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Emily Duong's Portfolio Page

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About Me

I am Emily Duong and this is my final semester at the University of Albany! I will be graduating from the CDIT program this December. This is my second year of full-time teaching and my fourth year of teaching in general. I teach 7th grade ICT math in Brooklyn. I am also finishing up my second master's in Middle School Education at Relay GSE! In my free time, I like to read the news, learn foreign languages, and play with my cats! I have two cats, Coco and Mimi, and I can speak Mandarin, Cantonese, and French!

My Topic and Purpose

My topic, as you can see on my project page, is mathematical modelling and how this is an important tool to develop a conceptual understanding of middle school mathematics. My project will include four parts: the importance of mathematical modelling, how to teach and use mathematical modelling in math class, important mathematical modelling in middle school, and independent practice. After taking my project, teachers will be able to name two important ways that mathematical modelling can support their teaching, and be able to use at least one mathematical model in the classroom immediately.

Scope of Learning Outcomes and Content

  • Define key mathematical modeling and their benefits
  • Connect mathematical models with state standards
  • Connect mathematical models with conceptual understanding
  • Analyze examples of how mathematical models and provide feedback
  • Analyze the progression of math models in middle school
  • Create a show-call sequence of questions for a mathematical model

Needs Assessment

Part 1: Intent

The NAEP achievement report for New York City reveals that only approximately 33% of 8th graders are at or above proficient at math. This brings up the issue of learning and teaching math for understanding in order for students to successfully solve math problems. Research has shown that students who use accurate visual representations are “six times more likely to correctly solve mathematics problems than are students who do not use them.” (Boonen, van Wesel, Jolles, & van der Schoot, 2014). The math models are also important to students who have learning disabilities or lower-performing students as they are more likely to solve the problems accurately. (Krawec, 2014). My hypothesis is that teachers need to start preparing students to use visual models while also internalizing the models themselves.

Part 2: Gathering Information

In order to assess the possible need for a mini-course on mathematical visual models, a survey of middle school math teachers was conducted. Ten surveys were distributed and received. Fifteen surveys were distributed and four responses were received.

Part 3: Summary

SUMMARY OF RESPONSES TO MIDDLE SCHOOL MATH TEACHER SURVEY

Related to modelling/drawing

  • Drawing helps me visualize the problems/ideas [2 agree, 2 strongly agree]
  • Drawing is an effective way to answer a question/state an idea [4 agree]
  • Drawing and modelling are similar because they both show the artist’s logical thinking and ideas [3 agree, 1 strongly agree]

Related to mathematical modelling

  • Mathematical modelling is an important practice standard of Common Core Math Standard for middle school students[3 strongly agree, 1 strongly agree]
  • I accept a mathematical model as a strategy in my classroom [4 agree]
  • I have taught at least two of the following: place value chart, ratio table, number line, and/or double number line [4 strongly agree]
  • My students benefit greatly from mathematical modelling [2 agree, 2 strongly agree]
  • My students struggle with mathematical modelling [1 agree, 3 strongly agree]

Related to professional development

  • My students will struggle less with mathematical modelling if I can teach them about the models in greater details [3 agree, 1 depends]
  • All mathematical models progress and can be used in different grades [2 agree, 2 neutral]
  • I understand how the models progress within middle school math contexts and can use them to solve most middle school math problems [2 neutral, 2 disagree]
  • I am well-prepared to teach any of the following models to any of middle school grades: place value chart, ratio table, number line, and/or double number line [1 agree, 2 disagree, 1 neutral]
  • I need targeted professional development about mathematical modelling, including how to use them and how to teach them [3 agree, 1 strongly agree]

All respondents indicated positive attitudes towards drawing and modellings as possible ways to express ideas and logical thinking. All respondents acknowledged the importance of mathematical modelling in academic contexts and indicated some knowledge on mathematical modelling, including at least two of the mentioned models. Most respondents, 3 out of 4, feel unprepared to teach mathematical modelling and all respondents indicated the need for professional development in this area.

All of the respondents in this survey have been teaching middle school, from grade 5 to 8, for more than 3, but less than 6 years. Based on the responses to this survey, although all respondents indicated positive attitudes towards and some knowledge on mathematical modelling, it appears that some teachers need support to understand the model themselves and how to teach them to the students. All respondents indicated that they lack knowledge of how mathematical models progress within middle school mathematics. This also explains why half of the respondents showed some confusion about when mathematical models can be used. More specifically, half of the respondents answered “neutral” when asked about whether mathematical models can be used in different contexts and different grades or not.

