddos and allows me a chance to be creative. Students need to have fun writing tasks in order to really understand that writing is more than just research reports and stories.

I think math is pretty easy to have kiddos write about. Why? Because they can explain their thinking when solving problems. Or, if they are playing a game, you can have them write about the strategy they used to win the game. Most kids are more than eager to tell you how they win.  If you want to create a RAFT task, you can have the kiddos take on the role of a game creator. I used to have my students create their own games to review specific math skills, so I would have them write out the rules to their game.
So an example of a RAFT task would be:
Role- game creator
Audience- any game company such as Hasbro
Format- directions
Task- Create a new game children can play to practice a specific math skill (you can allow students to select one or more skills, or you can assign students specific skills). You will need to write detailed directions for the children to follow in order to play the game.

Science/Social Studies
Science and social studies takes a little more effort, in my opinion, because you have to make sure you are thoroughly teaching the content if you expect kids to write about it in a meaningful way. Any kid can record facts about a topic. The purpose, though, is to have the kids write about the content in a meaningful way. Maybe have them describe a historical event using a first-hand account. Or they can describe how two processes are connected. Both of these require students to know enough about the content to apply their knowledge in a written form. Having students write about science and social studies content is also a sneaky way to find more hours in the day. Many teachers say that science and social studies is hard to fit in because of a lack of time or because of such an intensive focus on reading, writing, and math. Instead of having your students write a personal narrative about what they did over the weekend, have them write a personal narrative from the point of view of a child who is growing up during The Great Depression. I know that kids love to write about themselves, and I still had my students write about themselves and self-selected topics, but I had them do this as morning work before class started, or I had this as an option during literacy centers.

Here is one of my favorite RAFT tasks I love to give my students after we study habitats (click here for the complete task):
Role- keeper or aquarist
Audience- zoo or aquarium visitors
Format- comic strip
Task- You are in charge of providing information for visitors to read about a specific animal. You will choose one animal to research and create a comic strip that visitors can read to learn more about your chosen animal.

While we study each habitat, I let my students choose one animal from that habitat to research. I don’t have them write a report on that animal, though, because then they would be writing a LOT of reports. Instead I encourage them to choose one animal from that habitat they want to learn more about, and they fill out the graphic organizer using the information they find. They then keep this organizer in their folder. When we have finished studying all the habitats, and the students have found information on multiple animals, I have them choose the one animal to complete the writing task. They create a comic strip using the information pertaining to this chosen animal. The categories I had my students research for each animal tied directly to our science standards.

My students love Tim and Moby from BrainPop, so I have them create a comic strip similar in nature. Let’s say the student wanted to further research Emperor Penguins. Then in each frame of their comic strip they have one Emperor Penguin looking at the reader giving facts, and in the background there are more Emperor Penguins demonstrating the fact.  These turned out really cute! The comic frame is a large index card, or you can have a parent volunteer cut plain white copy paper in half. I had a parent volunteer cut strips of butcher paper and students glued their frames onto the butcher paper so they could roll it up and store it. I was able to display these in the hallway.  My students love this much more than the typical research report. I still have my students write research reports because it is important for them to be able to do this, but I also think that novelty is important in writing, too.

Want to try out a RAFT task? You can click <here> for my RAFT products in my TpT store.
What do you think about using RAFT tasks in your classroom? How might you incorporate RAFT tasks into your day? I would love to hear your thoughts!

Until next time!

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Grading vs. Noticing

My post today is going to be about something that hit me several years ago, and it is very timely because these days schools are hounded about assessments, teachers are hounded about assessments, students are hounded about assessments, and parents are hounded about assessments. I agree that we over-assess our students, but I do feel that assessments have a special place in the classroom. Used the right way, assessments can allow teachers to see what students are or are not understanding……but only if we take the time to NOTICE.

