Retesting in the Secondary Math Classroom

"How do you retest?"

Alright...here we go.

I work in a district where all math courses 7th-Geometry have retests; it is not the teacher's choice. That being said, I love retesting! My students learn so much, about math and study habits in general, between their first test and their retest.

Here is an overview of how retesting looks in my classroom.
All tests are written as a team and all courses give the same tests throughout the district. This helps to ensure that our students receive an equitable education. As we write the tests, we write them with testing/retesting in mind. Meaning, we write small sections with about one or two topics addressed per section. These are called competences or objectives. Most unit tests have 3-4 competencies of new material. Beginning on the second unit, we also include a review competency. These questions help keep ideas fresh throughout the year. So most tests are 4-5 competencies long. Every once in awhile we have a 6-comp doosey, but we try to avoid that.

During the unit students complete qualifiers. These are particular activities/investigations/homework assignments/projects that will qualify them for specific sections of the retest later on. In my classroom, we do lots of activities and assignments that are not qualifiers as well. I specifically tell students which assignments are qualifiers and which are not; I'm all about transparency! After I grade a qualifying assignment, I give it back to students and they record the grade on their grade sheet for the appropriate competency. You can see a copy of my grade sheet in this post. Like I said, we do other things that are scored, they are just not recorded on the grade sheet. I require that every qualifying assignment have a grade of at least an 80%. If a student receives less than an 80% they must correct the incorrect work and resubmit their work. I give full credit for resubmitted work. This also relieves a lot of the stress students feel and insecurity about having one shot to complete their math homework. They go home, they try, we discuss it again the next day, they submit their work, I offer feedback, they tweak and resubmit. I really like the system.

Anyway...moving on.
After an entire unit is complete, students do a review assignment and take their test. Each competency of their test receives a separate score out of 100 points. I hand back their tests and they record their competency scores. Any competencies that they scored at least an 80 on are considered "mastered" meaning they do not have to retest. They are welcome to try for a higher score, but they do not have to. Any competency where they scored lower than an 80, they are required to retest.

As an example, a grade sheet would be looking something like this right now.

This particular student would need to fix their qualifying assignment for competency 4, since it is lower than an 80%, in order to qualify for their retest.

I really like that my grade sheet shows homework and test scores for the same material stacked vertically. It is a very often occurrence that when a student makes a low test score, such as a 40, they also have a relatively low homework score. They can see their hard work (or lack thereof) really paying off.

I give students about a week between tests. During this time we go over common errors and misconceptions and I hold tutoring times during seminar (a 40 minutes block built into our day for tutoring, homework, and assemblies). I also remind students repeatedly throughout this week to check their grade sheets and make sure they are qualified. I will often create a second review-type assignment before the retest that also counts as a qualifier.

Once it is retest day, students turn in any qualifying assignments. These are often homework assignments they have been correcting to get their 80%. This also includes any test corrections that I assign for a particular unit. As students take their test, I quickly check the assignments that have been turned in, update their homework grades, and make sure every student that is taking a test is qualified for their test.

After their retest, we go over final errors and students record their retest scores. The sample grade sheet would look something like this now.

 Notice the student fixed their 70 in comp 4 and was allowed to retest that section. They did not retest comp 1 since they scored a 100 the first time. They tried to improve their comp 2-4 scores and succeeded in comps 3 and 4. I always keep the highest grades that students make in each section. So in this case, I would keep the highlighted 80 for comp 2 since their retest score was lower. Students usually like to calculate their overall grade, in this case 360/400, or 90%. I keep each competency score separate in my grade book.

Since this style is fairly repetitive, I also give a problem-based task for each unit that forces students to look at the material in a new way. Those tests do not have a retest opportunity and are worth half the points of the mastery test. In this case, since the mastery tests were worth 400 points the task would be worth 200 points. All of those scores are recorded at the bottom of the grade sheet in their own section.

I hope that answers some of your questions! Feel free to comment with more questions and I'll do my best to answer them.

Also...
Get your copy of my grade sheet here! I created the original file in publisher, email me if you want a copy of that one.

Solving Systems of Equations

One of my favorite pages from this year was our Solving Systems of Equations page. In my opinion, this page was truly interactive. Students were sorting, classifying, and studying with these notes. YAY!!

This page took a few days to complete. First, we discussed solving systems graphically. After some exploration and activities, we completed THESE notes (new file link that the bottom). They were still connected as one piece of colored paper. Students then put those notes away in their handy-dandy pocket. We came back the next day and completed notes over solving by substitution and solving by elimination (new file link that the bottom). Students then put those in their pocket as well.

After making sure students were comfortable with solving systems, we started talking about one/none/infinitely-many solutions. Students were already thinking about these ideas because each colored set (graphically, substitution, elimination) had one system with each type of solution set. Here's where the fun part happened!

On page 103 of their notebook we took basic boring notes about what a system of equations is, the notation for a system, and what a solution point means. On page 104 we created a flipable pocket. The pocket is one full sheet and one half sheet of blank paper. Fold the full sheet in half width wise (hamburger style if you know what I mean) and then put the matching sized half sheet inside the larger, now folded paper. I know... it sounds confusing... it's really simple! Tape up the sides and fold the whole thing in half. You have four pocket areas. We only used three for our purposes. Do these pictures help at all??

