Drew PollyUniversity of North Carolina at Charlotte, USA

Cases on Technology Integration in Mathematics Education

A volume in the Advances in Educational Technologies and Instructional Design (AETID) Book Series

Published in the United States of America by Information Science Reference (an imprint of IGI Global)701 E. Chocolate AvenueHershey PA 17033Tel: 717-533-8845Fax: 717-533-8661 E-mail: cust@igi-global.comWeb site: http://www.igi-global.com

Copyright © 2015 by IGI Global. All rights reserved. No part of this publication may be reproduced, stored or distributed in any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher.Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. Library of Congress Cataloging-in-Publication Data

British Cataloguing in Publication DataA Cataloguing in Publication record for this book is available from the British Library.

All work contributed to this book is new, previously-unpublished material. The views expressed in this book are those of the authors, but not necessarily of the publisher.

Cases on technology integration in mathematics education / Drew Polly, editor. pages cm Includes bibliographical references and index. ISBN 978-1-4666-6497-5 (hardcover) -- ISBN 978-1-4666-6500-2 (print & perpetual access) -- ISBN 978-1-4666-6498-2 (ebook) 1. Mathematics--Study and teaching--Technological innovations. 2. Educational technology. I. Polly, Drew, 1977- QA16.C37 2015 510.71--dc23 2014026482 This book is published in the IGI Global book series Advances in Educational Technologies and Instructional Design (AETID) (ISSN: 2326-8905; eISSN: 2326-8913)

Managing Director: Production Editor: Development Editor: Acquisitions Editor: Typesetter: Cover Design:

Lindsay Johnston Christina Henning Erin O’Dea Kayla Wolfe John Crodian Jason Mull

Copyright ©2015, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.

DOI: 10.4018/978-1-4666-6497-5.ch008

Chapter 8

162

The Port Lesson:Grade 5 Mathematics Modeling

for a Local Context

EXECUTIVE SUMMARY

The authors present a grade 5 mathematics lesson that resulted from a grant-funded teacher professional development experience, which promoted inquiry learning approaches such as problem-based, project-based, place-based learning, and the Common Core State Standards for Mathematics. A local industry was incorporated into the lesson to provide a real-world context. Design decisions and a descrip-tion of how technology was utilized in the lesson are provided. Reflections from the teachers delivering the lesson and recommendations for adaptations for other contexts are included.

INTRODUCTION

Two of the authors of this chapter are teachers who participated in the Problem-based Learning and Common Core Standards for Mathematics (PBLCC) project

Charles B. HodgesGeorgia Southern University, USA

Edie R. HipchenGolden Isles Elementary, USA

Traci NewtonGolden Isles Elementary, USA

The Port Lesson

163

led by the first author. The project was funded by Georgia’s Improving Teacher Quality initiative, which is administered by the University of Georgia. The proj-ect focused on a school system in southeastern Georgia that was eligible for the project based on a formula, which considers the number of students in the system receiving free or reduced lunch, and the number of teachers in the system defined as highly qualified. A teacher is considered highly qualified in this program, if he or she is teaching in an area in which he or she is certified. An assessment of need for this project was conducted in cooperation with the school system that included a discussion with administrators, a survey of teachers, and an examination of recent standardized test data.

PBLCC began during the summer of 2012 and continued until January 2013. PBLCC was a professional development experience for mathematics teachers in Glynn County Georgia designed to introduce teachers to the Common Core State Standards for Mathematics (CCSSM) (Common Core State Standards Initiative, 2012a); concepts from problem-based, project-based, place-based learning; and the integration of available instructional technologies. Eleven teachers from elementary and middle schools participated in PBLCC.

The teacher participants in PBLCC collaborated with each other and with uni-versity faculty experts in mathematics education, problem-based and place-based learning, and instructional design to create mathematics lessons that incorporated CCSSM and the other project concepts. The lessons developed during the summer were implemented during the fall 2012 semester by the teachers who created them. The teachers evaluated the success of the lessons using an action research approach. They presented their experiences at an end-of-project meeting attended by the participants and the university faculty members who participated in the workshop. The lesson highlighted in this chapter is the work of two grade 5 teachers, who co-developed the lesson and delivered it near the beginning of the academic year, during the fall of 2012.

