Differentiating Instruction Through Multiple Approaches

Program Standard 3

3. Differentiation – The teacher acquires and uses specific knowledge about students’ cultural, individual intellectual and social development and uses that knowledge to adjust their practice by employing strategies that advance student learning.

3.3 Element – Demonstrating Flexibility and Responsiveness in Persisting to Support Students

3.3 Example of Proficient – Teacher persists in seeking approaches for students who have difficulty learning, drawing on a broad repertoire of strategies.

Boaler (2016) emphasizes, “The new evidence from brain research tells us that everyone, with the right teaching and messages, can be successful in math, and everyone can achieve at the highest levels in school” (p. 4). During my coursework at Seattle Pacific University, I read the book Mathematical Mindsets by Jo Boaler and it opened my mind and changed my approach to math both as a learner and as an instructor. I used to assume that if I didn’t understand a math concept in the way it was being taught that I was incapable of learning it. Reading this book helped me see that each learner just needs to find the approach that makes sense to them. This book helped me develop confidence in my own math practice and to see how important it is to engender persistence and self-assurance in students. In order to be successful at math, learners need to explore multiple approaches to the same concept and determine which one works best for them. As educators, it is our responsibility to present students with multiple strategies for solving a problem and the growth mindset messages to encourage them to explore, make mistakes, and find their own path to mastering different skills.

During my coursework at SPU, differentiation came up frequently and I always pictured it taking form in the classroom through small group instruction or small group stations. While small group instruction is an integral part of differentiated instruction, it also requires multiple other strategies to be fully realized. What I have come to understand during student teaching is that providing differentiated instruction requires a multi-tiered approach that starts with how whole group instruction is presented. During my student teaching experience, I taught a group of 4th-grade students for math instruction. When the class got to the unit on multi-digit multiplication, many of the students were struggling to understand the concept. The curriculum had students first learning the partial products method, then the standard algorithm method, and finally the area model method. After the first day of instruction in this sequence, I could tell that the majority of students were not understanding the concept. During the second day of instruction on multi-digit multiplication, I not only introduced the two remaining methods but also drew connections between each method of solving the problem. This allowed students to see that each different way of solving a problem was actually doing the same function. At the end of class that day, the students engaged in a discussion about the different methods for solving multi-digit multiplication and were prompted to self-reflect and determine which one made the most sense to them.

After all three strategies were presented and students had the opportunity to reflect on the strategy that worked best for them, student learning gained momentum. I remember one student in particular who was struggling with multi-digit multiplication after the first day of instruction, but she lit up after the area model method was introduced. I sat with her the previous day and went over how to find all the equations for the partial products method but it was just not working for her. No matter how many different ways I explained this method, it did not make sense to her. However, after the area model method was introduced, I sat with her again and she was able to independently solve equations. This experience in the classroom helped me more fully understand how differentiated instruction starts with a foundation of providing students with multiple strategies for approaching concepts. Then once students have the tools that they need, small group instruction can be used to further scaffold and evaluate student learning. Jo Boaler (2016) asserts, “This is the time when it is most critical that teachers and parents introduce mathematics as a flexible conceptual subject that is all about thinking and sense making” (p. 35). Providing students with multiple approaches and encouraging them to reflect on their own learning, helps students understand that mastery of math concepts is an individual journey that each learner needs to take. I can continue to elevate my practice by integrating self-reflection as a daily practice in math class. This routine will help students to take control of their own learning and figure what works for them.


Using Questioning as Formative Assessment

Program Standard 6

6. Assessment – The teacher uses multiple data elements (both formative and summative) to plan, inform, and adjust instruction and evaluate student learning.

6.2 Element – Designing Student Assessments with an Emphasis on Formative Assessment

6.2 Example of Proficient – Teacher has a well-developed strategy to use formative assessment and has designed particular approaches to be used.

During the completion of my Teacher Performance Assessment (edTPA), I discovered the impact that questioning can have on student learning and achievement. Throughout my coursework at Seattle Pacific University, I learned about the importance of formative assessments and how they can be used to plan, inform, and adjust instruction to drive student learning and elevate achievement. While I knew that questioning was a valuable tool in this endeavor, it has become clear that it is the best way to truly tell the depth of students’ understanding and to measure their procedural fluency, mathematical reasoning, and conceptual development. During the math lesson sequence that I taught for my edTPA, I used small group lessons to probe students’ thinking and monitor their progress. What I discovered was that students who can easily fill out math worksheets often do not fully understand the concepts behind the procedures. While students were able to produce the right answers to math equations, they were not able to explain their reasoning or revealed that they had formed a misconception. These misconceptions might not have hindered that student’s ability to complete that particular task but left unchecked would cause knowledge gaps that would hinder future success. It is crucial that the information gained during these formative assessments is documented so that it can be used to adjust instruction and provide students with the targeted support needed. I used a monitoring sheet to record data about students’ comprehension and reasoning. The information on this monitoring sheet was used to provide scaffolding to struggling students and elevations to students who excel, as well as, provide mini-lessons to address misconceptions. As shown on the monitoring sheet, one student, in particular, developed a misconception about number bonds which was uncovered and addressed through questioning. By being asked strategic questions, the student was able to unpack the misconception without direct instruction from the teacher.