 

 Anyway...

Students cut their colored papers apart and sorted into three piles: one solution, no solutions, and infinitely-many solutions. They looked for themes and commonalities within these new groups. We then had a class discussion about their observations and added general notes to the fronts of each pocket. We visually represented how one/none/infinitely-many looks on a graph and the type of solution when solved algebraically.

 ifinitely??? yeah... I dunno either...

The sorting and processing part really made things click for students. I also saw them studying with these notes later. They were able to take out all notes of the same color to study how to solve with a given method, or take our all notes within a pocket to study solution types.
Overall...success!

How have you done systems of equations in the past? Any great ideas to share??

New links that should *hopefully* work!

General Interactive Notebook Pages

I have received a couple emails asking for the basics of my notebook before I do more content posts. So... here ya go!

When you open the front cover of each interactive notebook you see a title page. It includes the student's name, my name, my class room number, and our school name. This helps ensure that any lost notebooks find their way home. It has come in handy a couple times! Sorry... no pictures of that page. :(

Then flip the page and we start our table of contents. This year we used four pages, one for each 9-weeks. It worked pretty well!

 

After our Table of Contents is our "All About Algebra" pages. These can be seen here.

 

After those pages its our Interactive Notebook Guidelines.

All students taped in the notebook guidelines on page 3 and then completed homework on page 4.

Their homework was to illustrate two reasons they're excited to use their notebook this year and two questions/concerns they have about the notebook. We spent a few minutes at the beginning of the next class period sharing excitements and also addressing and answering some of their questions.

They were pretty pumped about this assignment!

**Note: we left these pages blank for about a week and a half and did most of Unit 1 content. I wanted to give students time to work with the notebook so they could have real ideas about excitements and questions. Doing this assignment on day 2 would not have been as productive in my opinion.

 

After our guidelines is our grade sheet and reference sheet.

The grade sheet on page 5 is relatively simple but a great resource for students. Almost every homework assignment and exam grade is recorded on their grade sheet. Also, my district implements Mastery Math so my students have a retest opportunity for most tests and must qualify to take that retest. This grade sheet helps students stay organized, record their test grades, manage their qualifiers (usually homework), and record their retest grades. We also use it periodically to calculate class grades. I like giving students practice calculating their own grades so they know exactly how it all works.

 

The Reference Sheet is folded to fit onto page 6. It is the same reference sheet that students are given for their EOC exam so we practice we it all year. I like students to have their own copies so they can reference it during any assignment as needed.

 

 

Alright... after that we start content pages! You can see the content covered in my table of contents pictures above, so let me know any requests of topics you want to see!

After all the content pages is our glossary. You can see a few pictures of those here as #2.

 

Until next time!

 

 

 

Top 5 Things I LOVE About Interactive Math Notebooks: #3-5

Well I'm back to share #3-5 with you. If you missed #1-2, check them out here.

The third thing I love about my notebook--the pocket! My students used this almost daily. Whenever we had pieces that they needed to keep track of from day to day, put it in the pocket. Whenever they received assignments back and needed to keep them to study for the next exam, put it in the pocket. Whenever we had a busy day and didn't quite get all the lose ends tied up, put it in the pocket. It was fantastic! Periodically if we had a few minutes left in class we would have "Pocket-Cleaning Sessions." Man, some of these kiddos are hoarders! :)

You can also see a couple other things I love (but didn't warrant their own Top 5 number) in the pictures above. We held our notebooks together with rubber bands once things started expanding. I got the idea here and let me tell you, it was a life saver! Most of my students' notebooks were still in great condition at the end of the year and I attribute much of that to the rubber bands. It helped keep things secure while bouncing around in a junior high backpack. YIKES!

You can also see our Speed Dial Partners peaking out in the picture on the far right. It's like clock partners but I made an iPhone template. While I still really like this idea, we hardly used it all year. Students filled in their partners on the first day of school during a Kagan getting to know you activity. The idea petered out for a couple reasons: 1) lots of students got schedule changes, moving between class periods, so lots of partners were messed up, and 2) I often rather paired/grouped students intentionally rather than going with whatever "get with partner #2" would yield. Oh well...
That being said, I plan to use that space to attach our pocket to the back cover next year. I think that will help increase the durability of the beloved pocket.

The fourth thing I love about my notebook--math notes are FUN! When you tell students to get out their notebooks during class time and there are audible cheers, it is music to a teacher's ears. We use colored pencils, highlighters, pockets, foldables, post-it notes, and tape all the time. Yes, 13/14-year olds LOVE it! They get excited to create their notes, color-code their important information, and add things to their personalized notebook. And of course nothing makes a teacher more excited than when students get excited about learning!

