I like to have big ideas hanging out in the back of my mind while I'm working on more routine tasks. So as I think of the day ahead, a day that mostly includes lots of student support as they lead the global cardboard challenge arcade, I'll be thinking about the math and science practices.
The chart above demonstrates the practices we want children to employ as they learn math. How can I deepen their efforts in that regard.
Positive learning tasks will lead the way for these efforts. As I choose, personalize, and create standards-based math tasks for fifth graders, I'll be thinking about the pattern of learning that helps students to utilize the math practices. Positive tasks will include the following steps:
- A meaningful question--the kind of question that inspires a child to "make sense of problems and persevere in solving them."
- Modeling and opportunities to explicitly witness and use "abstract and quantitative reasoning." Translating problems into number sentences or numerical expressions is the way that children will study and practice this math practice.
- Opportunities to present their learning and critique the learning of others.
- Using manipulatives, paper/pencil illustrations, and digital representations strategically to create structure and model math concepts, patterns (repeated reasoning), knowledge, and skill. I will spend significant time at the start of the school year teaching students about the manipulatives and digital tools available, and how we might use those manipulatives, digital tools, and paper/pencil to model math concepts, knowledge, skill, and patterns.
- Using math learning process that includes self-editing, peer-editing, teacher-student editing, and presentation will foster precision.
The first activity of the year will be an activity that relates to number knowledge including arrays, factors, multiples, proportion, and vocabulary. As students and I explore the number 24 together, we'll focus on the following questions:
- What do you think about and know about when you consider the number 24?
- What does 24 look like when turned into arrays? How can we draw those arrays? How do the varying arrays that equal 24 look the same (rectangles) and different (different dimensions, proportions)?
- When we consider the multiples and factors of 24, what patterns do we notice?
- How can we apply what we know about 24 to the number 48? What does this tell us about any numbers' arrays, factors, and multiples?
- Work with your team to complete a number card for 48. Be prepared to present your card to the class. Be prepared to critique the cards of other students.
This will be a simple way to introduce and use the math practices at the start of the year. Later we'll deepen that work with more meaningful, rich problems and tasks.
Cross-cutting math/science concepts are another area of focus for fifth grade. How will we focus on these. At first thought, I realize that questioning related to multiple situations will support these cross cutting concepts. Questions such as these will help:
- What patterns did you notice?
- What were the causes for this effect?
- What scale, proportion, or quantity do you notice? How can we illustrate that scale, proportion, or quantity?
- What is a system? What are the system parts; how do those parts work together to effect a singular or multiple effects.
- What is matter? What is energy? How do matter and energy work? How can we describe matter and energy?
- What is structure? What is function? How does the structure affect the function?
- What is stability? What is change? What creates change to a stable situation?
I want to explore this language more on my own and with the students as I work with the curriculum. By creating related mini posters with this language and hanging those posters up in the class, I will make this thinking and language readily available to students.
Looking specifically at the science practices, helps me to think about learning patterns we'll employ in the year ahead, patterns that support math and science education.
- Rather than always presenting a question or problem, making time to present a scenario or event, and letting students define the problem and ask the questions. This related to the phenomena routine and three-act problem solving I was introduced to last week.
- Developing and using models is a key focus of fifth grade math and science teaching. We'll explicitly focus on this throughout the year with particular attention in reviewing and explicitly teaching this skill at the start of the year.
- Planning and carrying out investigations. I'll begin by explicitly demonstrating this thinking and action with students. I'll give students a roadmap to initial investigations and provide the opportunity to come up with next step investigation plans and efforts. This will be a good way to teach this to fifth graders.
- Analyzing and interpreting data will begin at the start of the year. We'll collect and analyze data about our grade-level community and come up with a TeamFive profile. We'll play dice games, collect related data and come up with conclusions about numbers 1-6 using spreadsheets as one way to collect and analyze data. Further we'll collect data about multiples and factors of numbers 1-100. This will help students to warm-up their brains related to number knowledge, math/science practices, and more at the start of the year.
- Mathematical and Computational Thinking will be started via Massachusetts computational thinking tasks shared with me at a recent conference.
- Constructing explanations, designing solutions, engaging arguments from evidence, obtaining, evaluating, presenting/communicating information, and critiquing presentations will be a regular part of the teaching/learning day.
As I work on my own and with colleagues to organize and plan for teaching/learning projects in the year ahead, we will embed the vocabulary and efforts named above. This will help us to deepen the work we do in ways that are rich, meaningful, memorable, and standards-based. This is good work, study, and teaching.