When I began my teaching career, I would tote home loads of papers to grade. Grade, grade, grade. My time away from the classroom was not spent doing things I wanted to do because I had ALL.THESE.PAPERS.TO.GRADE. What was I grading? Daily work, homework, tests, quizzes. Then after I graded the papers, I would record the grade (back then it was numerical, now it is either a 1, 2, 3, or 4…which a 4 means perfect. Something I have  huge beef with, but that's for another post…I mean, who is perfect? I have mastered subtraction with regrouping, but I still make errors in my checkbook. So does that mean I shouldn't earn a 4?) Anyways, I record the grade, sent the papers home, students returned them, and I stuck them in their portfolios. I did look at the grades. I saw who had failed, who barely passed, and who obviously didn't need to spend anymore time on that skill. And I used the grades to make small groups: those who needed a lot of help, those who needed some help, and those who could learn new skills.

Flash forward a few years, and I was in my master's program taking an assessment course. And in this course, the professor said why give your students a whole page of addition with regrouping to see if they know how to do it? Give them 5 problems. That is enough to see if they have learned it. And as I thought back, I felt so dumb. Why didn't I realize that myself? Probably because my schooling had consisted of a whole page of addition with regrouping problems as a test. And some teachers say, "Well, if you only give 5 problems, it will be hard for them to make an A if they miss one. They need more problems so they can make a couple of mistakes and still get a higher grade." GRADE. Assessments shouldn't be for grades, they should be for understanding what a student doesn't get. They should be for figuring out the mistakes a student is making. I began to realize that I needed to take the time to NOTICE my students' work, NOTICE my students' thinking, NOTICE what they can and can't do. And, for those students who don't know how to add with regrouping, they are getting an entire page of problems that they will do wrong, and it will just further cement the wrong way in their minds, making a much harder habit to break and replace with a correct method (notice how I said A a correct method and not THE correct method….many ways to solve math problems besides using the standard algorithm). And for those students who already know how to do it, how bored out of their minds are they going to be to do an entire page of problems they already know how to do? Talk about busy work.

I vowed from that moment on to change the way I assess. Now some assessments you can't change, no matter how much you want. But you do have control over the assessments you create and give your students. Namely those formative assessments. Those quick checks to see if a student gets it or not, to see if they are ready to move on to a harder skill or if they need reteaching. My quick checks (as I called them) were going to be just that: quick.

Let's look at the difference between grading and noticing. Grade each row of problems. How did this student do?

1st row- Zero correct. Now notice what this student did. Quickly we go from thinking that this student can't add to realizing this student knows basic facts, but does not understand place value when adding.

2nd row- Two correct. Not too bad, but still failing. Now notice what this student did. We realize that this student knows basic facts including those that require regrouping as indicated by getting 17-9 = 8 correct, but this students doesn't understand how to extend using place value to subtract larger numbers.

3rd row- Two correct. Again, not great but not horrible. Now notice what this student did. This one may be a little trickier. If you teach a grade when student begin to learn multiplication, you probably know exactly what this student is doing. If we grade this row, we will think that the student needs more practice with subtraction and addition. But if we notice, we see that we just need to spend a few extra minutes with this students to straighten out the difference between adding and subtracting with zero versus multiplying with zero. This student has generalized the zero property of multiplication with addition and subtraction. Reteaching this student addition and subtraction would do him no good. However, doing a quick lesson or reminder about how adding or subtracting with zero does not equal zero would be a far better use of time.

When I finally began noticing my students' quick checks and not just grading them, I became a much more effective teacher, and my students began to progress and excel like they never had before. Why? Because I was noticing their errors. Instead of looking to see if they got it right, I began looking to see if they got it wrong, and, more importantly, WHY they got it wrong. I began noticing and stopped grading. I began giving no more than 4-5 problems during a quick check. Four or five problems is plenty to see a pattern in errors or to make sure they understand. I didn't spend time reteaching a skill when they didn't need reteaching. Sometimes all they needed was a quick one-on-one meeting with me to discuss their mistake.

What do you think about noticing versus grading? I would love to hear your thoughts and stories!

Until next time!

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