Interactive Mathematics Program: A Standards-Based Curriculum

Pamela R. H. Bailey

George Mason University

Interactive Mathematics Program: A Standards-Based Curriculum

Introduction

Our world has changed immensely since we were in school. So what about our schools? To address the changes, the National Council of Teachers of Mathematics (1989, 2000) researched and began promoting the process standards: collaboration, communication, problem solving, reasoning and justification, and representations. But how does a school system know if a specific standards-based program is the right one for their students, teachers, and community? The focus of this paper is on the Interactive Mathematics Program and how has it been evaluated by researchers in comparison to what has been determined as important in a standards-based program. Understanding the development of the program will be presented along with research studies that did analyze the program. Concerns, weaknesses, and suggestions will also be discussed.

History of IMP

The history of IMP is mentioned in numerous research studies and articles (Clarke, Breed, & Fraser, 2004; Education Development Center, Inc., 2005; Interactive Mathematics Program Resource Center, 2007; McCaffrey, Hamilton, Stecher, Klein, Bugliari, & Robyn, 2001; Merlino & Wolff, 2001; Webb & Dowling, 1997). Funded by the California Postsecondary Education Commission grant, IMP began working on the reform curriculum in 1989. Originally the development of IMP was headed up by Lynne Alper, Dan Fendel, Sherry Fraser, and Diane Resek. The California commission wanted the team to develop a curriculum that would overhaul the traditional three year curriculum within the courses of Algebra I, Geometry, Algebra II / Trigonometry. At the same time the team was to meet the criteria of the NCTM Curriculum and Evaluation Standards for School Mathematics (1989). Additional funding was received in 1992 from the National Science Foundation (NSF) to increase the curriculum to four years and as an integrated college preparatory course. Evaluation of the curriculum and dissemination aspects was also included in the NSF grant.

From 1989 to 1992 the IMP curriculum was field tested and each unit revised a minimum of three times before being considered a final product. When NSF funded the fourth year additional field testing was completed by a group of experienced IMP teachers working as a team discussing each unit. One year of the curriculum was released beginning in 1996. In 2002, the second edition of IMP was funded by NSF. As the development of IMP progressed many schools jumped at the opportunity to implement the curriculum. In order to do so the school had to agree to all guidelines set forth by IMP as the curriculum was expanded.

IMP Characteristics, Principles, and Goals

IMP Materials and Program Characteristics

Characteristics of IMP are that the curriculum is unit based with several units making up a year of study (Education Development Center, Inc., 2005; Evitts, 2004; McCaffrey, et al., 2001; Merlino & Wolff, 2001; Resek, 2007; Webb & Dowling, 1997). Twenty units were developed for the four year curriculum with each unit centered on a large problem that may or may not have a real-world context. Each unit will last between five to eight weeks. Units are problem-based and integrate additional topics recommended by NCTM such as probability, statistics, discrete mathematics, and matrix algebra. Student assignments include problems of the week (POW), daily homework, as well as activities and investigations completed in and outside of class. The POW is open-ended situations that encourage reasoning and thinking skills. Students will be expected to write up their analysis and result to explain their reasoning. Grouping of students will vary according to the activity and expectations so that they may be a part of a small group, whole class, or individually working. Supplemental and enrichment problems are included with the basic curriculum to assist the facilitator in meeting the needs of all students. Graphing calculators are required for students to complete many of the activities.

Assessments in the IMP curriculum vary but are not the traditional drill and kill or multiple-choice (Education Development Center, Inc., 2005; Resek, 2007). Teachers are encouraged to have students complete a portfolio of their assignments to show growth as well as make presentations to their peers. Daily homework and assignments, problems of the week, and in-class and take home assessments are part of the assessment packaged promoted by IMP.

Additional resources (Education Development Center, Inc., 2005) provided with the IMP package are a teaching guide for each unit (Teaching Handbook for IMP: A Teacher-to-Teacher Guide), a handbook of strategies (Introduction and Implementation Strategies for the Interactive Mathematics Program), and a handbook about using graphing calculators (Guide to Using TI Calculators with IMP). In addition to the handbook two units are included that are not part of the yearly curriculum but may be included as the teacher sees fit. A three week unit of study called “Baker’s Choice” comes with the teaching guide, student text, and blackline master. The student text is not included with the added one week unit of study titled “It’s All Write: A Writing Supplement for High School Mathematics”. All items are available in four languages, English, Spanish, French, and Hawaiian.

