Kelly Smith

Return to: ETAP 623 Spring 2017 | Exploratory Mathematics

About me

My name is Kelly Smith, and I am currently enrolled in ETAP 623, working towards my Master's Degree in Curriculum Design and Instructional Technology. I am a Syracuse University graduate, with a degree in Inclusive Elementary and Special Education. After I graduated from Syracuse I began working at P.S. 57 Crescent in the Bronx, where I am currently in my third year teaching third grade. My biggest passion is ensuring that all students receive a high quality of education with rigorous academic and social standards, regardless of ability or disability. Outside of teaching, I enjoy being outside at the pool or the beach. I also spend my free time reading books, going to the gym, and spending time with my family.

My Topic/Purpose

The title of my mini-course is Exploratory Math Lessons in an Elementary Classroom. The purpose of this course is to develop an understanding for the need of exploratory math lessons in elementary classrooms, and to be able to create exploratory lessons to fit the needs of your classroom.

The following questions will guide the design of this course:

What is exploratory learning?
How does exploratory learning deepen students conceptual understanding of math concepts?
How can you create exploratory math lessons to fit the needs of your classroom?

Learning Outcomes

Upon completion of this course, learners will be able to:

Explain the benefits of exploratory learning (verbal)
Create exploratory lessons based on various math concepts (intellectual)
Choose an exploratory math lesson to use in their classroom (attitude)

Needs Assessment

Problem

In 21st century classrooms, we are seeing a major shift in mathematics education. With the invention of smartphones and accessibility to calculators and technology, the need to memorize basic mathematics facts and equations is no longer a priority. Instead, mathematics today is important so that students can develop a strong number sense, as well as the ability to problem solve and think critically. According to An Up-close Look at Student Centered Learning, this new 21st century economy “requires workers who can make sense of and tackle complex problems, work on collaborative cross-disciplinary teams, use high-level mathematical reasoning skills and digital technology, and communicate their ideas clearly” (Walters et al., 2014, p. 2) In order for our students to be successful in this new economy, mathematics instruction must reflect these skills.

However, typical teacher led math instruction does not provide the conceptual understanding that todays students need to be successful in todays society, and often leads to student misconception and forgetting basic math knowledge that is learned in elementary school. The math mathematical concepts we are expecting children to learn require a great deal of mathematical thinking, and teachers often “overlook how complex of a process it actually is for children” (Bruce, Flynn, & Bennet, 2015, p. 2). In other words, teaching these concepts in a traditional lecture format may seem effective for adults, but children need more of an opportunity to think deeply about these concepts. In addition, this emphasis on memorization causes a negative stigma surrounding mathematics, and as a result leads to a lack of interest in mathematics, and any math professions (Darling Hammond, 2008, p. 122).

Teachers need to shift their mathematics instruction to allow students to explore, reason, and problem solve, in order to allow for mathematics to become relevant and valued among today’s students. According to a study done by Michael C. Brune, where he compared the results of groups of students being taught using a traditional lecture format and groups of students being taught using inquiry based instruction, exploratory learning lead to a higher level of understanding. The results showed that “Students involved in the inquiry-based lessons exhibited better retention, a better ability to problem solve, and better performance on decontextualized mathematical problems than their peers who were taught in the traditional fashion” (2010, p. 45). Another benefit of exploratory learning is for the teachers. Teachers reported that after observing students’ participation in exploratory lessons, they were able to more effectively identify areas of strengths and weaknesses in their students, and use this data to create subsequent lessons (Bruce, Flynn, & Bennet, 2015, p.11).

What is to be learned

Learners will learn the components of exploratory mathematics and the benefit this model has on student learning and understanding. They will also learn the steps to create an exploratory math lesson given various math objectives so that they can utilize this in their own classrooms.

The learners

Learners will include educators, preservice educators, or professionals in the educational field who are interesting in adopting exploratory math lessons into their classroom. Instruction will be geared towards teachers in elementary classrooms, although the activities taught could be modified to fit the needs of a secondary mathematics classroom. Learners will have varying degrees of experience teaching mathematics and have various knowledge about what constitutes an exploratory math lesson.

Instructional context

Learners will be engaging in instruction solely online. Learners can participate where and when they would like. Access to internet is required in order to participate in the mini course.

