Beyond Objectives: High School Reality

  • Beyond Objectives: High School Reality

    By Marjan Hong, posted December 19, 2016 —

    To clarify the idea (a beyond-objectives mindset in the classroom) that I introduced in my previous two blogs, I mean a mindset that focuses on developing mathematical thinking so to empower students to engage with mathematics content.

    I believe that inquiry-based learning provides a natural opportunity to strengthen the development of our students’ mathematical thinking. Taking small steps makes the transition to inquiry-based instruction appear effortless and prepares our students to be successful. To illustrate, let’s imagine that a group of algebra 1 teachers is meeting with the math coach as part of their weekly professional learning community. The conversation might go something like this:

    Teacher A: I want to try this at some point, but I don’t think we can really start right now because this week we need to teach properties of exponents.

    Coach: What prior learning involving exponents have students engaged in?

    Teacher B: Last year (in grade 8), students used properties of exponents to write equivalent numerical expressions. The exponents were integers only. One application involved scientific notation.

    Coach: What would “objective met” look like?

    Teacher A: I would say the objective is met if they could successfully complete an item like this:

    2016_12_19_Hong3 equation

    Coach:Impressive! As part of your students’ thinking process, what might you need to see and hear?

    Teacher C: To complete an item like this, they would need to be able to look at the whole as well as the relationships among the like bases; but I also wouldn’t want them to be overwhelmed.

    Teacher B: I would want them to be able to explain the details of their solution process.

    Coach: So, when we consider the eight mathematical practices from NCTM’s Principles to Actions: Ensuring Mathematical Success for All (2014, p. 10) or the Common Core’s Standards for Mathematical Practice (SMP) (CCSSI 2010, pp. 6–8) which might we need to see in play?

    Teacher B: I’d say the first one and the sixth one, for sure. (SMP 1. Make sense of problems and persevere in solving them. SMP 6. Attend to precision.)

    Teacher A: If they could look at someone else’s work and give feedback, that would be great.

    Teachers B and C: I agree; the third one would be something to push for. (SMP 3. Construct viable arguments and critique the reasoning of others.)

    Coach: What might happen if the students were presented with the expression and asked to discuss it? How might we use students’ prior learning from grade 8 to have them discuss and work with this expression?

    Teacher A: They’d need to know that they have to use properties of exponents.

    Teacher C: I agree, but I’m not sure all my students remember those properties or how they work together.

    After additional discussion, the teachers and coach draft the Jaime task:

    2016_12_19_Hong3 equation

    Jaime and his friends are walking by Mrs. Holbrook’s math class and see this on the board:

    Jaime says he would use “properties of exponents” to write an expression that is equivalent but looks a whole lot less complicated.

    Work with your team to develop answers to the following questions:

    • What do you think Jaime means by his statement?

    • What might Jaime’s “less complicated” expression look like?

    Before implementing the Jaime task, the teachers must ask themselves such questions as, What might be some benefits of using this task as opposed to some other tasks? Is the task accessible to all students? What questions might students have? Will this task lead to the desired objectives? What type of task should follow this one?

    Tasks like the Jaime problem take small steps in the direction of inquiry-based instruction—teachers drafted the question and suggested the “tools” (properties of exponents) that students should use to create an equivalent expression. Perhaps more significant in the transition is the dialogue that results among teachers as well as students.

    Hong Author Pic Marjan Hong,, has worked in mathematics education for nearly thirty years as a teacher, mentor, curriculum specialist, and consultant. She is currently curriculum content developer for Discovery Education. Her passions include access and equity in mathematics education, empowering teachers, and inquiry-based learning.

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    Nicole Schneider - 9/29/2018 8:10:56 PM

    I am currently a sophmore at Wartburg College and I am a secondary education major. I was just wondering how you would impliment this in a classroom. I did not fully understand how you would introduce this as the lesson? Or would this just be a question on the test that you woud want to make sure your students can understand? 

    Doug Mcdaniel - 8/31/2018 8:12:20 AM

    Wow! Swarovski crystals are all one can desire. I love the tabletop items. I have seen many pictures in a review magazine. I wish to buy a Swarovski photo frame someday. Thank you for sharing this post.

    Luz Renteria - 4/23/2018 12:42:19 PM

    Hello Mrs. Hong! I am a second year student at UC Berkeley studying math and education, and I really enjoyed your post! I never thought that a dialogue of this sort actually happened in high schools between math teachers. I knew they had meetings, but never thought about what they might be discussing. This was an interesting glimpse into what it might look like. I would like to ask, however, is the technical type of language used in this dialogue (i.e. common core standards (SMP 1, SMP 6), eight mathematical practices, etc) are common in these kinds of meetings? I thought that I would only be using this as I study education, but it does make sense to use it in practice. Thank you!