### Browsed byCategory: Algebra

Using IF-AT as Part of Exam Review

## Using IF-AT as Part of Exam Review

One of the highlights of the recent ICTCM conference was Eric Mazur’s keynote address about “Assessment For Learning.” He mentioned an assessment technique known as IF-AT (Immediate Feedback Assessment Technique) that reminded me a great deal of the review strategy I have been using in my intermediate algebra course. (Here’s a blog on that review strategy.) I thought it was a great idea to try, so immediately postponed my elementary algebra exams on systems of two linear equations in two unknowns by one day to give this a try. I added a second review day so I can introduce this strategy to my students over a two day period.

The idea is that students work on a series of problems individually. After half of the class period has ended, students submit their individual work and form groups of four students. They then discuss their answers as a team and submit a team answer to the first problem. If they get it right the first time they get full credit. If they get it wrong they can select a second answer to submit for 1/2 credit. They can even try it a third time if needed for 1/4 credit. I saw a video where the problems were in a  multiple choice format with 4 possible answers, and the teams were given a scratch off card. A star was displayed on the right answer – if students see the star they know they are right, if they see a blank space that counts as an incorrect attempt.

You can see a step-by-step demonstration of how the IF-AT works
on this web page posted by Epstein Educational Enterprises.

I am going to use a Learning Catalytics Team-Based Assessment to put my spin on this process. On day 1, students will work individually on 8 problems for 30 minutes. Some problems will be conceptual, some will be systems to solve, and there will be two word problems. They will submit their answers as they work. I will then launch the team portion of the assessment. Students will form their own groups of 4, with one person responsible for entering their team answers. I have decided to give teams only two attempts on each problem. A correct answer on the first attempt will receive full credit and a correct answer on the second attempt will receive half credit.

The individual portion will make up half of the score, with the team portion making up the other half of the score. I will be counting the score as an in-class activity in my flipped classroom model. I expect students to take a little time to get used to working with Learning Catalytics, so I have tried to select problems that they will be able to answer in the given time limit. I expect day 2 of the review will be smoother. My students work so well together, and I expect to see their bonding pay off in this review.

Later this week I will let you know how it goes.

Do you have any experience using IF-AT in the classroom? Do you use it for testing? I’m curious how you address students who have testing accommodations through the testing office. Let me know by leaving a comment, reaching me through the contact page on my website, or reaching out to me on Twitter (@georgewoodbury).

-George

Learning Catalytics- #ICTCM17

## Learning Catalytics- #ICTCM17

This Saturday I will be speaking at ICTCM about how I use Learning Catalytics in my Statistics and Algebra courses.

Collecting Homework

I started slowly in my Statistics courses, using Learning Catalytics to collect “written” homework. I often give written assignments to supplement MyStatLab exercises, and Learning Catalytics allows me to collect certain problems or parts of certain problems. The answers are automatically graded and scores are transferred to my grade book in MyStatLab. This strategy encourages students to do the homework and to be on time. Students, if you wish, can have conversations about their strategies or answers. As the results come in I can address common errors or misconceptions.

Reviewing for Exams

I found Learning Catalytics to be helpful for reviewing for exams. For example, while reviewing for an inferential exam I can post a problem and ask students to tell me which hypothesis test is the appropriate one to use. The same can be done for reviews on probability distributions, descriptive statistics, … I can ask conceptual questions or problems requiring calculations.

I can use these results to get a real time read on how my students are doing with their preparation, and determine which concepts to address in detail.

Flipping the Classroom/Peer Instruction

Here is where the real classroom power lies. When I flipped my Statistics class, I used Learning Catalytics to make the class sessions more interactive and engaging. I post a question and ask students to submit an answer. Then I either ask students to explain their answers to the class, discuss their answers in small groups, or I offer some insights of my own. At that point I allow students to change their answers if they wish.

This approach has turned my class into a conversation with my students, or a conversation among my students, which is more effective than the traditional “top down” lecture.

If you have any questions or comments about Learning Catalytics, flipped classrooms, Interactive Statistics, or anything else in this blog, please leave me a comment or reach out to me on Twitter @georgewoodbury.

