How do we know if our math lesson was effective? : Measuring Effectiveness of Lessons After and During Class
The goal of teaching math is that we are imparting knowledge and skills to students to be able to solve mathematical/mathematics problems. But how do we know if we are reaching our goal? How do we know if students are learning and we are effectively teaching during class? Today we will be exploring a few ways on how we can know if a math lesson was effective in the classroom.
What is a ‘good’ lesson?
Before we being talking about effectiveness of lessons and measuring student outcomes, it is important to talk about what a ‘good lesson’ is. As a teacher, we all want to find ‘good lessons’ to teach students that align to our content. However, we all have different interpretations of what this can be.
Before we define a good lesson, let us define (even further like a good mathematician) what I mean by ‘good’ and ‘lesson’. When I say ‘good’ I mean it has positive outcomes for students and by ‘lesson’ I mean the presentation to students and learning that takes place through teacher and student actions. This does not necessarily mean direct instruction, however it is the mode I mostly reference since I use it a ton.
By those definitions, I believe a good lesson achieves the student learning goal for the day through some measurable end, either quantitatively or qualitatively. For instance, if your learning goal for the day is to master the standard through an objective, then students averaging 80% on their exit tickets could mean that it was a good lesson. In the same vain, if your learning goal for the day is to provide a positive and meaningful learning experience for students and they rate on their exit ticket they enjoyed the experience then it was a good lesson.
Not all lessons have a quantitative outcome that needs to be met through a percentage, but it is still important to have a measurable outcome. Ideally, that comes through an exit ticket that students complete at the end of a lesson or a reflection activity later.
Thus, when you think about a good lesson, think of how you want to measure the success of your lesson. A mixture of both quantitative (% scores) and qualitative data (how students liked the lesson or confidence in the content) is important from students as they can help guide your planning decisions and how you measure your own success in the classroom as a teacher.
How do we know our math lesson was effective?
We defined a good lesson as a lesson that reaches the learning goal set for the lesson and has positive student outcomes. Therefore, how do we know when a math lesson was effective, and how can we promote these during a lesson? I habitually use these three every day that I constantly monitor:
Students master the content of the lesson by achieving mastery on the exit ticket
Students gain confidence towards achievement in mathematics by engaging in practice and activities
Students are actively engaged in the lesson through positive student actions
1. Students master the content of the lesson by achieving mastery on the exit ticket
In our society as it is, grades are an important aspect of education. Grading the exit ticket is the easiest and quickest way to determine whether a student has understood the topic of the day (notice I said easiest and quickest, not most effective; I have more thoughts on this for a later time). Therefore, it can be a valuable measurement of student mastery towards the overall standard. Try:
Making it a daily exercise of completing an exit ticket at the end of class, even if it is just a quick reflection. It allows you to see how students did with the material for the day and builds habit in the classroom. Furthermore, the testing effect shows that taking low stakes quizzes helps with longer term student retention
Grade your exit tickets daily (or when possible) through technology or student self grading and look at the average. This can help you gain an understanding of where students are at in the learning and if you need to spend more time on a topic.
Making sure your exit tickets vary with problem types. For instance if your exit ticket covers nonlinear equation types you should have multiple examples of different types of nonlinear equations.
Ensure your exit ticket problems align with the model and practice of the entire day. You don’t want to surprise students with a brand new problem type in the exit ticket as you are measuring what they have just been learning.
2. Students gain confidence towards achievement in mathematics by engaging in practice and activities
Practice is the time where students can put their brains to work and engage with the content. Thus, we want them to give effort and attention towards completing it. Therefore, as teachers we want to give them an environment that encourages achievement and confidence in mathematics. Try:
Strategically plan partners and groups of students who work well together and will promote staying on task
Strategically plan seating of students to minimize distractions during independent work
Actively monitor students during partner practice using proximity
Give lots of compliments towards groups that are working well together
Build your practice by scaffolding the difficulty from easier to difficult problems so that students can build confidence in their ability to solve the problems of the day
Redirect students who are off task and deliver consequences when/if needed
3. Students are actively engaged in the lesson through positive student actions
Positive student actions can be a variety of actions that student perform throughout the lesson and it is important that you let them know what you are looking for. This can be set at the beginning of the year or right before you begin the class period. Some positive student actions that I reward and positively narrate for are:
Taking notes during the model
Participating during class
Productively working with your partner during practice
Meeting silent and independent expectations during independent practice and exit ticket
Asking questions when they do not understand and advocating for themselves
These positive student actions let me know that students are working towards reaching their goals in class. You should work to create your own positive student actions you want from students during class and reinforce behavior that promotes those actions. Remember, you want these to be realistic and equitable for all students to meet in the class.
What happens if my lesson is bad? :/
At some point in your teaching experience or career, you are going to completely bomb a lesson. You are either going to get something wrong and teach something incorrectly, students are going to be extremely confused on the content during the model, the student practice is going to be too complicated and confusing for students, a student behavior is going to completely derail the entire lesson and escalate you towards anger, or all of the above. That is okay. I live by the 80/20 rule in teaching that 80% of your lessons will be good to amazing and 20% are going to flop. I still have a lesson a week that doesn’t turn out the way that I want it to, but I strive towards still trying to make my lessons as positive for student outcomes as possible. Maybe in another article I will discuss how we can actively save a lesson or at least make the rest of the time productive for student learning if possible.
Effectiveness is hard to measure, so don’t be too hard on yourself
All humans are extremely random and variable. Even the time of day can effect our behavior and temperament towards work and socializing. Therefore, it is important to know that, yes we are doing the best to provide students with a good lesson, however if your averages on your exit ticket don’t meet mastery, then it is ok. There could be a variety of causes as to why mastery was not reached. I have students get an answer wrong sometimes because I format a question differently. Furthermore, I regularly have students perform excellent in class with an A and they do poorly on a standardized test. Thus, don’t be too hard on yourself.
Then you may ask then, “Why do we even do the recommendations then if we don’t know that they work 100%?” Like most things in practice, it is hard to measure and control for all extraneous variables. They are the best tools we have to help students gain positive outcomes in mathematics and I have personally seen a lot of growth from students and myself using the ones above.
Let me know of any that you use regularly in the classroom. I am always intrigued in how teachers keep track of student success and regularly measure how they are learning in the classroom. Next time, I will talk about how terrible the objectifying of education is becoming and how we can properly utilize standardized tests to help student learning.