IMP Principles and Beliefs

Four basic principles were established for the foundation of the curriculum (Alper, Fendel, Fraser, & Resek, 1997; Key Curriculum Press, 1998). The first principle is having the students feel comfortable with the curriculum and see the usefulness of learning mathematics. Students will be expected to collaborate, the second principle. Collaboration that is constructive and practical is viewed as a method to influence a student’s productive disposition. Students working together lead to the last two principles. Number three is the involvement of the students in problem solving within real-world contexts thereby encouraging thinking skills and the making of connections. The last principle is about student empowerment. Students will feel empowered when they are able to communicate using mathematical language as they think, reason, problem solve, and verbalize their thoughts. These principles correlate with the current National Council of Teachers of Mathematics (NCTM) Process Standards (NCTM, 2000) of communication, collaboration, problem solving, reasoning and justification, and representations.

The authors of IMP wanted to stimulate students to achieve through the program‘s belief system (Clarke, Breed, & Fraser, 2004). This is in contrast to achievement produced by traditional tasks. If student beliefs are such that they want to learn based on curriculum, written and enacted, then they will be taking more courses in mathematics and their achievement will also be positive. Traditional classes, according to Clarke, Breed, and Fraser, do not typically encourage students to “like” mathematics and to want to take additional classes to further their mathematical knowledge.

IMP Goals

Clarke, Breed and Fraser (2004) summarized the goals of the program in five statements. First, mathematics should be accessible to all students, including groups that are typically underrepresented in college mathematics courses. Second, the curriculum should emphasize problem solving and the ability of students to communicate their ideas according to the NCTM Curriculum and Evaluation Standards (NCTM, 1989; 2000). Next would be the active engagement of students in learning and integrating technology. Following engagement would be the change in the role of the teacher from a guide to a facilitator. Lastly, assessments would be varied so that students are able to express their knowledge in different formats using mathematical language appropriately. The Interactive Mathematics Program Resource Center (2007) shortens the goals to one sentence by stating that technology is to be implemented to aid in students reasoning, problem-solving, and communication skills along with the mathematical topics of probability, statistics, and discrete mathematics. Publishers of standards-based materials claim that they meet NCTM standards (Kulm, 1999). Determining the best curriculum for your stakeholders is more than a checklist.

Evaluating a Standards-Based Curriculum

Alper, Fendel, Fraser, and Resek (1997) posit that a standards-based mathematics course should be centered on changing from a procedural focus to solving problems. In order to do so, they list several aspects that a curriculum needs to be implemented successfully. We need to take in to account all the past negative and challenging aspects of learning mathematics. The curriculum should fit in to the diversity and culture of the students while using various learning styles and concrete approaches. Meeting the academic needs of all students by embedding challenging problems in concrete approaches and providing supplemental activities to reinforce or extend the lesson should be included. A curriculum that uses situations, names, and places that the students are familiar with, will enable students to relate better to the problems. Involving students in activities using various types of grouping will enable them to explain and communicate, thereby increasing their understanding of concepts, strategies, and procedures. Involvement should go further to include the community. This might be done with data gathering or problems that are based in the community. Students should be given the opportunity to make sense of the mathematics by encouraging them to solve using their own methods. In addition to the needs of the students, teachers need to be provided with professional development. Sessions may cover strategies, questioning techniques, how to earn student’s trust and respect, while creating or facilitating problem solving that is of interest to students.

Stein, Remillard, and Smith (2007) discuss their thoughts on evaluating curriculum to determine if it will fit a school systems needs. Ascertaining whether the curriculum addresses the majority of mathematical topics is a beginning but then one needs to establish the presentation of the material. Is the text content based or does the text assist student’s with content in ways that promote learning and retention of material? Is the text written from low to high level, sections or units focused on procedural skills with the thought provoking problems given last, or in a flow that makes connections between the concepts? Balance between concepts and procedures, computations and calculators, and the expectation of multiple representations need to be considered when evaluating. The organization style of the text should also be taken in to consideration. Is the text set up in chapters and sections or in modules?