Exploring the problem and solution

In many schools, the math curriculum given is set up in the typical “I do, we do, you do” model, where teachers explicitly model the math skill or strategy, and then students practice exactly what the teacher just did. This model leads to a lack of student understanding, and a lack of student interest. Additionally, many teachers are not aware of the exploratory math model, and do not have the tools necessary to create exploratory math lessons out of the lessons they already have. Research indicates that teaching for understanding is extremely beneficial, with very little cost (Darling-Hammond, 2008, p. 133). This course will give teachers the tools and steps necessary to create exploratory lessons in their own classroom (based on the curriculum already in place), where students are actively engaging in mathematical practices such as problem solving and reasoning.

Goals

The goal of this mini course is for math teachers to be able to create exploratory math lessons for their students to promote deeper conceptual understanding among their students.

Performance Objectives

Given a video, a sample lesson plan, and a power point presentation, learners will be able to define the key components of an exploratory math lesson by answering 4 multiple choice questions.
Given two articles, learners will be able to explain two benefits of using exploratory math lessons in the classroom in at least 200 words, backing up their responses with relevant details and examples.
Given a math objective and a lesson template, learners will be able to create an exploratory math lesson that includes objectives, assessment, engage, explore, explain, and a closure, using the lesson plan template and rubric provided.
Learners will be able to reflect on student learning after implementing an exploratory math lesson in their own classroom by posting a 2 page response that explains what went well, what did not go well, and what next steps they will take based on student learning.

Task Analysis

Unit 1: Learners will understand the concept of exploratory learning and why it is important to student learning and understanding.

Lesson 1 enabling goal: Learners will define the components of an exploratory lesson

Activities:

Learners will watch a video about exploratory learning
Learners will read a sample exploratory math lesson
Learners will write down what they notice about the video and sample lesson
Learners will view a power point presentation about the components of an exploratory math lesson.

Assessment:

Learners will take a multiple choice quiz about the components of an exploratory math lesson.

Lesson 2 enabling goal: Learners will explain how exploratory learning deepens student understanding

Activities:

Learners will read two articles about the benefits of exploratory learning
Learners will write down thoughts or questions they had while reading the articles

Assessment:

Learners will write a 200 word response identifying two benefits of exploratory math lessons.

Unit 2: Learners will understand how to create and teach an exploratory math lesson in their classroom.

Lesson 3 enabling goal: Learners will create an exploratory math lesson

Activities:

Learners will identify an objective to be used to create an exploratory math lesson
Learners will use the template provided to create an exploratory math lesson

Assessment

Learners will upload their exploratory math lesson and assess themselves using the rubric provided

Lesson 4 enabling goal: Learners will implement and exploratory lesson in their own classroom and reflect on student learning.

Activities

Learners will teach their exploratory math lesson in their classroom
Learners will reflect on what went well, what did not go well
Learners will identify next steps based on student learning.

Assessment

Learners will post a 2 page response about their exploratory lesson that explains what went well, what did not go well, and what next steps they will take based on student learning.

Curriculum Map

File:Curriculum Map Kelly Smith.pdf

References and Resources

Bruce, C.D., Flynn, T.C., & Bennet, S. (2015). A focus on exploratory tasks in lesson study: The Canadian ‘Math for Young Children’ project. ZDM Mathematics Education. DOI 10.1007/s11858-015-0747-7

Brune, Michael C. (2010). The inquiry learning model as an approach to mathematics instruction (Master’s Thesis). Retrieved from Scholarworks.boisestate.edu.

Darling-Hammond, L. et al. (2008). Powerful Learning: What We Know About Teaching for Understanding. San Francisco, CA: Jossey-Bass. (ISBN 978-0-470- 27667-9)

Walters, K., Smith, T.M., Leinwand, S., Sur, W., Stein, A., and Baily, P. (2014). An Up-Close Look at Student-Centered Math Teaching. Retreived from: https://www.nmefoundation.org/getattachment/Resources/Student-Centered-Learning/An-Up-Close-Look-at-Student-Centered-Math-Teaching/An-UpClose-Look-at-Student-Centered-Math-Teaching-(1).pdf?ext=.pdf