ICTCM here I come …

A Student Shares a Great Observation

## A Student Shares a Great Observation

Today in my elementary algebra class we were reviewing solving systems of equations by addition or substitution. We were going over a system where students were having trouble determining what number to multiply each equation by in the system in order to eliminate the variable x. We had been discussing that the goal is to find the LCM of 12 and 14, but I told them that on exam day they could always fall back on multiplying each equation by the coefficient of x in the other equation (while making sure that produced one positive coefficient and one negative coefficient).

I then showed the class that they could find the LCM by finding the prime factorization of 12 and 14, gathering the results in a Venn diagram. Multiplying 6 by 2 by 7, the LCM is 84.

I finally showed them where the Venn diagram tells us that we can multiply 12 by 7 to get 84, and 14 by -6 to get -84.

One of my students pointed out to me (and the entire class) how he came to decide that he could multiply the two equations by 7 and -6. He started with 14 and -12, then divided both of those by their common factor of 2.

I loved the original thought, and repeated what he said to the entire class. I saw a lot of heads shaking in approval, and my students have a new strategy to use when the LCM does not jump out at them. It was a great day in elementary algebra!

Do you have a story about a student discovery to share? I’d love to hear from you through the contact page on my website, posting a comment, or by reaching out to me on Twitter (@georgewoodbury).

-George

Flipping Elementary Algebra

## Flipping Elementary Algebra

This semester I am teaching two sections of elementary algebra using a flipped classroom model. The approach is different than the way I have flipped my statistics course, but has been very effective. I am relying heavily on MyMathLab outside the classroom.

For each section that we cover …

• Students complete a “Flip” assignment before the material is discussed in class.
The assignment contains conceptual videos that introduce each topic as well as videos of examples where problems are worked out.
After students finish the videos, there are a handful of problems that they have to work through, and all of the learning aids (except “Show Example” are available. Students can try each problem as many times as they would like.
• The “lecture” period is intended to involve active learning.
Some days begin with a class driven recap of what they learned in the Flip assignment. I count on students to drive this discussion, stepping in only when I have something to clarify or add. I mostly ask questions and wait for students to respond.
Most days involve group work or collaborative learning. Some days students turn in their assignments. Other days we go over answers as we go, or I ask students to share their answers and strategies at the board.
Every day is different, and I am looking for my students to be as agile in their learning as I am in my teaching.
• After class, students take a 5 question “Reflect” quiz that focuses on the problems that I feel are most important.
The results on the student’s first Reflect quiz attempt load a personalized HW assignment, containing 3 exercises associated with each problem on the quiz. If a student gets a problem correct on the first quiz attempt, they get instant credit on the personalized HW for the 3 associated problems.
Students use the personalized HW for self remediation, then they can go back and take the quiz again as many times as they would like to.

One question many have about flipping the classroom is “What do you do if students arrive unprepared?” In my experience, having the Flip assignments due for a grade motivates students to do them. Also, because they hear their classmates participating in the discussions and contributing during “lecture they feel more compelled to be prepared themselves. I have seen some of my students in the tutorial center in the morning before class starts trying to get some help to make sure they understand the material, and that can only lead to good things.

I am happy with the way things are going, and I am progressing towards less discussion at the beginning of class as my students become stronger. It gives me (& my embedded tutor) more opportunities to walk around during class and talk to students one-on-one, clarifying as we go.

The classes just took the exam on Chapter 3 (Graphing lines, equations of lines), and 61 out of 71 students passed the exam. The mean score in each class was in the high 80s, with median scores of 92 and 93 in the two classes. This test was very similar to the test I gave last semester, but the results are much stronger. On to systems of equations …

Are you flipping your classroom? I’d love to hear what you are doing. Interested in trying this approach? Please leave a comment on this blog, contact me through the contact page on my website, or reach out to me on Twitter (@georgewoodbury).

I am a mathematics instructor at College of the Sequoias in Visalia, CA, as well as the author of algebra and statistics textbooks with Pearson.

Embedded Tutor FTW!

## Embedded Tutor FTW!

Thanks to the Transformation Grant, our college has begun to provide embedded tutors for developmental math and English classes. I have a tutor in each of my Math 200 (Elementary Algebra) classes. My tutors walk around throughout the class session, helping students and answering questions. I have had great results, and I am happy to say that my students feel that having a tutor in the classroom is very beneficial. Many developmental math students are much more comfortable asking questions in a one-on-one fashion, rather than stopping a lecture to ask a question in front of the whole class. I also have my tutors grading some of the in-class group work assignments.