The U.S. Department of Education (Stein, Remillard, & Smith, 2007) use eight questions to guide the evaluation of curriculum. The questions written with respect to IMP are:

1. Are the goals of IMP challenging, understandable, appropriate and is the content supported by the goals?

2. Is the content and presentation appropriate for IMP students?

3. Is the IMP curriculum engaging and motivating for students?

4. Will the varied assessments encouraged by IMP assist teachers in making instructional decisions?

5. Will the IMP curriculum be adaptable to different educational settings?

6. Do the principles and goals of IMP correlate with the NCTM standards?

7. Does IMP take in to consideration society’s needs as well as individual needs?

8. Will IMP make a difference in the way students learn mathematics?

Besides the US Department of Education, Stein, Remillard, and Smith also present Project 2061 of the American Association for the Advancement of Science (AAAS) and Mathematically Correct as additional analysis approaches. Project 21 analysis is based on content with a listing of benchmarks such as number concepts, number skills, geometry concepts, geometry skills, algebra graph concepts, and algebra equation concepts. Curriculum analysis also is seen as building on prior knowledge, engaging, concept development, promotion of student thinking, progress assessed, and an emphasis on connections and meaning. Kulm (1999) states that the AAAS analysis procedure is explicit enough to decide whether the curriculum is just covering content or is it encouraging students to explore concepts to develop understanding and skill development. Mathematically Correct (Stein, Remillard, & Smith) analysis includes determining if the curriculum has clear objectives, is presented clearly, contains numerous examples, contains numerous practice problems, and builds from the basics to the more abstract.

Kulm (1999) supports AAAS, stating that their analysis is explicit and assists individuals as they determine if the proposed curriculum just covers content or does it truly assist in building student understanding as well as skill development. The analysis topics are broken into content and instructional topics. Content analysis includes not only if all concepts are included for the unit or the lesson but extends to the depth that the concepts are explored and to what extent there is a match to the applicable standards. Seven clusters of analysis topics make up the instructional aspect: a sense of purpose is identified and maintained, student ideas are considered, engagement that is relevant and meaningful, concepts are represented correctly and makes connections, and reflection and self-monitoring is promoted, assessment is aligned with the goals and embedded in the tasks. Other features include the content knowledge of the teacher and if the classroom is inviting, a place of trust where students feel comfortable to explore situations.

Additional ideas that need to be considered according to Stein, Remillard, and Smith (2007) include a concern for context and the curriculum in general. Time needed to plan lessons and to provide the instruction is a factor of major concern for teachers. Determining whether the context of the program or book is aligned with the culture of the students so they might see relevance is important. What support is or will be given to teachers as they implement the curriculum? In general is the curriculum traditional or standards-based and how does either one fit in to the school and community culture?

Bay, Reys, and Reys (1999) looked at implementing a standards-based curriculum from a different viewpoint by focusing on only what is needed for positive results. They listed ten elements that they considered to be crucial during the change by asking teachers after they had been involved with a standards-based program for three years. The main and most important element is to have administrative support. Even when teachers are not on aboard but the principal is leading to positive results. Secondly, teachers need to have the opportunity to scrutinize the NCTM standards (2000) and their state standards. Knowing what is meant by the standards will help teachers to understand why they are approaching concepts with the new curriculum. The next element of importance was for the teachers to have an opportunity to try the materials, to experience what their students will experience in the classroom. Daily planning is the fourth element and crucial for the pacing of units and daily lessons. Having the opportunity to observe an expert will enable the teachers to view the implementation which they have never seen before, the fifth element. The sixth element, collaboration, goes along with the previous items of planning and observing others but goes further. Teachers need to share grading practices, student work, and classroom management in addition to planning the lesson. While collaborating teachers may also incorporate the seventh element, creating new assessments that support a standards-based curriculum. Creating rubrics, discussing how to handle assessment of group work, and what types of writing should students be doing and how should they be assessed is new and unchartered territory for teachers. The eighth element begins the consideration of items outside of the classroom, communicating with parents. Parent nights or some other type of communication will be necessary for parents to understand how and why the mathematics curriculum has changed. What was good for the parents when they were in school will not meet the student’s needs in today’s world. Students are the focus for the ninth element as they are not used to problem solving, collaborating, and being engaged in learning. It will take time for them to be comfortable taking risks and not being spoon fed procedures. The last element is the concern for students as they transition in to high school or college mathematics courses.

