Students struggle with math and especially Algebra.  Especially since schools closed and students participated in distance learning. This school year has proven to even be more difficult for Algebra and Geometry students and their transition back to the classroom.

Even in the best of times, students have had difficulty and here are some ideas that support those struggling learners.

1. Share Learning Goals

Not sharing a learning goal is like getting in the car to take a trip with no destination. Each day, students should be told what they need to learn, the purpose of the activities and how this relates to the goal of the unit.

They should also be given a measure of some type so they can see how well they have achieved the goal. It could be a quick formative assessment in google forms or paper. One colleague puts the most difficult problem for that content on the board and when students can solve that problem, they know they have achieved the goal

I have limited boards for writing so I have the goals on cards which have been laminated and I display the goal. Letting students know learning goals allows them to keep track of their own progress.

2. Use Warm Ups to Begin Class

Using a warm up (also called a Bell Ringer or Do Now) is a way to activate prior knowledge or review the previous days lesson. It also previews the needed skills for the current days lesson for students.

I currently use google forms for a warm up because it is easier to see the results of the class.

But for years I used a form, projected the problem and students showed their work/answer on a printed form. The form was then passed to the front where I checked. Sometimes a student reviews the form and stamps that it was done.

Once students have finished their warm up, I go over the problem and share the answer.

3. Pre Teach Vocabulary

It doesn’t matter if students were previously taught the concepts in prior grades, vocabulary is key. Assume they do not remember.

Pretest the students vocabulary for the current unit/lesson. Most curriculums have a “knowledge check” before starting the unit but that check is likely focused on content, not vocabulary.

Use notes that give pictures and definitions. When students take notes, have them use color, label diagrams, draw arrows to emphasize definitions.

Have students review notes and use stars and question marks next to each word or phrase. Stars–Knew this, Question Marks–New to me.

4. Provide Time for Practice

Though lessons should not be focused on foundational skills practice, research has shown that 10 minutes a day improves confidence and math competency.

Try using some card games, mental activities or even online math games for practice. This may be used as a closing activity on a regular basis.

5. When Teaching, Think Out Loud

This works for instruction and for student practice. As a teacher shows an example, instead of just repeating the steps, it is a discussion as in the example below:

3x +4 = 10

 Teacher: “ Hmm, I remember that the idea is to get the variable on one side and everything else is on the other side. This is called ‘isolating the variable’.  I think I need the 4 on the same side with the 10. If I add 4 to both sides, then I will have 3x + 8 = 14. That doesn’t help, so I need to subtract. This leaves me with 3x = 6. But I don’t need 3 x’s I just need one, so if I divide by 3, then I will have one. Remember to divide on both sides. So x = 2.”

The teacher can also pause between steps and ask students for advice. My students are always amused that I have ‘forgotten’ how to do math and are glad to give suggestions.

This also works well if students work in pairs and one student assumes the role of sage (speaks) and the other student is the scribe (writes). They work together to complete the problem.

The roles are then switched for the next problem.

6. Solve Problems in Multiple Ways

There is always more than one way to solve a problem. When beginning a unit, emphasize the results and ask students to develop the process.

For example: Solving an equation can be done with manipulatives, drawing pictures, and even trial and error.  Introduce a variety of ways to solve and allow students to use the method they prefer.

I recently taught surface area. I showed the students how surface area means to find the area of each face and add together. We make a list of all the faces and painstakingly found the area of each one. Once they were proficient with this, I introduced a formula. Some were excited to have a faster way, others were more comfortable using the “long way”.

7. Use Error Analysis

When students are asked to find and explain an error in a problem helps them practice using vocabulary as well as examine their own thinking. Research says that students who are presented with problems that contain errors have greater gains than students who only view correct problems.

Providing explanations helps students make sense of math and construct arguments. Logic skills improve. Error analysis materials are easy to find. Ask students to solve a problem showing all the steps and then display one problem at a time and let them find the errors.

8. The Final 7 Minutes

The last few minutes of the lesson are important to cement the ideas in a students mind before they leave the class. Try using one of these to end the lesson:

• Have the students write a summary of what they learned in the lesson and on a scale of 1-5 give a number to their understanding.
• Give a quick formative assessment of 1-2 typical problems. I use Google forms for this and use the results of the exit ticket to let me know how much to review the next day.
• Preview where the lesson is going the following day/week. Let students know how this lesson is going to support all the lessons that come after it.
• If you assign homework, then preview the problems assigned. Make sure students know when the work is due.

I have recently begun using a calendar in Google Sheets to record the lesson for students (I prefer Excel). The calendar is shared in Google Classroom for students and support staff. It lets everyone know what lesson I covered, all the assignments and what the next week (month) looks like. None of my students can say they did not know there was a test or quiz, it is all recorded.

Support staff love this as well. It is easy to help students with current work when they know exactly what we are working on now as well as what skills will be needed for following lessons.

These are some of my favorite ways to structure a lesson. Do all my lessons have these components? No, the lessons are varied depending on the content. Some days do not have a warm up, some days do not need an exit ticket. Oddly enough, though I have nearly 2 decades of school structure I dislike routine. I like variety and try to mix up the lessons depending on student needs.  If you have any additional ideas to add to the list, drop a comment or send an email to bluemountainmath@gmail.com.