Course Reflection: Planning Lessons for Effective Mathematics Instruction

4. Content Knowledge – The teacher uses content area knowledge, learning standards, appropriate pedagogy and resources to design and deliver curricula and instruction to impact student learning.

4.1 Demonstrating Knowledge of Content and Pedagogy
Teacher’s plans and practice reflect familiarity with a wide range of effective pedagogical approaches in the discipline.

4.4 Designing Coherent Instruction in the area of Lesson and Unit Structure
The lesson or unit has a clearly defined structure around which activities are organized. Progression of activities is even, with reasonable time allocations.

In order to plan successful math lessons, teachers should be familiar with a variety of pedagogical approaches in the discipline as well as understand the state standards for their curriculum. When reflecting on essential mathematics instructional practices, I agree with Ernst & Ryan (2014), that students should “interact in a safe, supportive learning community,” that teachers should “activate and build on [students’] prior knowledge,” that students should be led to “process information both visually and linguistically,” that problems should be solved with “meaningful contexts,” that students should “engage in reflection, self-monitoring, and metacognition,” and that students should “engage in complex thinking” (p. 17). In addition to following these guiding principles when planning curriculum, the mathematics teacher must also plan using the mathematical practices and standards that are appropriate for the given grade level, ensuring that the standards guide the design of their planning. Figure 1 illustrates how the Common Core State Standards (CCSS) are organized. These standards provide a guiding template to what needs to be learned but do not determine how students will engage with new knowledge. That is up to the district, school administration, and the teacher to determine. In addition, when designing math lessons, the eight standards for mathematical practice, as shown in the CCSS, should be applied to learning activities where applicable as well.

Figure 1: Domain, cluster, and standard formatting example (Common Core State Standards Initiative, 2015, p. 5)

When designing lessons to meet the CCSS, it is important to use a backward design approach to planning. The teacher should be familiar with the standards and use them to guide their planning. Beginning with the domain, it is important to understand what students need to learn and what mathematical practices can be utilized for the activity being designed. For example, when focusing on 3.NBT as represented in figure 1, students should learn the three standards in the cluster underneath this activity. Moreover, rather than pull out some base ten blocks and have students complete a worksheet, it is essential that the lesson be structured around the CCSS standards, having students “…use place value understanding to round whole numbers to the nearest 10 or 100” or “…fluently add and subtract within 1000 using strategies and algorithms based on place value…” and so on. These standards will not be met in one lesson but rather, one or several units of curriculum should be designed and students need to be appropriately assessed to facilitate that the standards are met. Throughout the course of the school year, students should be able to practice and demonstrate all of the eight mathematical practices as well. When the teacher observes the class, they should recognize mathematical practices that students are struggling with and teach those practices further. For example, students may struggle with using grade appropriate vocabulary. In such a circumstance, the teacher may decide to incorporate a lesson where students practice communicating precisely to others while using appropriate academic vocabulary. Once the data reflects that the standards have been learned, students will be prepared for the next scaffolded step in their learning when they reach the fourth grade.

In addition to designing lessons around the standards, it is imperative that students are provided time to explore mathematics. When observing all of the guiding principles of essential mathematics instruction as document by Ernst & Ryan (2014), the concept of good teaching can be quite overwhelming. One practice that can help drive all of these principles is allowing students time to explore their learning, let them do the thinking during the course of the lesson. Figure 2 highlights a model that visually allocates the ideal time frame of a mathematics lesson.

Figure 2: Football model representing percentage of time needed for student exploration (Soine, 2015)

While it is important to provide an introduction and time to summarize a lesson, students need time to think independently, utilize tools and classroom resources, work independently, work in cooperative groups, and explore different problems with increasing difficulty (Soine, 2015). The launch of the lesson, as shown in Figure 3, should be engaging and introduce material to prepare students for exploration.

Figure 3: Sample of lesson launch (Soine, 2015)

Exploration time, as shown in Figure 4, should allow students to further engage in the material while the teacher circulates, assesses student learning, and asks questions to guide students to think more deeply about the material they are learning.

Figure 4: Sample highlighting lesson exploration tasks (Soine, 2015)

As shown in Figure 5, the lesson summary should provide the class with time to review the content they just learned. Students should be provided time to reflect on and share their learning with the class as well as provide feedback about the lesson (student voice) to their teacher. Too often, this smaller time span is overlooked, especially when lessons take longer than originally anticipated. Summarizing a lesson is incredibly important and should always be addressed.

Figure 5: Sample of lesson summary (Soine, 2015)

Moving toward a time when I’ll be teaching in a classroom of my own, I plan to further familiarize myself with the CCSS and instructional practices that follow the guiding principles taught in this course. While Ernst & Ryan (2014) present many principles that pertain to mathematics instruction they are all relevant to all subjects taught in the classroom. Students should feel safe and secure, especially when sharing their thinking. Teachers should activate students’ prior knowledge and incorporate this into lessons. Students should be provided time to explore material in a variety of ways. Teachers should observe, assess, and question students so that they can develop deeper levels of meaning about the content they are learning when problem solving. Teachers should also allow time for students to summarize their learning, reflecting on what they learned. Lastly, curriculum should be designed around the standards, using a backward design approach to planning.

