STANDARDS, OBJECTIVE AND ASSESSMENT
Standards: Operations and Algebraic thinking 4.0A
Learning Objective(s)/Learning Target(s): Students will select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.
Knowledge of Students to Inform Instruction: Students had most difficulty with the distribution property. Once students were able to comprehend what a partial value was they were able to relation-expanded form to the distributive property. Understanding partial values is necessary to break apart multi-digit factors.
Daily assessments are completed at the end of the class our teaching cycle requires individual check. Weekly formative assessments are completed in our ITL room (computer lab) if the student fails the computer automatically provides a reteach lesson and retake quiz for the student. Data is given back to the teacher with in 48 hrs. The follow week if a percentage of students do not understand a concept it is retaught during our reteach block (40 minutes). Formative chapter exams on paper are given every 4 weeks to see if students are retaining the information not just memorizing steps.
For this lesson students will need to recognize and memorize a series of properties that must be followed when solving multiplication/division. To be able to remember these rules and to test to see what needs the daily assessments were curtail. I would not teach a new property until I saw the students were clear on the previous. If students were able to apply multiplication properties to one another it showed true mastery. This all comes to stand on the idea’s the Vygotsky championed. First, scaffolding is essential to the learning of these skills and concepts, as well as overall mastery. Students must be support as they are moved up towards the level of knowledge expected. Vygotsky championed the idea that what a child can do in cooperation with others, they can then do independently later, and thus the ideas of scaffolding, and the Zone of Proximal Development, are so key in this type of lesson. By both supporting a students, while also pushing them a bit outside of their current level of understanding on a subject, it allows for a more deeply cemented level of understanding. It avoids the issue of rote memorization and instead promotes mastery. The use of the computer lab as a tool for support allows for that scaffolding to be promoted both by the teacher, but also through a more impartial support. Vygotsky notes that culture plays a signification role in way students develop and learn, so there are inherent social pressures at play. The use of the computer format can help alleviate some of the pressures of operating and displaying knowledge within the classroom and with peers.
Webb’s Depth of Knowledge model was also keenly important to consider. While student should certainly be hitting on Level 1, the big push in this lesson is to push them beyond recall and support them as they approach DOK level 2. That second level and the transition into organizing the understanding of the concept in a more meaningful way is incredibly important. With math there is often an emphasis on rote memorization. That only gets students to DOK 1. Pushing to DOK 2, and allowing them to being to see the concept as a whole, leads to the shift towards being apply to apply the concept in similar, but different, contexts. This lesson serves as a stepping stone, or scaffold if you will, to allow students to achieve DOK’s 3 and 4. These is where the shift moves over to a deeper, theoretical understanding and not simply the ability to reproduce multiplication and division through surface level calculation. This relates to Bloom’s Taxonomy as well. Students are typically beginning this lesson on the “remember” and understand levels. However, the push is to support them to hit the ability to apply and analyze. These are much higher level skills, and while students can show basic understand of the mathematical ideas they are exploring, the use of the computer lab highlights who has reached beyond the “understand” level and moved up towards the ability to apply and eventually analyze the use of multiplication and division as they can be applied to other areas in learning.
Beyond Bloom, Webb, and Vygotsky there is also Gardner who points out a variety of learning styles and preferences for students. In having a lesson set up that allows for the use of a computer program, in person review of vocabulary, along with the individual checks, there are a variety of modes used to approach review and teaching. If a student struggles when something is delivered verbally, they have the chance to see it in writing in the computer lab. Writing in their notebooks allows students who process better in that way to highlight their understanding in writing. There are a variety of ways in which students can interact with the content and highlight their knowledge, and this was very intentionally built into the lesson.
Review the vocabulary of properties of multiplication and division. Identify relationships between each property.
If a student understands this lesson, then they will have the opportunity to tell me by identifying what does not belong in the given category.
Sample Student Products
Students will be able to independent define and give one example of each property in their notebooks.
“Erik Francis.” ASCD EDge - What EXACTLY Is Depth of Knowledge? (Hint: It's NOT a Wheel!), edge.ascd.org/blogpost/what-exactly-is-depth-of-knowledge-hint-its-not-a-wheel.
Gardner, John. Assessment and learning. SAGE Publications Ltd, 2013.
Mcdaniel, Rhett. “Bloom's Taxonomy.” Vanderbilt University, Vanderbilt University, 10 June 1970, cft.vanderbilt.edu/guides-sub-pages/blooms-taxonomy/.
“Scaffolding.” Scaffolding - Emerging Perspectives on Learning, Teaching and Technology, epltt.coe.uga.edu/index.php?title=Scaffolding.