Heidi A. Eisenreichhttps://works.bepress.com/heidi-eisenreich/Recent works by Heidi A. Eisenreichen-usCopyright (c) 2019 All rights reserved.Wed, 05 Apr 2017 07:00:00 +00003600Completing the Incomplete: Making Sense of Completing the Square Using Manipulativeshttps://works.bepress.com/heidi-eisenreich/1/<p>Participants will use algebra tiles to make sense of completing the square. This workshop will focus on collaboration to build a deeper understanding of the topic. Participants will also discuss student misconceptions, possible errors when completing the square, and how manipulatives can help students make sense of the process.</p>
Wed, 05 Apr 2017 07:00:00 +0000https://works.bepress.com/heidi-eisenreich/1/National/International ConferencesMaking Sense to Explore: Teaching Area With Coherencehttps://works.bepress.com/heidi-eisenreich/9/<p>Engage in experiences designed to develop a deeper understanding of teaching area with coherence. Make sense of the progression of area through elementary and middle grades by exploring tasks as learners. Area formulas for quadrilaterals and the circle will be of focus. Connect your experience to students through authentic classroom video.</p>
Wed, 05 Apr 2017 07:00:00 +0000https://works.bepress.com/heidi-eisenreich/9/National/International ConferencesPreservice Teachers’ Conceptions and Misconceptions of Physical and Virtual Manipulativeshttps://works.bepress.com/heidi-eisenreich/14/<p>It is necessary to assess virtual manipulatives’ impact on the learning process. A possible approach is a framework that combines the wellknown concrete, pictorial and abstract levels with a proposed Virtuallevel. We will discuss preservice teachers’ understanding of the framework.</p>
Thu, 09 Feb 2017 08:00:00 +0000https://works.bepress.com/heidi-eisenreich/14/National/International ConferencesConceptual and Procedural Understanding: Prospective Teachers’ Interpretations and Applicationshttps://works.bepress.com/heidi-eisenreich/5/<p>The preparation of prospective secondary mathematics teachers often revolves around working to improve knowledge of mathematics for teaching and understanding the conceptual development and trajectories of mathematics. “Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems” (NCTM, 2014, p. 42). Prospective teachers need to be prepared to teach concepts along with procedures (Ball, Thames, & Phelps, 2008) particularly with the implementation of the Common Core State Standards (CCSS). In their own experience as a learner of mathematics, however, many prospective teachers come with procedural understandings of mathematics and many struggle to understand the underlying concepts and why those procedures work. Challenging prospective teachers to examine their own understandings of mathematical concepts and their preconceived ideas of good mathematics instruction becomes an important aspect of mathematics teacher preparation.</p>
<p>In this study, prospective secondary mathematics teachers were asked to read Principles to Actions’ section on Conceptual Understanding and Procedural Fluency (NCTM, 2014). Having individually defined conceptual and procedural understanding in their own words, they were asked to apply those understandings to determine how a student might solve a percentage problem with a conceptual and with a procedural understanding. Prospective teachers’ definitions and student solutions were examined to answer the question: In what ways do prospective secondary mathematics teachers define conceptual understanding and procedural understanding and subsequently apply those definitions to solve a percent problem?</p>
<p>Using the prospective teachers’ own definitions of these two terms, the researchers compared the definitions with how each prospective teacher distinguished between the types of understandings when applied to the given percent problem. Data showed some disconnect between definitions and applications. Additionally, responses of prospective teachers to the percentage problem could have been either conceptual or procedural based upon varying aspects of student solutions.</p>
Tue, 01 Nov 2016 07:00:00 +0000https://works.bepress.com/heidi-eisenreich/5/National/International ConferencesHelping Preservice Teachers Make Sense of Whole Number Concepts and Operations: Working in Base 8https://works.bepress.com/heidi-eisenreich/6/<p>How to improve teacher education programs to allow preservice teachers (PSTs) make sense of mathematics for depth, is a topic debated among educational researchers, especially in mathematics education. PSTs and inservice teachers (ISTs) need to be prepared to teach concepts and to understand how and why students come up with different strategies and whether those strategies will work all the time. Teaching whole number concepts and operations (WNCO) in a base other than 10 can challenge PSTs and ISTs to think about mathematics in ways similar to an elementary student. Previous studies have reported PSTs and ISTs struggle when using base systems other than base 10 in an education class or a professional development workshop just like their elementary students might struggle with base 10 (Andreasen, 2006; McClain, 2003; Yackel, Underwood, & Elias, 2007; Zazkis & Zazkis, 2011).</p>
<p>At one university, PSTs work in base 8 for an entire 4 week unit to gain a deeper understanding of WNCO. While learning in base 8, PSTs have to make sense of mathematics strategies in a deeper level than if they were learning about them in base 10. For example, if students are asked to add 7+6 in base 10, they will say 13. When asked “how do you know?” their most likely response is that they just know. By asking the same question in base 8, PSTs make sense of regrouping in a way that is similar to how beginning learners make sense of regrouping in base 10. This can address an important barrier in supporting PSTs and ISTs to understand WNCO in ways that are important for teaching.</p>