*I'll do individual posts on the topics shown above later*

 

The fifth thing I love my notebook--planning! Now, this is a little different from the rest and doesn't have its own fun picture, but planning with the notebook in mind made me a better teacher. I had to think through the most important aspects of the topics covered, and plan concise and cohesive notes. No more slapping too many problems into a powerpoint and calling it a lesson. I thought carefully about which few problems would be most beneficial for students, and the best way to present these problems. I thought through information clustering and how to create foldables, what color-coding would be most beneficial, what application topics or activities would glean the most information for my students. I can say, hands down, that implementing Interactive Notebooks has made me better. I encourage you to try it in your classroom; I bet it makes you better as well. :)

 

 

Now, before I dive back in to topic-specific posts, I want to know what kinds of things YOU would like to see first. As I mentioned in the first paragraph of this post, my students and I learned a LOT of math this year. We went all the way from rational/irrational numbers, through basic algebraic thinking, and ended with parent functions and systems of multiple functions. Now, I'm not saying I created stellar pages for every topic we did, but if there's something you're curious about please leave a comment so I can get to that topic sooner rather than later. Also if you have a question about notebook logistics, leave that in a comment and I'll try to address it.

 

Here are a few pictures to get you started thinking!

(from a Donors Choose project)

 

Top 5 Things I LOVE About Interactive Math Notebooks: #1-2

Before I show any more of my individual pages, I wanted to talk about a few reasons I LOVE interactive notebooks! I have only used them for one year and I am sold! I have also talked about my love for them so much that I've convinced a few other teachers to try them next year. YAY!! So without further ado...

This list will probably change from year to year, but these are the five things I was especially smitten with this year. :)

The first thing I love about my notebook--the tabs! This was actually a students' idea mid-year. She mentioned wanting tabs for each unit and other students immediately latched on to the idea. I made a quick table in word, printed on colored cardstock, laminated, and by the next class period we were adding tabs! The students LOVED them! And I do too!! Definitely keeping this idea next year.

 

The second thing I love about my notebook--the glossary! We constructed a 143-word glossary/index as part of our EOC review. While some students moaned and groaned during the progress, many commented in their end-of-year survey how helpful it will be in the future. I created my own version of a Frayer model to include a space for page numbers. I provided students with the vocabulary words and definitions. I wanted to make sure they had an accurate definition and was more concerned that they could create an example and counterexample for each term. That would tell me much more about their understanding than copying a definition from a book or the internet. They also had a place to record the page number(s) that dealt with that topic in their notebook. While I will probably tweak a couple thing about the glossary/index for next year, overall I love it!

 



 

 

As you can see, different students set up their pages differently. Works for me! As long as it's something that doesn't have to be a certain way, I tell my students "do what makes you happy!" They enjoy the freedom and choice in areas like this!

 

Alright...we'll 2 is enough for today :) Check back soon for #3-5.
UPDATE: here are #3-5.

 

If you use Interactive Notebooks, what are some things you absolutely love? Please leave a comment, I'd love to hear about them!

 



Real Number System & Approximating Radicals

Here is one of the first lessons of the year in our curriculum - the Real Number System! During the 2012-2013 school year, my district opted to teach three years of curriculum in one year (AHHH!!!!) to the Pre-AP Algebra 1 students. Since we were implementing Common Core and wanted to make sure to fill in all the gap items before high school, we taught CCSS 7th Grade, CCSS 8th Grade, and CCSS Algebra 1. With that in mind, most of my lessons covered multiple standards and levels. This is one such lesson...

Students were already somewhat familiar with the idea of rational and irrational numbers. While it had been a year and the concepts were definitely fuzzy, they had a little familiarity with the terms.

This was the first year for most of my students using an interactive notebook and they were concerned about writing too big/spacing/logistics. So cute! I put up the following diagram before we got started and eased some of their worries. They felt more confident knowing the layout of the entire page as we filled in portions.

In the top rectangular section we completed the Real Number System information. We created nesting rectangles to show which groups were subsets of other groups. I really liked the way the layout created a number line! The students seemed to understand this layout very well.

Under that section we discussed how to approximate numbers without using a calculator. Some students panicked, but eventually became confident. Don't get me wrong, this was NOT and overnight transformation! Ha! But with enough encouragement and "put the calculator down!" moments, we all made it through.

That night students completed a few problems in classifying and approximating numbers.

We came back the next day, checked our answers with our cooperative teams, and then did a little Stand Up, Hand Up, Pair Up Kagan activity. Students all divided the right side of their notebook into quadrants and drew a card with a radical. They worked individually for a few moments to approximate their radical, then they began pairing up. I also had a card and was a member of the activity. I've found that students partner up much more quickly and wander less if there's the impending doom of having to partner with the teacher, especially during the first week of school! Ha! I'm okay with that, whatever it takes.

Once students had found they partner, they each worked to approximate the other's radical. Then they compared their decimals using <,>, or =, added their decimals, and multiplied their decimals. This gave students four different practice opportunities very quickly, as well as the added benefit of meeting their classmates and learning that our classroom is a place of active learning. Success!

What ideas do you have for this topic that I could implement next year? Any tips to make these pages better? I'd love to hear from you!!