Instructional Strategies
InTASC Standard #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
One of my school’s most important goals is to ensure that scholars receive the majority of their instruction in differentiated small groups. As such, adapting instructional strategies to meet the specific needs of individuals and small groups is a critical component of my daily pedagogical practice. I monitor student learning through in-class activities and formative assessments every class period and then use these data to shape subsequent instructional practices and identify groups of scholars who might benefit from similar learning experiences. In fact, I rewrite virtually every lesson plan a day or two before I teach it so that my instruction remains sensitive to recent trends in student understanding of the content.
Unsurprisingly, all of this differentiation requires me to wear many hats within my classroom. During whole-group guided notes, I am an instructor delivering new knowledge to my students. However, my style during this phase of class is fundamentally Socratic; I ask students numerous higher-order questions to gauge how effectively they are learning and push them to think more deeply about the content. I always plan out these questions in advance, and I strive to put students in dialogue with each other (e.g., by asking them how a classmate might have gotten a particular answer). In addition to learning how to use math, my scholars learn how ask engaged questions that dig deeply into new material and justify their thought processes verbally and in writing. I attempt to be a model of both engaged questioning and thoughtful justification throughout whole-group mini-lessons.
That said, my scholars spend most of their time working in small groups and investigating new problems with their peers. During this portion of a period, I am more of a facilitator. I sometimes answer questions, but it is my students who break down a problem and work together to build new knowledge. In fact, two of my most common stations during a lesson are Investigation and Illumination, which feature students delving into new content and discovering answers for themselves. Sometimes, I am merely an audience member. Once my algebra students identify a long-term group project, I provide the materials that they request and then let them work fairly autonomously. I check in with each group on a regular basis, but I give students a lot of latitude to pursue new ideas and test new approaches. I do not grade their work until they are delivering their final presentation of a project to their peers, me, and other adults from the school community.
This year, I have been working conscientiously to add another layer of differentiation to my classroom based on students’ engagement with their own learning and progress. Feedback from my scholars about their own areas of strength and weakness has become an important source of data for me and drives critical instructional choices that I make about how I teach, what my students do on computer-based interventions, etc. My scholars are increasingly responsible for tracking their own assessment data and using it to reflect on their abilities and their needs as learners. As they build metacognitive skills, their feedback about what they want to learn and how they want to learn it becomes even richer and more helpful.
Click the buttons below to learn more about the variety of instructional strategies I employ in my classroom.
Teacher-Driven Strategies
Student-Driven Strategies
Technology-Based Strategies
Guided Notes
After a short “do now” activity, most of my lessons contain 15 to 20 minutes of guided notes. I write notes under a document camera connected to the projector, and students ensure that their notebook pages match the image of mine. Guided notes are a great time to introduce a new strategy that students can apply to more difficult problems during rotation time. I usually base the structure of the notes on an “I Do/We Do/You Do” model. I explain a strategy for the first problem, have students explain it for the second, and then ask students to try it for themselves on a third.
Unsurprisingly, all of this differentiation requires me to wear many hats within my classroom. During whole-group guided notes, I am an instructor delivering new knowledge to my students. However, my style during this phase of class is fundamentally Socratic; I ask students numerous higher-order questions to gauge how effectively they are learning and push them to think more deeply about the content. I always plan out these questions in advance, and I strive to put students in dialogue with each other (e.g., by asking them how a classmate might have gotten a particular answer). In addition to learning how to use math, my scholars learn how ask engaged questions that dig deeply into new material and justify their thought processes verbally and in writing. I attempt to be a model of both engaged questioning and thoughtful justification throughout whole-group mini-lessons.
Samples from sixth- and eighth-grade student math notebooks. These pages typify the gradual release of control that my students experience as they learn a new skill and then have to take more and more ownership of using it to solve problems.
