Consistent Routines
inTASC 8: The teacher understands and uses a variety of instructional strategies to encourage learners to develop deep understanding of content areas and their connections, and to build skills to apply knowledge in meaningful ways.
Introduction
Students know what to expect every day because my classroom runs on a regular weekly schedule. I try to cover one concept a week start to finish, and students are reminded of the weekly goal at the start of every lesson. Notes, practice, application, assessment, and reflection are the cornerstones of learning, and each day of the week has a different focus. This cycle reinforces students’ understandings of the topic. The pace of the content is guided by formative assessment.
Table of Contents
Guided Notes
Guided Notes
The approach taken for delivering new content depends on the material students need to master. For many rote skills in math, I have found it helpful to introduce relevant background material before working through examples. This gives me a chance to define terms in the way I will use them and ensure that I am not relying on students mastering the content previously.
The Cornell note format lets me draw special attention to major vocabulary that students need to feel comfortable with. The structure is helpful for my students who struggle to organize their thoughts. I can introduce fundamental concepts in broader terms before applying them to the specific problems I’m interested in.
The structure of the notes builds in study methods for reviewing material. The note taking area is where students are taking notes and writing down the important takeaways from the lesson. Each concept is identified along the left side near the relevant definition and/or examples. Students can hide the note taking area to quiz themselves on the vocabulary and concepts of the lesson to see if they can recall pertinent information.
The "examples" section is where students are given an application of the concepts they just learned. They will see the same problem during independent work later in the lesson and can refer back after they have applied the concept. They will have context for a problem they may not have understood at the beginning of the lesson. If they still don't understand at this point, I will be able to recognize and assist students who need intervention.
The most important section for my classroom is the "summary" section at the bottom. Students come back to this section at the end of the lesson after practicing the concept. They summarize the major ideas of the lesson and write hints and tips that helped them understand the math. This helps students solidify their learning and also provides an effective touch point for reviewing before the unit test. This is where deep understanding of the content comes in. Students are not just practicing a skill until they master it. They are engaging in the learning process and learning how to build connections between content areas. This method makes it easier for students to recognize recurring themes and identify methods of teaching and learning that work best for them.
In this lesson on simplifying radicals, I needed to ensure that students understood how exponents work. I introduced exponents as if students had never seen them before. I touched on the pieces that should sound familiar and introduced the way I want students to think about exponents. I did not want to teach students shortcuts for simplifying exponents in radicals, and this approach lets students uncover the shortcuts themselves. These notes prepare students to explore math in novel and interesting ways. Students can expand the exponent every time and it will always help them solve the problem, but more advanced students can start to identify patterns and develop deeper mathematical thinking. The foundational thinking is what I reinforce in these lessons, rather than a specific process for solving a specific type of problem. After these notes on exponents, students are equipped to answer more challenging problems that involve the same knowledge.
Practice
Practice
The form practice takes depends on the nature of the content students are engaging with. Bellwork is used to determine the level of assistance students will need to master the content. Multiple methods of practice need to be prepared in order to respond to students’ needs.
A simple worksheet can become an engaging activity depending on how it is assigned. I prioritize collaborative learning in my class and have a few fall-back methods for engaging students in pairs or teams. I have routines for independent practice and team work that I turn to as necessary.
Independent Practice+
Some topics are beneficial to have students engage with independently. Skill drills, for example, do not necessarily require a partner. It is helpful for students to engage with content without support to see what they are capable of. I do not want students to get stuck, however. When students run into a wall and aren’t making progress, they can ask a teammate, me, or the internet for help. I want students to be able to rely on available resources. It is more important that they master the content than how they master it.
In this practice sheet, I wanted students to review factoring out common factors and distribution involving variables. This is a skill that benefits from rote practice, and students likely won’t need much support. Those that do can be helped relatively quickly by myself or a classmate. When teaching a new topic to students, it's important to see what students are capable of answering before moving on to other forms of practice.
This student produced a few errors in their work, and it's clear to me that they are having trouble dealing with variables. I can use this information to remediate individually, address common issues in student work, make mixed-ability teams for group assignments, or reteach the topic to the class. I ended up addressing this issue with the whole class to clarify operations on variables.
Peer Coaching
This method pairs students together for an assignment. They take turns answering questions on an assignment and teaching the solution to their partners. One partner is responsible for explaining the solution to the problem clearly enough that the other partner knows what to write. The other partner is responsible for writing what is said and reproducing it in mathematical terms.
Some assignments are designed with this method in mind, but it works for almost any worksheet. It gets students in the practice of explaining their thinking rather than just recognizing patterns within a problem set. It has lower stakes and is less embarrassing to make an error, but it also puts some pressure on students to really master the content since they are teaching half the problems and writing answers on the other half.
This is an example of what students are provided for this activity. The first page is a fairly standard worksheet, but the real lesson is in the following pages. Students are tracking their partners reasoning on the problems as they get increasingly complex. The problems follow a pattern, and when students get stuck they can refer to their prior thinking to solve the problem. Their early answers provide hints for the harder ones, and they have a partner to assist them if necessary. The purpose of these lessons is to ensure that every single student has mastered a concept well enough that they can express their thinking to a classmate. This is a highly demanding lesson, and students spend much of the period answering only a handful of questions.
"Backstreet Boys"
This activity puts students in the teacher's position. They are presenting to the class as if they are teaching their peers how to answer the problem they're given. When I have students speak in front of the class, I try to lessen the pressure of public speaking in every way I can. I make it a bit goofy with pop culture references and lower the stakes by giving students the answers. Their task is simply to “tell me why” that answer is correct. Students can relax but still engage with content in a meaningful way. They still have to be able to answer the problem, but they don’t have to worry about embarrassing themselves by being wrong. They have to be able to express their thinking clearly enough that their classmates understand the thought process. After each student’s turn, the rest of the class cheers and offers praise or other positive feedback. It is an excellent tool for remediation before a unit test because every student is benefiting in one way or another. Students are hearing several different approaches to answering the same type of problems and are getting practice with public speaking.
This is an example of student work in demonstrating a problem in a Backstreet Boys lesson. They used the grid method to prove that these two binomials multiply to make a difference of squares quadratic.
The student is cropped out of the photo for privacy.
Reflection
Periodic reflection is a major focus of the learning process. It gives purpose to the assessments students participate in. I want my students to take ownership of their own learning, and that starts with giving them the time and the tools to understand it.
At the end of each week, students complete an End of Week Reflection that asks them about their comfort with the content of the week. I use these to jump start conversations about the week and revisit content as needed to help students master the material. Students also use this time to reflect on projects or other large assignments and answer questions about the application of math in the real world.
Students also reflect in other ways to help them build literacy skills and apply their knowledge in meaningful ways. Students write discussion board posts and participate in class discussions to solidify their learning in collaborative ways. Reflection is a key part of the projects students complete in my class. More information on project reflection can be found in Challenge-based Learning.
Reflection
Conclusion
The consistency of a routine is beneficial in and of itself in the classroom, but I believe the strongest impact comes from the intentionality of each and every day students come to Algebra II. There is a clear purpose and goal to each activity. Time for assessment and reflection is built into each week to help me ensure that every student is mastering the key skills they need. I can maintain high expectations for my students while addressing their preexisting gaps in knowledge because of the support structures built into my classroom.