An important component to implementing the backward design strategy is to differentiate between the words “understand” and “know.” If students are to understand a concept they must be able provide evidence by demonstrating they know specific pieces of knowledge. Understanding is different from knowledge because it requires thinking beyond the facts. Wiggins & McTighe (2005) state, “To understand is to have done it in the right way, often reflected in being able to explain why a particular skill, approach, or body of knowledge is or is not appropriate in a particular situation” (p. 39). Unlike facts or skills learned through memorization or drill, understanding requires students to apply what they learned to different contexts. The goal then is for teachers to design instruction that focuses on applying what students learn to larger contexts so they can transfer their knowledge. Otherwise, students will likely learn topics in isolation through memorization without understanding their relation to other ideas or the purpose for learning the content.
It is true that a lot of instruction in classrooms today is designed for coverage. This is a problem that exists in classrooms with pressure of state testing and so much content to cover. The problem with this approach is that it is not always engaging for the learner and often students forget content later because memorization does not stick. This is why a lot of re-teaching and review has to happen prior to the state testing and at each grade level. In order to determine if students’ understand, assessments must include evidence of transfer. Wiggins & McTighe (2005) state, “Getting evidence of understanding means crafting assessments to evoke transferability: finding out if students can apply their learning and use it wisely, flexibly, and creatively” (p.48). So students have opportunities for transfer, assessment that requires students to inquire and apply their knowledge is important. This type of assessment allows teachers to learn more about a students’ understanding. Otherwise students may have gotten the correct answer by accident or memorization.
Our math curriculum is designed to develop conceptual frameworks that will endure as they progress to higher mathematics. For example, students develop an understanding of place value prior to learning operations. In my own classroom, students are reviewing and building on concepts they learned previously until they can apply what they learned to a new concept or strategy. Students use many models to construct their understanding of math concepts. What is frustrating to teachers at the primary level is that students are developing strategies and concepts but are not prepared to solve an algorithm or the multitude of problem types on the MSP. As teachers feel the pressure of the MSP and revise the pacing guide they struggle with questions like, “At what point do we move away from the strategy and teach the content directly? Should we continue to spend time developing these concepts or ensure that all of the standards are taught prior to the MSP?” I struggle with the answers to these questions. It is understood that we might see a drop in scores in the primary grades but the conceptual models students are building will benefit them in high school. It is difficult to make decisions about what to teach next when we know we are ultimately responsible for our students passing the standardized test. In response to the question, “Do these innovative approaches produce better learners?,” Green replies, “I don’t have a doubt in my mind, but it depends on what the measure is. If it is how successful they are going to be in the real world, definitely. If it’s how well they perform on standardized tests, not necessarily” (Diamond & Hopson, 2008, p.84). Our constructivist approach to math has allowed us to reach all learners at their level. The conceptual models have helped students who struggle to solve an algorithm or solve a fact. When comparing American and Japanese-style lessons Diamond & Hopson (2008) state, “The American lesson required mostly memorization and guesswork” (p.77). Green says she was a great memorizer and learned a process, but remembered nothing after the test. Her husband was a self-taught learner and read what interested him. Years later he is still able to carry on a conversation about his learning (Diamond & Hopson, 2008, p. 84). This validates the value of engaging all students in conceptual learning including students who can solve the algorithm quickly or have their facts memorized. They may continue to be successful throughout their education but will have difficulty transferring their learning beyond their schooling
Wolfe (2001) states, “One of the most effective ways to make information meaningful is to associate or compare the new concept with a known concept, to hook the unfamiliar with something familiar” (p.104). Accessing students background knowledge is one teaching strategy that can help students make connections and add to their schema. Some teaching strategies for accessing background knowledge may include KWL charts, graphic organizers, think-pair-share, preview of texts, and read alouds that connect to the content. This artifact, LearningSlip, is an example of one way I activate prior knowledge before a lesson. Students complete an exit slip before and after a lesson. Before the lesson students list prior knowledge that will help them with the new learning. This allows students to apply new knowledge to their existing schema in order to develop a deeper understanding of the learning.
Diamond, M., & Hopson, J. (2008). The Jossey-Bass Reader on the Brain and Learning. San Francisco: John Wiley & Sons, Inc..
Wiggins, G., & McTighe, J., (2005) Understanding by Design. Alexandria, VA: ASCD.
Wolfe, P. (2001). Brain Matters: Translating Research into Classroom Practice. Alexandria: Association for Supervision and Curriculum Development.