<p>The purpose of this research was to use qualitative data from interviews and observations to attempt to answer the question: In what ways do PSTs perceive learning WNCO in base 8? Interviews were conducted to ascertain how PSTs may or may not have changed their views on learning in base 8. Data from interviews of four PSTs indicated they initially struggled with learning WNCO using base 8 during the four week unit. In the beginning, PSTs were frustrated with learning in base 8 and did not understand why they needed to learn this way. However, as the unit continued, researchers found that PSTs were more accepting and realized the importance of learning in base 8. Most understood that although they will not be teaching their elementary students in base 8, learning in this base system had benefits they did not initially realize, for example understanding WNCO in depth.</p>
Tue, 01 Nov 2016 07:00:00 +0000https://works.bepress.com/heidi-eisenreich/6/National/International ConferencesParent Workshops Focused on Mathematics Knowledge for Parenting (MKP): Shifting Beliefs About Learning Mathematicshttps://works.bepress.com/heidi-eisenreich/10/<p>The purpose of this study was to investigate the extent to which parents of first, second, and third grade students who attended a two-day workshop on mathematics strategies shifted beliefs about learning mathematics as compared to parents who did not attend the workshops. Parents impact their children’s mathematics learning when the students are at home working on homework. This can be an important barrier to overcome. The results suggested parents could benefit from workshops focused on solving mathematics problems in multiple ways, similar to ways their children are learning mathematics.</p>
Tue, 01 Nov 2016 07:00:00 +0000https://works.bepress.com/heidi-eisenreich/10/National/International ConferencesConnecting Fraction Manipulatives to Contexthttps://works.bepress.com/heidi-eisenreich/7/<p>Participants will build a conceptual understanding of fraction subtraction by using fraction circles to solve word problems. This workshop will focus on discourse, as participants will work in groups to make sense of fraction subtraction. Participants will practice writing and solving fraction subtraction problems.</p>
Sat, 01 Oct 2016 07:00:00 +0000https://works.bepress.com/heidi-eisenreich/7/Regional/State/Local ConferencesWhat Have I Done? Connecting Fraction Manipulatives to Contexthttps://works.bepress.com/heidi-eisenreich/15/<p>Participants will build a conceptual understanding of fraction subtraction by using fraction circles to solve word problems. This workshop will focus on discourse, as participants will work in groups to make sense of fraction subtraction. Participants will practice writing and solving fraction subtraction problems.</p>
Sat, 01 Oct 2016 07:00:00 +0000https://works.bepress.com/heidi-eisenreich/15/Regional/State/Local ConferencesMaking Sense of Quadratic Equationshttps://works.bepress.com/heidi-eisenreich/2/<p>This session will engage participants in exploring quadratic equations using a variety of tools. Connections to the Standards for Mathematical Practices will be made, and mathematical tasks, which are designed to provide opportunities for rich discourse and student engagement will be shared. Participants will also discuss student misconceptions and possible errors as they solve quadratic equations.</p>
Sat, 01 Oct 2016 07:00:00 +0000https://works.bepress.com/heidi-eisenreich/2/Regional/State/Local ConferencesAlignment of Lecture and Lab in Introductory Microbiology and Biology Courses: Analysis of Current Practiceshttps://works.bepress.com/heidi-eisenreich/8/<p>Laboratory activities are a vital component of college-level introductory biology and microbiology courses, yet there is little evidence of a standardized approach to the implementation of the laboratory section across different institution types. Kolb’s experiential learning cycle suggests student understanding of complex scientific topics progresses from abstract conceptualization, to active experimentation, to concrete experience, and finally reflective observation. Alignment of topics between the lecture and lab may assist students in making meaningful connections between abstract concepts studied in lecture and their concrete experience in the laboratory. The hypotheses for this study were: 1) Smaller institutions and community colleges are more likely to align lecture and lab topics than large research institutions and 2) Professors with a focus on teaching are more likely to align lecture and lab topics. One hundred thirty introductory biology, microbiology, cell biology, environmental biology, and other biology instructors from various institution types were surveyed to determine the degree of alignment between lecture topics and lab activities in their courses. A chi-square test of association on self-reported data indicated a significant effect of institution type (chi 2 = 32.33, df = 16, p < 0.05) and instructor type (chi 2 = 38.07, df = 24, p < 0.05). Regional and comprehensive universities showed the highest degree of alignment among institution types (chi 2 = 15.69, df = 4, p < 0.05). Though not significant, instructors with equal teaching and research duties contribute heavily to alignment of topics (chi 2 = 8.56, df = 4, p = 0.73). Results of this study may have implications for the development of more effective curriculum practices in large research institutions that assist students in completing the experiential learning cycle that may lead to improved student learning outcomes and retention of students in biology and microbiology courses.</p>
Fri, 01 Jul 2016 07:00:00 +0000https://works.bepress.com/heidi-eisenreich/8/National/International Conferences