Graphic Organizers
One of the first words I teach students at the beginning of a new year is “autonomy.” Math problems often have only one correct answer, but there are many valid ways to find a solution and I want my students to feel empowered to follow the intellectual path that feels most appropriate to them. Part of my job as a teacher is to provide students with tools that support them as they select and employ a particular method. For example, some of my students prefer to use an algebraic approach for division problems that involve fractions (i.e., multiplying by the reciprocal of the denominator). Others like to create a visual model in which they graphically depict the divisor and dividend. Visual tools are not just valid solution strategies; they also deepen students’ understandings of the processes that they are using. As such, I create many visual organizers for my students. Below is the most ubiquitous of these organizers, which my students use to restructure word problems as they work toward a solution. It was developed in collaboration with my principal and the special educator who supports my students.
CASPER Organizer. Note that students must explain what the question is asking them to find before seeking a solution and that the final step prompts students to consider whether the solution they have found is a reasonable answer to the question that they were asked. These strategies help students to make sense of word problems and encourage them to think more deeply about what they are being asked to do rather than merely applying an algorithm that seems to fit a given situation.
Sound clip of me introducing the CASPER model to a small group of students. While I spoke, students took notes on the strategies I was using rather than actually trying to solve the problem in question. This strategy helps students focus on what is being done and why it is being done without getting distracted by the need to perform mathematical computations. After my students and I discussed the strategies that I had used, I gave them a copy of the work that I had done on the problem so that they could evaluate the math as well. This final step of the modeling process is very important; knowing that they will get notes on the problem later helps students to focus on the process itself during the modeling exercise.
Interdisciplinary Connections
I work closely with many of my colleagues to design tools and experiences for my students. One of my most successful collaborations produced the “rate organizer” featured in the document below. It transcends the traditional cross-multiplication approach to rate problems by encouraging students to think about what multiplicative operation is being performed to transform the numbers on the left into the numbers on the right. That operation goes into the middle of both arrows; the content of the arrows matches for any proportional relationship. This organizer is used across all of our middle school grades and even in some upper elementary school classrooms at our school. Most students report that it helps them to map out and then solve problems more effectively. Rate organizers have become so important in the way that my school teaches math and science that the science teacher (with whom I developed the organizer) and I presented the tool to an audience of parents so that they could help their children use rate organizers at home.
Comparison of rate organizers and cross-multiplication. This document was used for our presentation of the concept to parents this fall. Accordingly, the second page of the document connects rate organizers to real-world situations that deal with ratios and proportional relationships and math and science concepts from the middle school curriculum. The rate organizer continues to serve as a helpful tool and reference point for both parents and students.
Brain-Targeted Teaching
During the Effective Practices in Teaching and Learning II course, degree candidates learn about brain-targeted teaching. Since learning about this model for education, I have attempted to integrate its principles into my approach to unit planning. These principles are detailed in the presentation I prepared for Effective Practices II about my first brain-targeted unit plan.
Brain-Targeted Teaching Unit Plan. This plan was previously submitted as an assignment for Effective Practices in Teaching and Learning II in the spring of 2017. The principles and strategies it details are illustrative of the approach I now use for planning all of my units and structuring my classroom environment. The brain-targeted teaching approach has been particularly useful in visualizing a warm, welcoming classroom learning space and planning strategies to help students remember key information in fun, accessible ways.
Bridge Enrichment Cluster
My school uses a school-wide enrichment model in which all students have access to the sort of special programming that is often reserved “gifted and talented” students at other schools. Enrichment clusters meet during the instructional day once per week. I run a cluster in which students learn to play the card game bridge. Once students have learned the fundamentals of the game, the cluster will expand into a sort of mentoring program in which bridge-playing mentors will visit the school for a friendly “pro-am” game with the students. Students will be connected with mentors whose careers match their own aspirations.
Students learning bridge. I encourage students to pace themselves as they learn. Bridge is a very complicated game, so I introduce one or two new rules at a time and have students practice until they are comfortable learning more and increasing the complexity of the game. This lets students learn the game on their own terms and avoids anyone feeling confused or left behind. I frequently employ versions of this approach in mathematical instruction as well.
Student-Led Investigations
I do not present all new material via guided notes. Instead, my students discover a lot of it for themselves while working in small groups. I particularly like using this strategy for geometry standards because students love creating visuals and then identifying the patterns that they represent. For example, instead of giving my eighth graders notes about the Fundamental Theorem of Similarity (which explains that the ratio between two components of an original image is the same as the ratio between the two corresponding components of a dilated image of the original), I asked them to investigate the problem for themselves. They all produced different images and then compared them to see that the theorem held true regardless of the size and shape of their original images. Discovering the theorem through hands-on exploration helped them to accept its validity far more confidently than they might have had I simply explained it in notes. Whenever possible, I structure lessons so that at least some of the essential content is learned through investigation.