BACKGROUND

The CCSSM include Standards for Mathematical Practice (Common Core State Standards Initiative, 2012b). The eight standards of practice “describe varieties of expertise that mathematics educators at all levels should seek to develop in their students” (2012b). The standard of practice most relevant to this project is CCSS.Math.Practice.MP4 Model with mathematics:

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this

The Port Lesson

164

might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of inter-est depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose (2012b).

The “life, society, and workplace” (2012b) aspect of this standard was addressed in the workshop by introducing the concepts of problem-based and place-based learning to the participants. Problem-based learning is a “learner-centered approach that empowers learners to conduct research, integrate theory and practice, and apply knowledge and skills to develop a viable solution to a defined problem.” (Savery, 2006, p. 9). Long-term retention, skill development, and student and teacher satis-faction have been found to be benefits of problem-based learning when compared with traditional forms of instruction (Strobel & van Barneveld, 2009).

Place-based education grew out of environmental education and is “an approach to curriculum development and instruction that acknowledges and makes use of the places where students live to induct them into the discourses and practices of any and all school subjects” (Smith, 2013, p. 213). The introduction of these concepts was accomplished by providing presentations and reading materials to the participants and engaging them in discussions. University faculty members with expertise in these content areas provided the presentations and led the discussions.

Problem-based learning was introduced because of the emphasis on learners reasoning, data gathering, and reflection on the solution strategies (Driscoll, 2005, p. 405). Project-based and place-based learning were offered to the participants because of the perceived power of the authenticity of the lesson if it involved a connection to the local community.

Authentic learning “offers an alternative instructional model based upon sound principles for the design and implementation of complex and realistic learning tasks” (Herrington, Reeves, & Oliver, 2014, p. 401). In general, authentic tasks require learners to problem-solve, reason, think critically, and reflect on their approach to the problem at hand. Authentic assessments are supported from several educational psychology perspectives in theories such as situated cognition, meaningful learn-

The Port Lesson

165

ing, and constructivist philosophies. Dunlap (2008) notes that authentic tasks are thought to enhance transfer of learning from one context to another, and the various elements of authentic tasks are in alignment with several techniques for motivating learners (Keller, 1987).

In mathematics, word problems, or story problems, are often offered as exer-cises where students are supposed to apply concepts they have learned. However, providing a narrative description of a problem is not enough to classify a problem as authentic; the scenarios often included in these types of problems feel contrived. A classic example is a math word problem where trains are departing two cities and various facts about the two trains are asked: Which train arrives at its destina-tion first? When do the trains pass? Table 1 lists characteristics that scholars have identified as typical for a task to be considered authentic.

Upon review of Table 1, it should be apparent that designing authentic tasks requires one to break out of the school context in some way. Ideally, an authentic task might involve field trips or guest speakers, but those are not always possible. The current resources available to many teachers and school systems, however, may limit the ability to get out of the physical school context. Other factors such as school travel policies, the availability of experts or suitable locations to visit, and school culture may be limiting factors as well.

The PBLCC project was designed with field trips to take the participants into their local environment with the plan of gathering information, examples, and ar-tifacts like photos and handouts so that they could at least bring some of the local

Table 1. Typical characteristics of authentic tasks

Characteristics Citation

“worthwhile, significant, and meaningful” Ronis, 2008, p. 94

“a real-life problem has a personal frame of reference”

Renzulli, J. S., Gentry, M., & Reis, S. M., (2004), p. 74

“have meaning and applicability beyond academic success in school”

Koh, K.H., Tan, C., & Ng. (2012), p. 139

learners “examine a meaningful task, chose how to complete it, use appropriate resources, and then make sense of their learning”

Polly, (2010), p. 85

“The outcome of an authentic assessment should be in the form of a performance or product”