Today we were reviewing for the test on graphing linear equations and inequalities in two variables. I was going over one of the problems that students had worked on (finding the equation of a line that meets given conditions) when one of my students stood up and told the entire class that he noticed that many students found m and b, but neglected to write the equation. It was a great example of feedback provided at an important time, and I am sure that students will benefit from that tomorrow.

I am so proud that the tutor felt comfortable enough to make that observation. I feel that the embedded tutor has increased the sense of community in our classrooms, and look forward to encouraging more instructors to take advantage of this opportunity.

Do you have classroom tutors? Are there any successes you want to share? Words of warning? I’d love to hear from you through the contact page on my website, posting a comment, or by reaching out to me on Twitter (@georgewoodbury).

-George

New Algebra Review Strategy

## New Algebra Review Strategy

This semester I am teaching a short term intermediate algebra class. I taught this last year, and I taught a chapter each week followed by a week to review for the midterm. I repeated the same schedule for the final. This semester I have changed the schedule and have had great success. After I finish covering each chapter, I devote a day to reviewing that chapter immediately.

I bring in an old copy of a chapter exam, and the review takes place in 3 parts.

• I give the students 30 minutes to work the exam on their own. I do not allow them to use notes or any other reference materials.
30 minutes might seem a little short, but I do write my (1-hour) exams to be on the short side, and most students can get through a majority of the problems in 30 minutes.
I then have the students identify each problem as a 1 (I have this under control), 2 (I need a little help), or 3 (I need a lot of help).
• Once students have rated each problem I have them pair up and try to help each other. Many times students who have a problem marked as a 3 can find a student who has it marked as a 1 who can hep them to understand the problem. If the pair of students struggle with the same problem, they can refer to their notes to try to make sense of the problem.
After another 30 minutes I have the pairs rate each problem again.
• The third part of the review involves me. I ask students to tell me which problems are still giving them trouble. We have done this for 4 chapters, and each time we narrow it down to 3 or 4 problems that several students are struggling with.
I work through each problem, asking for students in the class to lead the discussion. What did you try? What is important to remember here? I also offer my advice.

My students have found this very rewarding. One of the strengths of this approach is encouraging students to use retrieval practice. So many times I have heard students say that they thought they had it under control only to have things fall apart on the exam, but if they had put themselves in a test situation without test consequences they may have realized that they were not as prepared as they thought they were.

Another strength of this approach is that students get a chance to turn to each other for help. Often the advice of a classmate will be more helpful to a student than just watching me solve a problem again.

After the midterm I asked my students if they would rather review after each chapter or save all of the review days until the end of the semester, right before the final exam. They overwhelmingly voted to continue with the same review process.

I’d highly recommend giving this a try in your class. Do you have a class that only meets for one hour a day? Try having the students work through the problems, both alone and then in pairs on one day. Then have a debriefing session the next day where you can address their questions.

– George

I am a mathematics instructor at College of the Sequoias, and an Algebra/Statistics author with Pearson. Follow me on Twitter (@georgewoodbury) or reach out to me through the contact page on my website.

Why >= How: Homework

## Why >= How: Homework

I hear many instructors lamenting that their students are not doing their homework to the instructor’s satisfaction. If we agree that homework is an important part of the learning process, then it is important to tackle this problem.

Do your students know why they are doing homework? Don’t be so sure that they do. Many students do it because it’s part of the game, because they are told to do it, because they get points for doing it. They should be doing homework because homework can increase their understanding. You cannot assume that they know this.

On the first day of class I often ask my algebra or pre-algebra students “What do good students do?” They can develop quite a list of good student behaviors – coming to class every day, taking notes, doing homework, studying, etc. But when I ask why they take notes I hear crickets- everybody seems to do it, I’ve always done it, … We have a quick discussion about what notes are for, how to use them after class, and what belongs in them.

In my class homework does not directly impact a student’s grade unless they are passing exams. I make sure that students understand that the goal of the homework is to increase their understanding, and that will be measured on the exams. Equally as important: the goal of doing homework is not to simply accumulate points.