In order to gain valuable insights, I first had to prepare questions that would reveal students’ mathematical reasoning and conceptual development. Worksheets are useful in assessing students’ procedural fluency but often fail to measure much more. Questioning also allows teachers to give immediate feedback on student progress which is critical to success. Smith and Stein (2011) assert, “Good questions certainly help. They can guide students’ attention to previously unnoticed features of a problem or they can loosen up their thinking so that they can gain a new perspective on what is being asked. Good questions also force students to articulate their thinking so that it is understandable to another human being; this articulation, in and of itself, is often a catalyst for learning” (p. 62). During small group instruction at the half circle table pictured to the left, I would assess student progress starting with prompts for students to demonstrate their basic knowledge, comprehension, and application of the skills required to solve a problem. Then, students would be asked to analyze their understanding of the problem by explaining their reasoning. Next, students would be directed to synthesize and evaluate their understanding of the concept by identifying what math strategies and tools they found most helpful in solving equations. Finally, questioning was used to help students uncover their own misconceptions and confront them directly. Even though the students that I am working with are only in kindergarten, I found that they are easily able to explain their reasoning and evaluate their progress when asked the right questions. For my students, the act of explaining their mathematical process helped them to work through problems and correct their own mistakes. When I used the prepared questions, students would often come to their own revelations about math which is much more impactful than just receiving an explanation from the teacher. This practice has become a daily part of my math instruction throughout my student teaching experience. Moving forward, I would like to begin using questioning to this degree in all subject matter as it has been so effective during mathematics instruction.

Smith, M.S., & Stein, M.K. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Fostering an Inclusive Classroom

Program Standard 5

5. Learning Environment – The teacher fosters and manages a safe and inclusive learning environment that takes into account: physical, emotional, and intellectual well-being.

5.1 Element – Creating an Environment of Respect and Rapport

5.1 Example of Proficient – Teacher-student interactions are friendly and demonstrate general caring and respect. Such interactions are appropriate to the age and cultures of the students. Students exhibit respect for the teacher.

Inclusivity is a crucial element to consider when fostering a positive learning atmosphere. Students spend a great deal of time in school interacting with their peers and with their teacher and because of this fact it is important that their physical, emotional, and intellectual well-being are considered. Creating a classroom community requires teachers to take into account the unique experiences of each student. Kohn (2008) asserts that a classroom community is “a place in which students feel cared about and are encouraged to care about each other. They experience a sense of being valued and respected; the children matter to one another and to the teacher” (Chapter 7, Section 1, para. 2). During the first few weeks of my student teaching internship, I have taken note of the many ways in which my mentor teacher cultivates a respectful and inclusive environment. A foundational element of creating this type of classroom is respect. My mentor teacher nurtures a climate of caring between her students. This task is accomplished not only through meaningful interactions but also by exposing her students to the cultural heritage of their peers. She has discovered that reading books discussing differing experiences helps to make her students classroom-booksunderstand each other better and imbue them with a sense of community. The picture shows just a few of the books read aloud to students in this classroom which expose them to a reality outside their own. These books often deal with complex issues in a manner accessible to the kindergarteners that she teaches. During read aloud time, these books often serve as a springboard for discussions that open students’ minds to new ideas.

Throughout my coursework at Seattle Pacific University, I have learned the importance of assembling a classroom library that represents the diversity that exists in America. I knew that it would be important to curate this kind of classroom library and select books for read aloud time that expose students to experiences outside of their own. However, I did not anticipate how profound of an effect it would have on students or how impactful it would be in helping students bond with one another. My mentor teacher just finished reading The Year of the Rat by Grace Lin to her class at the suggestion of one of her student’s parents. This book provides insight into the unique experiences faced every day as an immigrant to America. It is told through the eyes of a young girl and details her triumphs and challenges as she navigates school. While this book was being read aloud, the student whose parent suggested it would often interject anecdotes of personal experiences. These narratives often started interesting conversations and allow the rest of the class to connect with this student. These types of interactions have a deep and meaningful impact on the classroom environment and serve to help students relate to one another. As a teacher, it will be important for me to institute this kind of practice into my routine. It will be essential to enable meaningful dialogue which will serve to strengthen the respect between classmates. Establishing a good relationship with students’ parents is an essential first step in accomplishing this goal. Getting to know my students’ parents will help me to understand their unique experiences and how they can be incorporated into the classroom community.

Kohn, A. (2008). Beyond Discipline: From Compliance to Community. Alexandria, VA: Association for Supervision and Curriculum Development. [Kindle DX version]. Retrieved from Amazon.com