Photos of Fundamental Theorem of Similarity Investigation. Students used straightedges and lined paper to measure precisely and then compared their finished products (see middle image) to recognize the relevant patterns: that the ratio between the two crosspieces matches the ratio between the short and long segments on each side of the “V” and that the two crosspieces are parallel to one another.
Project-Based Learning
Student-driven investigation is always on display in my algebra class, for which I employ a project-based learning model. Small groups of students meet with me to discuss ideas for projects that involve math, and I procure the materials they need and then give them the autonomy to work through problems on their own with support at regular teacher-group check-ins. My students have created some truly exceptional projects in algebra class, from a marshmallow catapult to test factors that affect projectile motion to a full cost-analysis for a week-long trip to Atlanta that some of our middle schoolers will take this spring to an animation designed to explain the concept of slope in a student-friendly way that utilizes real-world examples. The students who built the marshmallow catapult used the Pythagorean Theorem to calculate the distance that marshmallows traveled and then designed a lesson about the Theorem for the full eighth-grade math class, complete with notes and example problems. Presenting about the topic helped them to learn it even more effectively, and other students were very excited to start planning the topics that they wanted to introduce to their classmates.
Marshmallow catapult and graphs of launch data. Although simple in design, the catapult enabled students to run some interesting experiments about how well different objects fly. They then used Microsoft Excel to create visualizations of the data that they had collected. Each student produced a different graph, and the team had a lively discussion about what information they could find most easily using each one.
Stump Your Partner
One of my favorite games to play in the classroom is “Stump Your Partner.” In this activity, students write their own story problems that can be solved using a topic about which we are learning. I usually offer prizes for the most creative stories, which incentivizes students to write about fun, detailed scenarios. Once a group of students has written their stories, they all pass them to the person on their left, who must read and solve the problem. Teachers (at least at my school) often remind each other that we are all literacy teachers, and this game helps students to practice their writing while in math class. Moreover, it forces students to think about situations in which the math we are learning might be useful and helps them see how word problems can be constructed around mathematical operations. This makes it easier for them to connect their learning to their lives and to solve future word problems that they may see.
Sample products from a round of Stump Your Partner. Students were learning how to divide whole numbers by fractions and had to write story problems that required that skill to solve. Connecting division problems to creative stories is a great way to practice as critical skill in an engaging way.
Performance Tasks
Another common rotation activity in my room is a collaborative performance task, in which a group of students complete a project together. Such tasks are often closely connected to real-world issues and situations; topics from earlier this year include income inequality and the sugar content in beverages. I try to provide students with just enough hints that they can succeed on the task by discussing it together and reasoning through challenges. For example, for the beverage sugar content task, I asked them to draw a bar graph. Most of my students had never actually constructed such a visual before, but the instructions I gave them and their conversations together enabled them to produce some very strong charts. Performance tasks also generally feature some sort of individual reflection at the end. In the case of the beverage sugar content problem, students had to write complete-sentence answers to interpretive questions about their data and more general questions about beverage labeling.
Student work from the beverage sugar content performance task. Note that students gathered their own data based on drink labels before creating bar graphs and answering the reflection questions. Most students reported that they had seen bar graphs before but had never been asked to draw them.
Student Presentations
I frequently ask students to present their work and findings at the end of a class period. In addition, I periodically have a small group of students teach their classmates a mini-lesson (e.g., my algebra students who introduced the concept of the Pythagorean Theorem to their peers). Students usually create posters when they know that they will have to present something—indeed, the Investigation and Illumination stations generally come equipped with poster paper and markers for students to use—and I hang these posters on one wall of my classroom to remind students about what we have learned and how impressive our classmates’ presentations were. This wall is directly opposite my word wall, which helps students to remember the technical vocabulary we have learned in colorful, visually-appealing ways.