References:

Common Core State Standards Initiative (2015). Common core state standards for mathematics. (NGA Center and CCSSO, and NGA Center and CCSSO). Retrieved from http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf

Ernst, K. & Ryan, S. (2014). Your first years teaching elementary mathematics: Success from the start. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Soine, K. (2015, July 8). EDU 6130: Lesson planning and reflection [PowerPoint slides]. Retrieved from https://bbweb03.spu.edu/webapps/blackboard/content/listContent.jsp?course_id=_89224_1&content_id=_1076101_1

EDU 6526: A Layered Approach to Instruction

O – Offer an organized and challenging curriculum.

O1 – Offer an organized curriculum aligned to standards and outcomes. Teacher candidates align instruction to the learning standards and outcomes so all students know the learning targets and their progress toward meeting them.

If a model of instruction is beneficial to the learner, facilitating that a “vast amount of content can be effectively and meaningfully understood” then an old-fashioned instructional method is beneficial in the classroom (Scheuerman, 2014). In other words, presentations and lectures may have been used in schools for a long time, yet at times receive criticism. It may be useful to consider that these methods have been used for so long because much of the time, they work (Scheuerman, 2014). In addition, if students have interest in what they are learning and practice using the information they receive, this material may also be retained in their long-term memories. Situated and distributed cognition also promote “…more powerful interpretations and understandings…” of content (Pressley & McCormick, 2007). Therefore, classroom instruction should engage learners and ensure that they have a vested interest in the material they’re being taught.

As my own teaching philosophies continue to mature, I am embracing older and newer methods of teaching. As older teaching models have presented evidence that they are effective and still being used in the classroom, it is important to appreciate advances in technology, inductive learning practices, and discovery. For example, advance organizers given prior to a lecture provide an introduction to learning that prepares the students’ thinking for a given lesson. Expository and comparative organizers help students grasp concepts and hierarchies prior to receiving presented material, further enabling them to understand and reference the information they are taught (Joyce, Weil, & Calhoun, 2015). While advance organizers and lectures are effective in providing students with content, it is also essential that the teacher allow students to have time to explore new knowledge, practice problem-solving with it, explore different outcomes, and discuss this knowledge working with other students. A layered approach to pedagogy enables many different types of learners to also explore material in ways that works for them. In addition, while one method of instruction may be backed with evidence that it is proven to be effective, it is important to realize that this individual instructional method may not work for every student.

In the past, I observed a third grade class that was introduced to rocks and minerals with an advance organizer called a KWL chart. As the teacher questioned the class about what they already knew about rocks and minerals, they discussed and documented this information (K). They also noted what they wanted to know (W), and left what they learned blank (L) for future discussion during the course of the lesson. This chart was displayed at the front of the classroom for weeks as a reference. As the students read aloud together, listened to lectures, performed labs with rocks and fossils, went outside to find rocks they were learning about, drew the rock cycle in their science journals, created jewelry with rocks, worked in groups to problem-solve the classification of some mystery rocks, and took occasional assessments to test their knowledge, they continued to document new facts that they were learning about these things on the L column of the KWL chart. I see my future classroom following a similar model of instruction and organization, discovery and problem-solving, and group collaborating, working together to fulfill many levels of my students’ education.

As teachers, we are faced with the responsibility to provide meaningful organization in the way that material is to be presented in order to activate the learner’s prior knowledge and experience while we assist learning to organize new material and integrate it with existing knowledge (Scheuerman, 2014). Traditional methods of instruction grouped with many other teaching models helps to further incorporate a learning environment that reaches many different types of learners. I embrace the lecture and presentation (of course time length is dependent on age) but also embrace many other approaches to teaching. While I absolutely do not condone older methods of instruction I also embrace many others to try to reach all of my students.

References:

Joyce, B., Weil, M., & Calhoun, E. (2015). Models of teaching (9^th ed.). Boston: Pearson Education, Inc.

Pressley, M., & McCormick, C. B. (2007). Child and adolescent development for educators. New York, London: The Guilford Press.

Scheuerman, R. (2014). Session 4: Advance organizers and lesson framing. Personal Collection of (Scheuerman, R.), Seattle Pacific University, Seattle, WA. Podcast retrieved from https://bbweb-prod.spu.edu/webapps/blackboard/content/listContent.jsp?course_id=_84477_1&content_id=_1027789_1

EDU 6120 Session 9: Authentic Applications

When exploring curriculum and educational delivery methods, one approach will not facilitate effective teaching. In every classroom, regardless of age level, a layered approach to curriculum design is most effective to reach a large variety of learners. Reflecting on this week’s reading by Arthur Ellis, I am further convinced that a layered approach to educational philosophical practices accomplishes dynamic and intriguing classrooms. There are advantages and disadvantages to every teaching style, therefore it is important that instruction is flexible and dynamic based on student populations every given school year. Teachers should model curriculum based on age-levels, abilities, and knowledge of individual student populations; it is therefore of the utmost importance that teachers assess and gather data on every classroom consistently throughout the year to evaluate individual students’ progress and growth. Furthermore, learning should be intriguing and curriculum should be designed to facilitate a yearning to learn.