Studies Evaluating IMP

Quantitative Analysis of IMP

Webb and Dowling study.

The Wisconsin Center for Educational Research (WCER) oversees IMP however a study done by Webb and Dowling (1997) clearly states that their findings did not reflect on the beliefs or opinions of WCER. Alper, Fendel, Fraser, and Resek (1997) report on the same study in general terms along with Webb and Dowling’s explicit report. The participants in the study were from three of the original pilot sites located in three different areas of the country. School A was a public school with a diverse population in western United States. Students were in the ninth grade and took either IMP year 1 or a traditional Algebra I course. The assessment for the analysis was a statistics test with four items. School B was also a public school in north-central United States but required a minimum achievement level for admittance. Students were in the tenth grade and took either IMP year 2 or a traditional Geometry course. The assessment for the ethnically diverse population for this analysis was a problem solving test with two activities. Located in the east, School C is a college preparatory magnate school with only about one-third of the applicants to the school being accepted. Students were in the eleventh grade and took either IMP year 3 or a traditional Algebra 2 course. The assessment for this study was a test created by a prestigious university for incoming freshmen and based on quantitative reasoning.

Even though it is one study with three different sites, each of the sites was analyzed individually (Alper, Fendel, Fraser, & Resek, 1997; Webb & Dowling, 1997). Each of the schools was also viewed as implementing the IMP curriculum effectively. The various assessments given to the students were created independently without the influence of the IMP curriculum and were given during the last six weeks of the 1996 school year. In all of the studies the IMP students outperformed students in traditional courses in their corresponding assessments. Even when student prior achievement, grade 8 standardized test, is taken in to consideration, IMP students still scored higher. A matched group analysis was performed with only students who had scores available on the grade 8 test. Doing so allowed for control of student’s prior achievement, gender, and ethnicity. The results were the same. In conclusion, the authors of the study believe that IMP students were learning mathematical concepts beyond the traditional curriculum.

By using three schools of varying populations in different areas of the United States, Webb and Dowling (1997) was able to assess the program for some of the U.S. Department of Education (Stein, Remillard, & Smith, 2007) questions. They determined that the goals of IMP were challenging, understandable, appropriate, and that the content supported the goals by the diversity of students, school types, school locations, and types of assessments. These items also verify the adaptability of the curriculum to different educational settings. The content and presentation of the curriculum was appropriate for IMP students and seen in the scores on the various assessments. Presentation of the material, balance between methodologies or computation versus calculator was not assessed nor was the coverage of content material specifically except for the ability of the students when assessed. We do not know if the types of assessments employed by the teachers aided their instruction or the role that the students and community played.

Clarke, Breed and Fraser study.

Clarke, Breed, and Fraser (2004) utilized an end of year questionnaire and SAT scores to investigate how students self-assessed their mathematical ability, their beliefs about activities in the IMP classes, and the source of mathematical concepts. The purpose of the study was to look at the program’s belief system that stimulated the students to achieve. This is viewed as a contrast to the achievement produced by traditional tasks. If student beliefs are such that they want to learn based on curriculum, written and enacted, then they will be taking more courses in mathematics and their achievement will be positive.

Participants are from three high schools in California and made up of 182 IMP students, 74 students taking Algebra II, and 143 students taking Algebra 4 (Clarke, Breed, & Fraser, 2004). Academic achievement levels of students taking IMP were normally lower than the corresponding students in the traditional Algebra classes. The questionnaire the students took was a modified version of one given in Australia. In order to compare students taking the IMP course with those taking the traditional courses, all were expected to take the SAT the following fall.

Results from the questionnaire showed that more of the IMP students considered their mathematical ability positively in comparison to students taking the algebra course (Clarke, Breed, & Fraser, 2004). A lower number of girls taking IMP held negative dispositions toward mathematics in comparison to the girls taking the algebra course. Those taking IMP also considered mathematics as a mental activity and that mathematics arose from individual and society’s needs. Mathematics was a path to express their world and allowed concepts to be understood. Students in traditional classes thought mathematics was absolute and unvarying. The questionnaire also showed that the IMP students valued interacting with others while they were learning. Writing and talking about the problem aided their ability to understand the situation and to brainstorm paths to find a solution. In contrast, students taking traditional algebra valued the teacher’s words and the textbook, even considering drill and practice as beneficial. IMP student SAT scores were than the non-IMP students.