Ashford-Rowe, K., Herrington, J., & Brown, C. (2014), p. 207

“set in a scenario that replicates or simulates the ways in which a person’s knowledge and abilities are tested in real-world situations”

Wiggins, G., & McTighe, J. (2005), p. 154

“ill-defined…opportunities for students to define the tasks…a sustained period of time for investigation…opportunity to collaborate”

Herrington, J., & Oliver, R. (2000). p. 30

The Port Lesson

166

businesses and industries into their classrooms. The field trips allowed the partici-pants to address what Doering, Miller, Lecheler, and Henrickson (2014) describe as “layers of authenticity” (p. 1). Doering et al. identified four layers of authenticity for learning tasks: authentic content, authentic context, authentic narrative, and shared authentic experience. Bringing information from the field trips back into the classroom in the form of authentic tasks let the participants at least address the authentic context and authentic narrative aspects of the Doering et al. layers. The field trips also were designed to introduce the participants to the concept of field trips for mathematics, which they might replicate for their students. The concept of field trips for mathematics was explicitly discussed during the workshop. If the participants could take their students on similar field trips, then authentic context could be achieved as well.

The participants visited a local electricity generating plant and a local port au-thority. The PBLCC project director made advance visits to the field trip locations and discussed the need for the project visits to highlight any mathematics used in the facilities. The electricity generating plant employed engineers and many techni-cians. Mathematics was in abundance at the plant. For example, steam pressure was constantly monitored, levels of fuel in large storage tanks for the burners at the plant was monitored, and water temperature in a nearby river was monitored regularly to assess impact of discharged cooling water from the plant on the river ecosystem. At the port authority, there were many obvious examples of mathematics such as the depth of the harbor, the size and capacity of the large ships, distances travelled by the ships, the time required to load or unload a ship, and the land area required to store cargo waiting to be loaded onto ships or transported by land to other locations.

The lesson highlighted in this chapter utilized the port authority visit for the created lesson’s local context. The teachers developing this lesson chose the port authority because they believed their students would be interested, and motivated by the cargo that many of the ships transport, automobiles. The local port authority and affiliated businesses are major employers in the community. The port is an important entry and exit point in the United States for roll-on/roll-off cargo. Automobiles are a significant proportion of the roll-on/roll-off cargo, which arrives on large ships that can be seen from various points in the community. In 2012, the time this project was conducted, the port was the third busiest in the United States for roll-on/roll-off cargo, handling over 500,000 units of automobiles and machinery (Mayle, 2012).

In this particular case, the teachers identified CCSS.Math.Practice.MP4 Model with mathematics as the Standard of Practice most relevant to the project. There are, however, several points of alignment between concepts of authentic tasks and the Standards for Mathematical Practice and the CCSSM. For example, CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them aligns with Herrington and Oliver’s (2000) notion of an authentic task requiring “a sustained

The Port Lesson

167

period of time” (p. 30). Hallerman (2013) notes similarities between the CCSSM and problem-based learning such as authentic problems requiring learners to craft reasoned arguments for approaching and solving problems and authentic problems requiring collaboration and communication, which also is highlighted by Doering et al. in the notion of a “shared authentic experience” where students communicate and collaborate with peers as they work toward a problem solution. Now that a connection has been made between authentic tasks and the CCSSM, a description of the lesson developed by the teachers will be provided.

THE LESSON

Standards and Plan

The teachers created a lesson to be delivered near the beginning of the school year in grade 5. It was designed for three days of mathematics instruction time, and to address standards CCSS.Math.Content.5.OA.A.1 and CCSS.Math.Content.5.OA.A.2:

• CCSS.Math.Content.5.OA.A.1 Use parentheses, brackets, or braces in nu-merical expressions, and evaluate expressions with these symbols.

• CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calcula-tions with numbers, and interpret numerical expressions without evaluating them.