Ellis (n.d.) determines that there are several models of instruction that can be employed in a classroom, the didactic model, the problem solving or inquiry/discovery model, and the interpersonal learning model. Ellis states, “…A teacher will want to combine these elements for the most effective approach to teaching. The teacher will want to encourage creative thinking and intuition as well as a firm understanding of the basics of education” (p.11). People receive information through various sources throughout their lives and educators should recognize that the classroom is a real-world model of a miniature society; students in the classroom environment should learn to coexist, receive factual information, experience learning in different ways, effectively solve problems, organize and group content, adapt information making comparisons to information they already know, and receive information in cooperative, competitive, and individualistic settings (Ellis, n.d.). I embrace multiple teaching methods understanding that certain situations allocate different pedagogical styles and philosophies. The approach that I favor is the experiential approach to learning, as Jerome Bruner states:

We teach a subject, not to produce little living libraries from that subject, but rather to get a student to think mathematically for himself, to consider matters as a historian does, to take part in the process of knowledge-getting. Knowledge is a process, not a product.

            –Jerome Bruner, the Process of Education (1960)

While I embrace this approach, I also understand that various methods to conveying knowledge will effectively reach more learners.

Reference:

Ellis, A. (n.d.). School curriculum. Personal Collection of (Ellis, A.), Seattle Pacific University, Seattle, WA.

Scheuerman, R. (2014). Session 9: The courts and education. Personal Collection of (Scheuerman, R.), Seattle Pacific University, Seattle, WA.

EDU 6120 Session 1: I Learned (Reflection on Career Change)

The concept of the role of knowledge really stood out for me during session one of this foundations course. In my previous career, I designed interpretive learning environments, layering the way a story could be told, or experienced, to reach various visitor audiences. In the classroom, it is important to also layer the way content is taught in order to reach a variety of learners while also carrying a thorough understanding of the material being provided to students. One of my personal goals as an educator is to try to reach every student, organizing my planning to educate learners utilizing the three levels of knowledge acquisition, knowledge “received/revealed, discovered, and constructed”. My secondary goal is to be collegiate throughout my career, consistently enhancing my curriculum to increase and maintain its effectiveness as time progresses.

An enlightenment that presented itself when reviewing the materials presented in session one was the reminder of why I chose to work in a profession like this. When I made the decision to become an elementary educator, I received an incredible amount of support from colleagues/friends and family; I also received a lot of constructive criticism about this decision. Many people were curious to hear from me after I had spent some time in the field, probably thinking I was out of my mind to leave the exhibit design trade (after years of building my career) to become a low-paid, overworked teacher. Arthur Ellis presented some interesting points in The Teaching Decision, on the possibilities and limitations educators face, or may potentially face. It was interesting to review some of the data presented in this reading, especially the number of reasons educators leave the teaching profession, as gathered from the Gallup/Phi Delta Kappa Poll of Teachers’ Attitudes toward the Public Schools, taken in 1989:

1. Low teacher salaries
2. Discipline problems in schools
3. Low status of teaching as a profession
4. Students are unmotivated, uninterested in school
5. Lack of public financial support for education
6. Parents do not support the teachers
7. Outstanding teacher performance goes unrewarded
8. Difficulty of professional advancement
9. Parents are not interested in children’s progress

What I found humorous about this list is I can reflect on when each reason noted on this poll for leaving the profession has come up in conversation about my career change in the past year. This is not discouraging to me, but reinforces that I made the right decision to teach. Furthermore, the article on Native American Influences, Sharing the Fire: Exploring Our Place and World through Native American Mythology encouraged me to reflect more on my decision. I agree with the concept that “storytelling fosters understanding of experience,” noting that I myself have learned a lot of varied information over the years with a career of storytelling (Scheuerman, Gritter, Schuster, Fisher, 2010). I relate this story-telling idea to a charette process I’ve used with many clients, where I asked them what the “big message” was that they wanted their audience to take with them, the over-arching theme of the exhibit “experience”. This primary message would create a hierarchy of the story topics to be told and their arrangement in the exhibit environment. Visitors would then “experience” these stories through a layered approach, with lectures, readings, videos, games, immersive environments, docents, websites, and other activities. By experiencing different approaches to storytelling, visitors would be further enabled to take some knowledge with them after they left the exhibit.

Although I will probably increase my workload significantly, I’m excited about the notion of educating children at the elementary level, utilizing many of the ideas that have been presented so far in the first couple of weeks of my education at SPU and some of the connections I have made thus far to my previous career. In my previous career, I designed how knowledge was received/revealed, discovered, or constructed and am excited to do the same when I am a certified teacher.

Reference:

Ellis, A., The Teaching Decision. Personal Collection of (Ellis, A.), Seattle Pacific University, Seattle, WA.

Scheuerman, R., Gritter, K., Schuster, C. J., Fisher, G. (May 2010). Sharing the fire: Exploring our place and world through native American mythology. The English Journal, 99:1.