Clarke, Breed, & Fraser’s (2004) study follows more closely the analysis goals as discussed previously by Stein, Remillard, & Smith (2007) with the U.S. Department of Education questions and the Project 21 by AAAS. The SAT scores increased for IMP and non-IMP students but were higher for the IMP students. This implies that the goals of the program are challenging and understandable with the content supported. Results of the questionnaire revealed that the curriculum was engaging and motivating with the content being appropriate for the students taking the course. Assessing students was not mentioned by the author’s of the study. Due to the small number of students and the centralized location of the schools, the study is not generalizable to other school systems and cultures. Student’s positive progress suggests that the course was acceptable to their needs and those of the society and at the same time changed the way they are learning. The types of analysis discussed by Stein, Remillard, and Smith do not encompass the affective results that are the basis of the study.

Cost of implementing IMP, study by Merlino and Wolff.

When proposing a new curriculum a school division must consider the cost of doing so. Merlino and Wolff (2001) conducted research to answer the question “All things being equal, does an NSF sponsored standards-based mathematics curriculum, such as the Interactive Mathematics Program (IMP), have a greater positive impact on student achievement than a “traditional” pre-standards program to such a degree as to justify the time, energy and cost of implementing it (p. 2)?” They found that if the students were taught by instructors trained in the expectations and methods of IMP then they did better than students who learned through lecture and pre-NCTM standards curriculum. This includes lower and higher achieving students in relationship to the same level of student in a traditional setting.

Six schools in Philadelphia during the 1993-1994 school year began implementing IMP. All teachers involved in teaching the curriculum received professional development for ten days a year, mentoring in the classroom, a reduced course load of 1.5 class periods, team taught for one class period, had a classroom set of graphing calculators, along with other manipulatives.
The cost of the training for all four years was $102,000 or about $21,000 per teacher. This was mostly due to reducing the number of class periods taught. By 1999-2000, class period reduction was eliminated. Philadelphia schools found the curriculum beneficial with student mathematics achievement but also in reading and science achievement. Teachers were acknowledged for the achievement and not the curriculum but without the professional development the teachers would not be able to implement the curriculum as intended.

The study addressed some of the areas of analysis listed by Stein, Remillard, & Smith (2007) such as professional development and support needed by teachers. In doing so the authors inadvertently addressed some of the issues brought forth by Project 21 and the U.S. Department of Education. Successful student scores implies that they are learning and in this case, differently. Engaging and motivating the students was shown to also be an outcome of the program. However, cost of implementing a program is a major concern for school systems so the study is informative for those considering IMP.

McCaffrey, Hamilton, Stecher, Klein, Bugliari, and Robyn study.

Tenth grade students in an urban area were the participants in efforts to implement a standards-based mathematics program as part of the NSF’s Urban Systemic Initiative (USI) (McCaffrey, et al., 2001). Focusing on professional development, teachers received assistance on instructional practices that promotes reform. Some of the major shifts that teachers encountered included learning to facilitate classrooms as mathematical communities instead of lecture halls. Logic and evidence was to be given and or discovered by the students where they would justify and make sense of a situation and the mathematics involved. Concentration was to be on the problem solving process instead of the correct answer. Connecting to other mathematical concepts and to real-world situations was to be the beginning of instruction instead of an afterthought which was many times looked over in the past. The reform movement encouraged teachers to use small groups for collaboration, manipulatives to assist in understanding concepts, inquiry methods to learn material, and open-ended problems and assessments.

Students had the option of what mathematics course they wanted to take (McCaffrey, et al., 2001). Choices included IMP or the College Preparatory Mathematics program (CPM). These two courses were grouped together for the study and referred to as the integrated courses. The other choices were the traditional courses of Algebra I, Geometry, and Algebra II / Trigonometry sequence. The researchers gathered data about student achievement in their prior course in order to determine the achievement level of students that selected a particular course and if those in the course were of the same of different academic level. Additionally, student’s Stanford 9 scores and demographics were obtained as well as a questionnaire developed by Horizon Research, Inc. that was completed by the teachers.