Therefore, a mini-course on mathematical modelling training that aids the understanding of three core models, number line, ratio table, and place value chart, is needed. This will not only support the teachers in understanding how to use the models to explain their reasoning themselves but allow them to support their learners to successfully use these models. This will aid mathematical visualization and allow teachers to differentiate the content for struggling students and students with IEPs.

Analysis of the Learner and Context

  • Learner Characteristics

Who are the learners? They are Middle school Math teachers
What personal characteristics do these learners possess? They have solid math content knowledge with little to no background in mathematical model
What contributes to the reason for learning about the topic? The reasons are lack of content mastery across all grade level of math and lack of conceptual understanding for new content
What is the reason for enrolling in the course? Learners want to have a professional development on mathematical models for math pedagogical improvement
What are the student’s learning styles? They share prefererence for asynchrous lessons and flexible schedule

  • Prior Knowledge

What do learners already know? They can solve any problems algebraically or using number sense but cannot accurately use a model to visualize or solve a problem with confidence

  • Demographics

Where are the learners coming from in terms of their education level, ethnicity, demographic, hobbies, area of study, grade level? All learners have at least one Master's degree in Education or Eduation-related field
Why are these demographics important for the material you will be teaching? Because they will be the active facilitator and promotors of mathematical use within the classroom

  • Access to Technology

All learners have access to laptop and Internet. They are also proficient in basic computer skills

Performance-Based Objectives

  • Learners will be able to reflect on the importance of mathematical visual model and how it connects to the Common Core Math Standards and Practice
  • Learners will be able to correctly use a mathematical visual model (number line, ratio table, or place value chart) to correctly solve three out of three problems
  • Learners will be able to craft sequential scaffolding questions on the visual models during whole-class discussion for push students' deeper understanding
  • Learners will be able to give sample feedback on the use of mathematical model in their classroom

Task Analysis

Unit 1: What is Mathematical Modeling? And Why Should We Teach it in Middle School? - At the end of this unit, learners will be able to:

  • Define key benefits of mathematical modeling
  • Identify the need for mathematical modeling in middle school mathematics
  • Identify the valuable skills students will develop from learning to solve middle school mathematics using models
  • Interpret the Common Core Math Practice Standards and identify the standards that require mathematical modeling

Unit 2: Key Mathematical Modellings in Real-Life Word Problems - At the end of this unit, learners will be able to:

  • Identify key mathematical models that students will use in middle school
  • Identify at least two models that their students can benefit from in the current grades
  • Explain how mathematical models support students’ logical thinking and deeper understanding of new concepts
  • Analyze examples of how mathematical models can be used in their respective grade level

Unit 3: Progression of Mathematical Modelling in Middle School Mathematics - At the end of this unit, learners will be able to:

  • Identify the common standards across grades 5-8 that can benefit from the same mathematical models
  • Connect specific grade-level content to the mathematical model
  • Solve different grade-level mathematical problems using the same model
  • Explain how key mathematical models progress within middle school mathematics

Unit 4: Classroom Strategies and Planning for Mathematical Models - At the end of this unit, learners will be able to:

  • Analyze an example model to teach mathematical models using questioning and show-calling
  • Connect information from previous units to the mentioned example
  • Identify exemplar and non-exemplar sequence of questions that can support students’ analysis of the new mathematical model
  • Collaborate to create a sequence of questions to support students’ analysis of the new mathematical model
  • Modify the sequence of questions based on given feedback to meet the criteria of success

Unit 5: Application of Mathematical Modelling in The Classroom - At the end of this unit, learners will be able to:

  • Review the available resources to refresh their memory of key mathematical models
  • Create their own sequence of questions for a new mathematical model for an upcoming lesson
  • Promote the use of mathematical models in their own classrooms
  • Modify their upcoming weekly lesson plans to incorporate the use of mathematical models
  • Provide feedback for sample work on the use of mathematical models

Curriculum Map

Refer to the graphic on the right side for the map of the curriculum

References

Extended Resources

Author Types of Resources and Name Link Description of Resources
Sarah Hampton Blog, "Modeling in the Middle School Math Classroom" https://my.nctm.org/blogs/sarah-hampton/2018/12/19/modeling-in-the-middle-school-math-classroom What is and what is not mathematical modelling?
Nancy Wolf Book, "Modeling with Mathematics" https://www.heinemann.com/products/e06259.aspx Support for and examples of incorporating modeling in the classroom
Achieve the Core Interactive Media, "Coherence Map" https://achievethecore.org/coherence-map/ All grades' math standards are linked together based on progression. Each standard includes a sample assessment, including the solutions that mostly consist of a supporting visual model}
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