The lesson also was designed to give the students the opportunity to reason quantitatively, justify their findings, and to persevere in solving problems. It was designed for a diverse group of students, ranging from low socioeconomic back-grounds to students from homes where both parents worked and were highly involved with their child’s learning. Both classes involved in the lessons included African Americans, whites, Asians, and Hispanics. Academic abilities of the students ranged from gifted learners to students with individualized education plans. Altogether, approximately one third of the targeted learners were classified as below average, one third as average, and one third as above average learners. Some special educa-tion students were in both classes. There were gifted learners in one teacher’s class, but none in the other’s.

The teachers began the lesson by displaying a picture of car manufacturers and posing the question “What importance do you think all these cars have to Brunswick, GA?” Students were given several minutes to answer. The teachers facilitated a discussion about cars, finally telling the students that the cars shown and mentioned are imported and exported through the town’s shipping port.

The Port Lesson

168

Students were allowed to give additional comments, such as remarks about family members and friends who may work in businesses or industries associated with the port. After introducing the different types of car manufacturers who use the local port, and facts about the port, the teachers explained how cars were imported through the local port from around the world. The teachers had taken pictures on their trip to the port with the PBLCC project and they were able to share those with their students. Google Earth was used for viewing satellite photos of the port authority facilities. A short YouTube video (smithysup, 2014) was available to show the students how the large, car hauling cargo ships work. The video highlighted a ship that sometimes visits the local port and is one of the largest car carriers in the world.

The teachers explained the importance of the port to the community and shared various facts about it. They stressed that math was a very important skill used at the port every day because the port needed to know how to get the most cars trans-ported for their budget. The students were told they would use order of operations to simulate working at the port and determining how many cars they could import on the ship carrier for the least amount of money. The students were allowed to pick different ship carriers and were required to use different combinations according to vehicle capacity and transport fees. They were given a pre-determined list with this information on it. As the students worked several combinations and tried to figure the best possible prices for their budgets, the teacher facilitated the students’ work by moving from group to group.

The Students’ Task

The class was divided into teams consisting of three to four students. The teams were given a card with the name of a port in the United States. They were told that they would be working as a team representing the port along with a data chart (Figure 1). Each team was to create a presentation to be delivered to a group of car manufactures in an effort to attract the business to their port. The teams were given the descriptions of roles for the members of their teams. The teams would consist of a port director who would keep time and make sure the team stayed on task, carrier captains would consist of one or two team members who would choose and present the three ships that provided the highest capacity and lowest cost, and a port manager who would make the final decision regarding the car manufacturer that the team would represent. During each teams’ presentation, the rest of the students in the class would serve as the group of car manufacturers making decisions about which port to choose.

The Port Lesson

169

The teams were instructed to find three ships for their ports that would be the most economically efficient for the car companies to select. Each team was required to select three ships that would hold the most cars at the lowest price. Students were required to show all of their work in solving the problem, which required the skills in the standards addressed. Figure 2 shows the formula that the teams were given to help with the task. This work would be displayed during the presentation.

The data from this activity was analyzed through a teacher created rubric. Al-though students worked in groups of three to four, each student was accountable for their own activity task sheet and rubric. The rubric evaluated them on the presenta-tion from their group, their calculations, written expressions, participation in their groups, and responses to reflection questions on the activity. The reflections asked the students to respond to questions such as:

• “What new concepts did you learn from doing this project?”,• “Was there any part of the project you liked best? Why did you like that

part?”• “Did you find any part of this project difficult? If so, which part?”

Figure 1. Data chart provided to teams

The Port Lesson

170

Design Decisions

Once an authentic context for a project is established by breaking out of the school context, or bringing the necessary context into a school, it is often observed that authentic tasks are messy. The well-defined and predetermined calculations, proce-dures, and results that standard curriculum materials typically offer are not present in authentic tasks. The PBLCC project stressed the scholarly definitions of problem-based, project-based, and case-based learning, but also stressed the reality of needing to create materials that would work in their schools. The teacher participants in the project were allowed to incorporate the concepts in ways that would work in their schools, classrooms, and with their students.