Word Wall. This early-year picture shows the beginning of the word wall. By the end of the year, the wall will contain over 100 terms organized by domain within the Common Core State Standards.
Posters containing student work. My students create a lot of posters, so this display changes throughout the year. Shown here are student-created projects and anchor charts about scientific notation, proportional relationships, parallel lines cut by transverses, and even test-taking strategies.
Metacognitive Feedback
This year, I am trying to increase the number of opportunities that students have to give me feedback about their own learning. To that end, I often ask students to write a couple of sentences at the end of an exit ticket about where they feel most comfortable and what they want to improve upon or learn next. This feedback is especially useful at the beginning of a unit because it allows me to identify groups of students whose knowledge and confidence might be improved via similar activities.
Sample of feedback from a recent eighth-grade exit ticket. Students are still learning to be specific in their metacognitive reflections, but I am always impressed by the honesty that they display when answering questions like these.
ALEKS and i-Ready
My algebra students use a computer-based intervention called ALEKS. Students can watch their knowledge grow as regions of their “ALEKS Pie” expand. The pie is divided by mathematical domain, and students are always eager to get close to completing a slice.​
ALEKS Pie. Students see this image every time they log on, and it is always just a click away as they learn and work through problems using the program.
One of the many great features of ALEKS is that students have some autonomy about what topic to learn next. Although the program always has a suggestion, it enables students to see a set of possible topics and select from among them. This invests students in mastering topics quickly because they feel like they have chosen to learn about a particular concept. Inspired by this functionality, I have started surveying the rest of my students about which mathematical domains on i-Ready (another computer-based intervention) they find easiest and most difficult. Although i-Ready does not give students the same level of control, I am able to organize new lessons for students by domain. Even knowing that they are able to choose to work more heavily on one domain than another helps my students take ownership of their learning process. I intentionally alternate areas of strength and weakness, so motivation to complete hard lessons is high because students know that they will get to work on something less daunting next.
Samples of feedback forms about i-Ready strengths and weaknesses. Student investment in i-Ready is much higher when they feel like the program is more responsive to their needs and preferences.
Newsela
Although Newsela is a web-based news service, it can be very useful in a math classroom. The site regularly features interesting articles about mathematics, and even students who struggle with mathematical operations may enjoy learning about the history of the subject or current discoveries within it. Newsela articles are frequent “can do” assignments available in my classroom after students have finished their work, but they are also sometimes a critical component of a station.
The Newsela landing page for science and math articles. Each article is written at multiple different Lexile levels, so different scholars can receive different articles based on their unique reading abilities. Articles also come with a short comprehension quiz at the end, which is a great way to see which students are reading the article carefully enough during station time.
Bloomz
Differentiated instruction in small groups can sometimes feel like an intractable classroom management problem. Bloomz, a web-based app that tracks student behavior (among other things), helps me and the rest of the middle grades team connect incentives with choices in the classroom. It is easy to deduct points for off-task behavior and to add them for great teamwork and engagement. Every two weeks, students with 95% positive Bloomz feedback are eligible for an exciting award or activity (like the ever-popular scholar-staff dodgeball game).
Conclusion
My first full-time job in education was teaching English at a public middle school in Daegu, South Korea. In each of my classrooms, I had 40 to 45 students with wildly disparate English abilities and experiences. Some knew no words beyond “hello,” “goodbye,” and “OK,” while others had lived in English-speaking countries and were fully capable of reading novels in the language. This presented significant challenges for me, but it also prompted me to start building the skill of differentiating effectively early in my career. My understanding of instructional planning and delivery has always been guided by the reality that every learner is different and deserves to be met where he or she is academically, socially, emotionally, etc.
One of my favorite parts of teaching is testing out a new form of communication in my classroom. I love brainstorming new ways for students to give answers via hand signals, creating student-friendly graphic organizers that can be utilized on multiple types of problems, and designing performance tasks and other collaborative activities that ask students to present their work or new content to me and their peers. In practice, this means that my classroom has to be a very flexible environment. Students are always excited to see which station activities they will enjoy during a given lesson, from individualized computer interventions to hands-on explorations of new topics with a small group of peers. I strive to offer my scholars a varied experience that, like the subject of math itself, always leaves room for creative new approaches to learning.