The results of the study revealed that the integrated student’s scores on the Stanford 9 were slightly lower for their previous ninth grade year and remained low in tenth grade in comparison to the traditional student’s scores (McCaffrey, et al., 2001). Teacher questionnaire results showed that the relationship between the teachers’ self reported usage of reform practices and the student’s mathematical achievement for the integrated math courses was positive. This was not true for the teachers and students in the traditional courses. The researchers suggested that the content and the organization of content in the integrated course were responsible for the positive relationship. This hypothesis implies that professional development should include instructional practices and curriculum issues.

This study pulls from the influence of the U.S. Department of Education questions, Project 21, and additional topics mentioned by Stein, Remillard, and Smith (2007). McCaffrey, et al., (2001) listed items that were brought to the attention of teachers in professional development sessions such as focusing on the content and its presentation along with how to facilitate instruction using reform practices. Since the basis is on reform practices, we can assume that the professional development followed NCTM standards. The items mentioned above with regard to Project 21 were also mentioned in the goals of the professional development. Not assessed in the study was content, assessment, student engagement, generalizabilty to other educational settings, and cultural or society’s acceptance of the reform movement. None of the concepts mentioned by Mathematically Correct (Stein, Remillard, & Smith) were addressed in the study by McCaffrey, et al.

Qualitative analysis of IMP, Evitts Study

Probing in to what it is like to teach and to learn mathematics using IMP was the motivation behind Evitts’ action research in a Pennsylvania high school (Evitts, 2004). Evitts taught an IMP unit titled “Baker’s Choice” to his Algebra I classes. The suggested timeline for the unit is eighteen days however it took Evitts longer to cover the material. He believed that the additional time needed was due to the student’s discussions and activities but that as he gained experience implementing the program that time management would become less of an issue. Even though the study was self directed, Evitts’ did collaborate on lesson creation and facilitation with another teacher, Chris, in his building. Evitts’ stated that he placed his trust in the curriculum and attempted to facilitate the instruction as intended. Data was gathered through Evitts’ journaling about lesson development and facilitation, taped conversations with Chris, and his own personal reflections. Also gathered were student work, assessments, and a videotaped lesson.

Six themes emerged in the qualitative analysis: trusting the curriculum, time management, classroom roles, affective considerations, assessment issues, and personal deeper understanding (Evitts, 2004). Working to interpret what the IMP designers intended led to Evitts’ encountering situations that were different from those he had experienced in the past such as patience with scaffolding the curriculum and the concern between balancing conceptual and procedural approaches. The roles of the students changed as they began taking ownership of the mathematics they were learning and at the same time Evitts’ became more of a listener and questioner. Students appeared to enjoy coming to and being involved in the class but there were some students who did struggle with wanting an algorithm so they could get the correct answer. Evitts’ employed portfolios in assessing the students along with the problem of the week, homework, group activities, and specific assignments. His grading practices changed from the correct answer to assessing the strategies utilized and the student’s ability to find patterns.

Stein, Remillard, and Smith’s (2007) analysis of reform techniques were partially addressed. The questions by the U.S. Department of Education that were addressed include the engagement and motivation of students by the IMP curriculum and that the assessments enlightened Evitts’ ability guide student learning. Evitts’ observations led him to informally assessing the content and presentation of the curriculum through his student’s interactions and discussions indicating that the way they were learning mathematics was changing. Project 21 (Stein, Remillard, and Smith) analysis ideas may also be seen in the action research by Evitts’ as he attempted to implement the curriculum as it was intended and promote student engagement and thinking. Assessment issues were considered in this study from the viewpoint of the instructor. None of the ideas promoted by Mathematically Correct were addressed in Evitts’ study. Additional items mentioned by Stein, Remillard, and Smith that were explored by Evitts are the concern for time and the support he needed from Chris.

Studies and the Evaluation Concepts

Implementation Concerns

Along with implementing IMP comes concern from many avenues. Parents and political groups have voiced misgivings about students not being tracked and how one curriculum can meet the needs of all students (Alper, Fendel, Fraser, & Resek, (1997). Will the academically challenged students pull down those who are considered advanced mathematics students? As with any curriculum, teachers will still need to adjust for the diversity of the students in his or her classroom. Merlino and Wolff’s (2001) study about the benefits versus cost of implementing IMP were apprehensive about false positives. Such things as the better mathematical students were taking the IMP course, the teacher’s grading was more lenient toward students taking IMP, there is increased attention on the course, or the teachers of IMP are receiving more professional development than the teachers of traditional courses. Teachers in the Merlino and Wolff study did have a reduced course load so that might also have led to a difference in the outcome.