Pure problem-based, project-based, and case-based learning fall into the con-structivist paradigm, but these ideas can be problematic given the constraints of school system pacing guides, class sizes, and other variables that impact a school setting. Alison Carr-Chellman (2011) observes that the “constructivist classroom resists the notion of pre-established goals and objectives” (p. 96), but notes that “scaffolding is a concept in more recent conceptions of constructivist classrooms” (p. 96). Edelson and Reiser (2006) noted the need for “making authentic practices accessible to learners” (p 335). If a problem is so ill structured, or involves skills far beyond the abilities or knowledge of the learners, then the learners may simply

Figure 2. Formula sheet provided to student team

The Port Lesson

171

refuse to engage in it. Edelson and Reiser suggested the following strategies for teachers to use when authentic tasks become overwhelming for learners (p. 336):

• Reduce task complexity by offering scaffolding, while maintaining key ele-ments of the task.

• Discuss authentic practices of experts, which might not be easily observable due to the speed or ease with which experts execute them.

• Sequence learning activities so that students’ prior knowledge and skills al-low them entry to the authentic task.

In a true problem-based or project-based scenario, the students would not have had the structure provided in this lesson, but adaptations like the formulas and data sheets were needed to make the lesson work in the particular context of this school and they are congruent with Edelson and Reiser’s (2006) recommended modifica-tions. Adaptations like these were expected as the teachers used the project to create lessons to be implemented in their classrooms. The link to the local shipping industry, the roles of the team members, and the presentation of results provided a realistic context, which provided the students many of the elements of an authentic task as described by Wiggins and McTighe (2005) and others (see Table 1).

Technology Use

Overall, technology enabled the authentic nature of this lesson. The port authority was located in the same community as the school, but time and financial resources for field trips were not abundantly available. The use of the teachers’ photos from the PBLCC professional development experience, the YouTube video and Google Earth allowed some of the local port to be brought into the teachers’ classrooms. These technology tools allowed students who did not know about the port to make connections with it to the local community, and it activated prior knowledge for students who were aware of the port’s operations.

The teachers used various technologies during the implementation of the lesson. They used YouTube to access the video about the cargo ship. Google Earth was used to show satellite images of the port. Microsoft’s PowerPoint was used to pres-ent information about the port authority. Interactive whiteboards were incorporated with the applications as appropriate. Students used the teachers’ document cameras to present their solutions to the task. The lesson was delivered near the beginning of the school year when schedules for the computer lab were still being developed, which inhibited the students from using technology for this lesson. Under differ-ent circumstances, this lesson could have been designed to involve student use of technology.

The Port Lesson

172

Recommendations

The teacher participants did an admirable job incorporating concepts from the PBLCC project into their instruction. Aside from the information related in the conclusions below, the lesson was successfully implemented with their students, and the teachers indicated that they would use the lesson again. There are elements of the lesson that could be modified for teachers who want to try similar ideas, but who have access to different resources. The two most significant areas for change are the level of adherence to the concepts of problem-based and place-based learn-ing, and student use of technology.

The teacher participants highlighted in the present case adapted the project con-tent into their teaching in the best way possible for them, their school environment, and their students. Others who wish to follow a similar lesson may have the ability to incorporate more of the concepts of problem-based or project-based instruction. For example, rather than choosing a specific business context like the port author-ity, teachers could allow students to explore local businesses or industries on their own and to look for applications of mathematics in whatever contexts they select. In addition to choosing the context, the type of problem within the selected context could be student-driven. Allowing the students to have this level of control over the lesson, however, introduces many issues that need to be considered carefully. Probably the most significant of these issues is time. In the case highlighted in this chapter, the teachers made decisions that would allow the lesson to fit within their otherwise, system-driven pacing.

