This post is a reflection on my strategies for instruction (Domain 3) for the American School Foundation of Monterrey Track 1 project.
|DOMAIN 3: INSTRUCTION||Level|
|3a. Communicating clearly and accurately.||Meets Standard|
|My directions and procedures are specific and clear, and my spoken and written language is clear, correct and age-appropriate.|
|3b. Using questioning and discussion techniques.||Approaches Standard|
|My questions invite a combination of lower and higher order thinking skills and I reinforce, dignify and build on student responses. I make some attempt to engage all students into a true discussion with inconsistent results.|
|2c. Following the lesson schema.||Meets Standard|
|I have a clearly defined objective but do not organize the class into sub-objectives and have limited success drawing on students’ past experience. I model correct performance to enhance retention. Knowledge is consistently applied through practice but not all students are consistently involved.|
|3d. Demonstrating flexibility and responsiveness.||Approaches Standard|
|I have a general understanding of my students’ different approaches to learning and attempt to accommodate their questions and interests. Lesson pacing and checks for learning can be inconsistent.|
Like classroom management, in the domain of instruction I have found natural strengths and weaknesses in my teaching. I have plenty of experience and skill in presenting and explaining a topic and I regularly model good mathematical practice through examples; on the other hand I could improve my strategies for checking for understanding and creating genuine participation via discussions. I use a variety of instructional techniques prevalent in math classrooms and follow the ASFM lesson schema, and overall I believe that I meet the standard expected of ASFM teachers.
A starting, hopefully obvious, note: good teaching in a math classroom will look very different from good teaching in, say, an English classroom. Of course there are some similar best practices, but by necessity the teaching techniques will differ. In an English classroom (to the best of my knowledge) the learning objectives are broad and each may take several weeks, while in a Mathematics classroom each individual learning objective is specific, requires at least some new content knowledge, and must be covered in one or two lessons.
With that in mind, most of my classes follow a similar pattern (see example class notes): the students connect to previous knowledge, I introduce new content knowledge and model correct procedure, questioning students along the way, and students practice collectively and individually. Here are some techniques I use on a regular basis in presenting new material:
- Using a prime time task (PTT) to engage students immediately at the bell and connect to a previous lesson
- Explaining concepts lecture-style and responding to student questions
- Having students take notes in a provided outline
- Modeling good practice and procedure for students through math examples
- Having students offer exemplars, for example having them demonstrate a problem on the board
- Questioning students, both by soliciting volunteers and directing questions
- Allowing students time to practice in class, individually and with a partner
- Moving around the classroom to observe students and check progress
I have found these techniques to be successful in a number of ways. My lessons are generally entirely focused on the main objective; other than quickly reviewing homework from the previous day all of these are directed at the lesson objective, from PTT to practice. The consistent sequence of activities helps students prepare for what they will be learning as they know when in the lesson they will need to acquire new information, when they need to apply this information, etc. As well, I try to sequence my explanations, modeling examples and having student exemplars in such a way to be clear to students and reinforce their learning. I often will start with an explanation and an example, ask the students to do a few examples, then return to myself modeling a (perhaps more complicated) example, helping students reinforce their understanding after practice.
Along with having students present examples, take notes and perform individual and partner practice, my use of questioning helps ensure most of my students are engaged during my lessons. I regularly mix up questions to specific students, sometimes directed randomly and sometimes at students who seem to be off-task, with questions for which I solicit a volunteer. Sometimes, for a question with a particularly obvious answer, I ask the class to call out the answer. These questioning techniques keep students alert and involved, though sometimes I need to be clearer to the class which type of question I am trying to use.
I make attempts to question students at a variety of levels of thinking with some success. My questions usually involve at least the need to understand how to solve a problem and then to follow a mathematical procedure to give the next step in an example. I also ask “why” or “how” questions to prompt students to think not just about procedure but about the real mathematical meaning. For example, in the class observed by my supervisor, I ask questions such as “How would you do that?” for procedure, and “I just put in these two right angles, what does it tell me about those angles?” for meaning.
Students also ask me questions which I answer in class. I encourage this, and it often turns into a back-and-forth dialogue, though rarely a full-fledged class discussion. Occasionally I will ask another student–there is often a volunteer–to try to answer, then build on their point if necessary, but usually I find it more efficient to answer student questions myself, since I can demonstrate the proper procedure or give a correct explanation in the often-tight time frame of a math classroom. One of my ongoing goals (see Domain 1) has been to make my transitions tighter, partially in an effort to give me more time to open up class discussions–to make space for student-provided answers, and use the wrong ones as learning opportunities.
One area of improvement in the instructional domain that I will be working on for next year regards checking for my students’ understanding. I currently do this through questioning as mentioned above, class walk-arounds during practice time, checking homework, and formative assessments such as quizzes. I have used closure survey methods such as Socrative, but not as consistently as I should be. While I do get a general sense of how my students understand the lesson, I am not collecting individual data and this limits my ability to assess my lesson’s effectiveness and make adjustments, either on the spot or for upcoming lessons.
Also linked with checking students’ understanding and assessing the effectiveness of a lesson is the use of class- and homework, which I will discuss more in Domain 4.
As well as classes to introduce new material, I use a few other lesson types to achieve other learning goals throughout the year. In each unit, I try to devote one class period to work on the unit assignment. This consists of a PTT, brief announcements, an individual or group period depending on the assignment, and a closure. Before each summative unit assessment, I also have a review period. We again start with a PTT, then dive into a review presentation prepared by a group of students (to right). The presentations run from 15 to 20 minutes and include participation from other students. After this, I collect class feedback on the presentation, answer any student questions about material on the upcoming test, and give students the rest of the class to work independently on a unit review package. I find that having the unit summarized by their peers helps students understand and relate better to the material.
I also experimented for one Math 9 unit with a “flipped classroom” approach. Partially since I had to leave due to a family emergency and partially since I wanted to see how the approach would work, my Math 9 classes approached the Algebra Review unit as a self-directed learning exercise. I gave them a work package, a list of resources (including Khan Academy videos) and four class periods, and I supported and answered questions without lecturing. The results were promising but not overwhelmingly so: students who traditionally have done well in my classes continued to do well, and the test average was not out of line with other unit tests. Some of those that usually struggle in class were really lost and did not have the tools or focus necessary to teach themselves the unit material without the traditional teacher-led environment. If I choose to use that approach again in future years, I will make sure the students are better scaffolded as they approach the learning.
Near the beginning of the year, my department head stopped by my room to compliment me on my spoken delivery: you have a way of speaking that is easy to listen to, he said. My classes not being 400-person university lectures, this is only a small part of my instruction, but overall, while I have areas to improve on, my instruction generally follows the standards set by ASFM and good practices of math teachers. I will work on my consistency: in closure activities, in involving all students through questioning and discussion, and in checking for understanding and using this to improve future instruction; I will also continue to emphasize my strengths and focus each class on its instructional objective.