Because my students know why I assign homework they understand its importance. They do not view it as some sort of busywork. And they do it. And they do it well. Of course we have discussions about how to approach doing homework in such a way that students will maximize their learning, just not before they understand why they are doing it.

Game On in Algebra: Unexpected Rewards

## Game On in Algebra: Unexpected Rewards

If you think back to some games you have played, what can be more fun than an unexpected reward? Unexpected rewards can be fun AND motivating.

On the day that I pass back the first exam, I walk around with a bag of plastic gold coins. I hand one to each student who earned the full 3 points on the exam. (That means they leveled up by meeting the performance benchmarks on each HW assignment and quiz, and also scored 80% or better on the pencil & paper exam.) The classroom starts to buzz. Students are wondering what’s up with the coins. A couple of students will be saddened to learn that the coins are not chocolate. An occasional student will be saddened to find out that the coin is not actually made of gold, but that’s pretty rare.

When I am done giving the coins to the students I explain that they can turn in their coin to open any one assignment or quiz. My theory is that their performance deserves some benefit, and being able to save yourself from a missed assignment is a nice perk. I will not reopen any assignment unless a student gives me a coin.

Daniel Pink in his book Drive explains that expected rewards can actually “de-motivate” students. (If you haven’t read his book, you need to. It will open your eyes as to how to get students to respond.) I believe that this is true. To avoid this problem, I tell the students that there may be other benefits for students who still have coins left at the end of the semester. This way they are never sure exactly what will happen. And I like it that way.

I just passed back the first elementary algebra exam and will write a new post in which I will discuss how I will proceed from here. Spoiler Alert: I gave out 7 coins in a class of 44 students.

Game On in Algebra

## Game On in Algebra

This semester I am continuing to use a grading policy in my elementary algebra class that incorporates elements of game design. I begin by telling my students about my discussions with a well-known game designer (who happens to be my son Dylan – check him out on Twitter) that school should be fun, and he challenged me to come up with a grading system that incorporated some of the elements of game design. It took a long time to come up with a system that we both felt would work.

Homework and Leveling Up

Online homework and quizzes do not count directly to a student’s grade. I want students to understand that they must be able to demonstrate their understanding on exams. Homework helps students to learn, and I wanted to reward students who did well on the homework.

Students can level up by scoring at least 90% on each homework assignment during a testing unit (there are 2 assignments per section – a basic HW section that covers all of the topics and a personalized assignment that contains only problems that the student has struggled with) and 100% on each sections 5-question “reflect quiz”. Students are allowed to repeat the quiz as many times as they would like with only the highest score counting.

Exams

I give 6 exams, and they are graded as pass/fail. A student who passes earns 1 point and a student who fails receives 0 points. If a student has leveled up that unit they can earn 2 points for a score in the 70s and 3 points for a score of at least 80%.

That means that students can earn up to 18 points from exams.

Other Points

I do have one exam (Rational Expressions and Equations) that is a special double-points test where students who level up can earn up to 6 points. I do not tell my students about this until the end of the semester, and the fun associated with this unexpected reward helps to increase focus on the toughest exam of the semester. The extra 3 points get us up to a possible total of 21 points.

I give 4 points to students who pass a final exam review quiz (34 questions) and score at least 90% on the corresponding personalized homework assignment containing problems that they missed on their first quiz attempt. Adding these 4 points brings the possible total to 25 points.

Students can earn up to 5 points by completing the Real World Math project. This is a project in which students choose a real-world math topic they are interested in, plan a strategy for learning about it, and devise a plan to show me how they learned about the topic. (I will blog about this more in the near future.) These 5 points bring the possible total to 30 points.

Students can earn up 5 points by passing an optional cumulative midterm exam. In order to qualify to take this exam a student must level up on one of the first 3 exams and earn 2 or 3 points on that exam. Possible point total after these 5 points is 35 points.

Final Exam

The cumulative final exam, which is often a common exam taken with several other classes and graded by a team of instructors, is worth 100 points. That means that the final exam is worth 100 of the 135 points that are possible during the semester. My students have a clear goal – they must be able to demonstrate understanding of the course material at the end of the semester and everything they do all semester is to put them in position where they can do well on that exam.