Technology use is another area where there could be significant modifications to the lesson. Polly (2010) recommends that authentic tasks can benefit from the integration of technology through “providing immediate access to information, dynamic tools to support task completion, flexibility for students’ work in OELEs [open-ended learning environments], and more options for students to create artifacts of knowledge” (p. 87). If students had regular access to the Internet during their mathematics instruction, then they could have conducted research on local busi-nesses and industries to help them select their own problem. The students could add additional authenticity to the problem by researching ships, the ship capacities, and actual costs. The real-world numbers discovered through this research, however, could lead to numbers and calculations that are outside of the students’ level of un-derstanding. There is an obvious trade-off between the amount of realism involved and the ability levels of the students involved. The students needed numbers that were easy to work with and flexible for working with the order of operations. The teachers felt that is was more important for the students to understand the concept and procedures rather than working with truly authentic values that could be messy for the students. Working with whole numbers selected for their level allowed the

The Port Lesson

173

students entry to the concepts and procedures. Students could be required to create a multimedia presentation explaining their solutions. These multimedia presentations could be shared with parents or others in the community to demonstrate the type of work the students are doing, and could be used as evidence that students also are achieving technology standards.

CONCLUSION

Problem-based or project-based approaches to teaching and learning align well with the standards for mathematical practice. While the CCSSM standard for practice related to modeling with mathematics (CCSS.Math.Practice.MP4) was a focus of this lesson, the lesson clearly addresses, or could be slightly revised to address, additional standards of practice for the CCSSM. In particular, when working a problem like the one used in this lesson students must make sense of problems and persevere in solving them (CCSS.Math.Practice.MP1), construct viable arguments and critique the reasoning of others (CCSS.Math.Practice.MP3), and use appropriate tools stra-tegically (CCSS.Math.Practice.MP5). In addition to meeting several standards for mathematical practice, there are opportunities for a lesson like the one described to cut across different content areas. The teachers who developed this lesson were able to incorporate the local port authority into social studies discussions involving geography and trade involving importing and exporting.

The observations that Polly (2010, p. 87) makes with regard to technology sup-porting authentic learning make it clear that technology standards can be addressed along with mathematics and other content standards. The International Society for Technology in Education maintains National Educational Technology Standards for several groups involved in teaching and learning. Their technology standards for students (NETS, 2007) include skills such as using technology to assist with research, problem-solving, communication, and collaboration, which are all impor-tant in solving authentic problems.

During the planning of this lesson, a differentiated task sheet was created for students with special needs or below average learners. During the lesson, it was apparent that most of the students needed the differentiated task sheet. Even though this activity was given after full instruction of order of operations and multiple step problems, the students still needed to be prompted on what was needed to solve the equation. This may indicate that more scaffolding and adaptations like those recommended by Edelson and Reiser (2006) may be required in future iterations of this lesson.

In the future, additional instruction and practice will be needed on real world problems and thinking creatively with mathematics to solve written expressions.

The Port Lesson

174

An extension to this activity would be to challenge students to design a simulation of a processing plant, or business, in which they derive their own calculations using order of operations to solve real-world problems related to their industry. As their skill with mathematics increases, working with actual measurements or data obtained through Internet research into authentic contexts would be possible. The teacher may need to model various ways of finding a solution to multiple step problems. Technology tools could be used to work with the real-world numbers that may make some calculations difficult for fifth-grade students.

In the end, the lesson was well received by the students and teachers. The teach-ers decided to implement more problem-based or place-based learning concepts into their classes to give students the practice and opportunities they need to see the importance of mathematics in real world situations.

REFERENCES

Carr-Chellman, A. A. (2011). Instructional design for teachers: Improving classroom practice. New York: Routledge.

Common Core State Standards Initiative. (2012a). Common core state standards initiative. Retrieved from http://www.corestandards.org

Common Core State Standards Initiative. (2012b). Standards for mathematical practice. Retrieved from: http://www.corestandards.org/Math/Practice

Doering, A., Miller, C. D., Lecheler, L., & Henrickson, J. (2014, April). Layers of authenticity: Designing for learner experience. Paper presented at the annual meet-ing of the American Educational Research Association. Philadelphia, PA.

Driscoll, M. P. (2005). Psychology of learning for instruction (3rd ed.). Boston: Allyn and Bacon.

Dunlap, J. (2008). Getting to the heart of the problem: Using the problems of practice approach as a starting place for creating problem-centered instruction. Performance Improvement, 48(8), 26–34. doi:10.1002/pfi.20020

Hallerman, S. (2013, December). The role of PBL in making the shift to common core. Retrieved from http://www.edutopia.org/blog/pbl-role-shift-to-ccss-sara-hallermann

Herrington, J., Reeves, T. C., & Oliver, R. (2014). Authentic learning environments. In J. M. Spector, M.D. Merrill, J. Elen, & M.J. Bishop (Eds.), Handbook of research for educational communications and technology (4th ed., pp. 401-412). New York: Springer Science+Business Media.

The Port Lesson

175

Keller, J. M. (1987). Development and use of the ARCS model of instructional de-sign. Journal of Instructional Development, 10(3), 2–10. doi:10.1007/BF02905780

Mayle, M. C. (2012, September). Autos, biomass drive Brunswick port growth. The Savannah Morning News. Retrieved from http://savannahnow.com

NETS. (2007). NETS for students 2007. Retrieved from http://www.iste.org/stan-dards/standards-for- students/nets-student-standards-2007

Polly, D. (2010). Employing technology to create authentic learning environments. In H. Song (Ed.), Distance Learning Technology, Current Instruction, and the Future of Education: Applications of Today, Practices of Tomorrow (pp. 83–94). Hershey, PA: IGI Global.

Renzulli, J. S., Gentry, M., & Reis, S. M. (2004). A time and a place for authentic learning. Educational Leadership, 62(1), 73–77.

Savery, J. R. (2006). Overview of problem-based learning: Definitions and distinc-tions. Interdisciplinary Journal of Problem-based Learning, 1(1), 9-20. Retrieved from http://docs.lib.purdue.edu/ijpbl/vol1/iss1/3/

Smith, G. A. (2013). Place-based education: Practice and impacts. In R. B. Stevenson, M. Brody, J. Dillon, & A. E. J. Wals (Eds.), International handbook of environmental education (pp. 213–220). New York: Routledge.

smithysup. (2014, February 14). Faust-car carrier [Video file]. Retrieved from: http://www.youtube.com/watch?v=_bbPJhS0byw

Stobel, J., & van Barneveld, A. (2009). When is PBL more effective? A meta-synthesis of meta- analyses comparing PBL to conventional classrooms. Interdisciplinary Journal of Problem-based Learning, 3(1), 44-58. Retrieved from http://docs.lib.purdue.edu/ijpbl/vol3/iss1/4/

Wiggins, G., & McTighe, J. (2005). Understanding by design (2nd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.

ADDITIONAL READING

Bender, W. N. (2012). Project-based learning: Differentiating instruction for the 21st century. Thousand Oaks, CA: Corwin.

The Port Lesson

176

Cennamo, K. S., Ross, J. D., & Ertmer, P. A. (2013). Technology integration for meaningful classroom use: A standards-based approach (2nd ed.). Belmont, CA: Wadsworth, Cengage Learning.

Guskey, T. R. (2000). Evaluating professional development. Thousand Oaks, CA: Corwin Press, Inc.

Hendricks, C. (2012). Improving schools through action research: A reflective practice approach (3rd ed.). Boston: Pearson.

Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do stu-dents learn? Educational Psychology Review, 16(3), 235–266. doi:10.1023/B:EDPR.0000034022.16470.f3

Hodges, C., Grant, M., & Polly, D. (2013). Beyond one-shot workshops: Three approaches to STEM teacher professional development. Proceedings of Society for Information Technology & Teacher Education International Conference, 2013, 4795–4800.

Jonassen, D. H. (1997). Instructional design models for well-structured and ill-structured problem-solving learning outcomes. Educational Technology Research and Development, 45(1), 65–94. doi:10.1007/BF02299613

Jonassen, D. H. (2010). Learning to solve problems: A handbook for designing problem-solving learning environments. New York: Routledge.

Loucks-Horsley, S., Stiles, K., Mundry, S., Love, N., & Hewson, P. (2010). Design-ing professional development for teachers of science and mathematics. Thousand Oaks, CA: Corwin Press, Inc.

McComas, W. (2014). Place-based Learning. In W. McComas (Ed.), The Language of Science Education (pp. 73–73). Rotterdam, The Netherlands: SensePublishers. doi:10.1007/978-94-6209-497-0_63

Polly, D. (2010). Employing technology to create authentic learning environments. In H. Song (Ed.), Distance Learning Technology, Current Instruction, and the Future of Education: Applications of Today, Practices of Tomorrow (pp. 83–94). Hershey, PA: IGI Global.

Polly, D. (2011). Preparing teachers to integrate technology effectively: The case of higher-order thinking skills (HOTS). In S. D’Augustono (Ed.), Adaptation, Resistance and Access to Instructional Technologies: Assessing Future Trends in Education (pp. 395–409). Hershey, PA: IGI Global.

The Port Lesson

177

Powers, A. L. (2004). An evaluation of four place-based education programs. The Journal of Environmental Education, 35(4), 17–32. doi:10.3200/JOEE.35.4.17-32

Promise of place: Enriching lives through place-based education. (n.d.). Retrieved from: http://www.promiseofplace.org/

Ronis, D. L. (2007). Problem-based learning for math & science: Integrating inquiry and the Internet (2nd ed.). Thousand Oaks, CA: Corwin Press.

Savery, J. R. (2006). Overview of problem-based learning: Definitions and distinc-tions. Interdisciplinary Journal of Problem-based Learning, 1(1), 9-20. Retrieved from http://docs.lib.purdue.edu/ijpbl/vol1/iss1/3/

Smith, G. A. (2013). Place-based education: Practice and impacts. In R. B. Stevenson, M. Brody, J. Dillon, & A. E. J. Wals (Eds.), International handbook of environmental education (pp. 213–220). New York: Routledge.

Smith, G. A., & Sobel, D. (2010). Place- and community-based education in schools. New York: Routledge.

So, H.-J., & Kim, B. (2009). Learning about problem based learning: Student teach-ers integrating technology, pedagogy and content knowledge. Australasian Journal of Educational Technology, 25(1), 101–116. Retrieved from http://ascilite.org.au/ajet/ajet25/so.html

Stobel, J., & van Barneveld, A. (2009). When is PBL more effective? A meta-synthesis of meta-analyses comparing PBL to conventional classrooms. Interdisciplinary Journal of Problem-based Learning, 3(1), 44-58. Retrieved from http://docs.lib.purdue.edu/ijpbl/vol3/iss1/4/

Wiggins, G., & McTighe, J. (2005). Understanding by design (2nd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.

Williams, D. C., Pedersen, S., & Liu, M. (1998). An evaluation of the use of problem-based learning software by middle school students. Journal of Universal Computer Science, 4(4), 466–483.

Wirkala, C., & Kuhn, D. (2011). Problem-based learning in k–12 education:Is it ef-fective and how does it achieve its effects? American Educational Research Journal, 48(5), 1157–1186. doi:10.3102/0002831211419491

The Port Lesson

178

KEY TERMS AND DEFINITIONS

Action Research: A reflective approach to research conducted with the purpose of enhancing one’s professional practice.

Authentic Task: In education, a task that is grounded in some authentic context or scenario.

Common Core State Standards: Content area standards for k-12 mathematics and English language arts developed by the Common Core State Standards Initiative.

Mathematics Modeling: The mathematical representation of problems or phenomenon for the purpose of exploring solutions of visualizing relationships.

Place-Based Learning: A student centered pedagogy where students explore problems that they discover or encounter in their local environments, research the problems, develop solution strategies, and document their solution process along with their proposed solutions. Place-based learning often includes an aspect of environmental education.

Problem-Based Learning: A student centered pedagogy where students typi-cally establish problems, research the problems, develop solution strategies, and document their solution process along with their proposed solutions.

Project-Based Learning: A student centered pedagogy where students typically research problems presented by a teacher or other entity, develop solution strategies, and document their solution process along with their proposed solutions.

Standards for Mathematical Practice: Principles established with the Com-mon Core State Standards for Mathematics that establish observable practices that demonstrate mathematical thinking.