Wu (1997) raised an alarm over textbooks that are considered to be standards-based as not clearly stating the rules and that the graphical approach appears to be promoted more than the symbolic. This had led to a concern about students being ready for college. Reform mathematics and IMP is based on the belief that all students can learn mathematics but will they be lacking sufficient practice with symbolic manipulation. What will be the outcome when these students go to college and are expected to be able to perform manipulations effortlessly? Wu also expressed that there is an overemphasis on real-world problems that are relevant to students. The two sides of the issue are that the real-world applications will turn on more students to mathematics but at the same time there is an increasing concern that we are losing the “…intellectual appreciation of this structure and cohesion (p. 948).” Lastly, Wu posits that the usage of mathematical language is lacking in standards-based classrooms due to the students first building their knowledge then being introduced to the vocabulary. Algorithms and formulas are also not stressed in the texts.

Ridlon (2009) conducted a study with sixth grade students and their teachers who were implementing problem based learning. Even though it was not IMP, teachers and students still had to go through the evolution of change. The study revealed that one of the limitations was the competency of the teachers. She stated that teachers need a large amount of sustained professional development in order to understand standards-based teaching and learning and learn how to implement strategies to support the approach. Support from administrators and their peers are essential to the success of the reform. Lubienski’s (1998) study of seventh grade students and their teachers brought up the point that students labeled as having a higher socio-economic status (SES) were better prepared and preferred the standards-based approach whereas students with a lower SES preferred the traditional classroom. The preference for the “old way” was presumed to be due to a lack of confidence and wanting to know the right way to do the math. So the issues posed by the U.S. Department of Education (Stein, Remillard, & Smith, 2007) about a program being able to be adapted to different educational settings along with meeting the needs of the society is in question. Implementation concerns lead in to the weaknesses in the studies mentioned but also in the program.

Weaknesses

Weaknesses in the Studies

The report done Merlino and Wolff (2001) was funded from a grant from the NSF. Determining whether the program will be cost efficient for the subsequent results may be considered biased toward a positive result due to the influence of the financial backing. Teachers involved in Clarke, Breed, and Fraser’s (2004) study volunteered to do so. They were ready to be challenged and wanted to learn to implement IMP. Accepting change, and being open to new ideas, is not the norm for some teachers so what would be the result if they were adamant to keep conducting their mathematics classes using the same methods.

IMP Curriculum Weaknesses

As mentioned under “Implementation Concerns,” Wu (1997) expressed weaknesses with IMP that included textbooks, lack of focus on algorithms, and the need for professional development in order to have success with the methodology. Will school systems have the funding to provide their teachers with the education needed to implement IMP appropriately? Whereas Wu considered textbooks a concern, one needs to look at the text with a different lens. Teachers are well versed in traditional instruction so are the textbooks providing the extreme alternate view so they will have tasks applicable for the standards-based approach. The same response might be expressed about the lack of algorithms. Teachers know the algorithms, but do they know how to develop them or investigate situations that will promote or lead to the algorithm. McCaffrey, et al., (2001) also stated that professional development was necessary for successful implementation but included that the focus of the sessions should meet the needs of the standards-based approach.

Suggestions for Improvement

Teachers normally teach using the methods that they have experienced. This leads to the importance of sustained professional development but also to a focused collaboration with peers. Encouraging the collaboration of teachers as an essential ingredient to those purchasing IMP should be stressed. Finding good problems is a definite need as well. Some teachers believe that they are not creative enough to develop good problems while others might not know the connections that can be made to real-world situations and content. By providing supplemental books with real-world problems that will fit the criteria for a specific course, school systems may begin the process of change and educating the stakeholders that may not be ready. Teachers must cover concepts presented to them in a traditional format so there is a need for ideas about how to cover the concepts that is typically taught in the traditional courses using a standards-based approach. The units of study provided by IMP are supposed to be interchangeable but teachers would like to know if there is a better flow or will one path through the material enable students to reach or make more connections.

Conclusion

Change is not easy and takes time. Providing the material and problems enhances the ability for teachers to follow the program but interpretation along with trust and confidence is another story. Merlino and Wolff (2001) state “…we have found that without strong top-level administrative support and direction, systemic change will not happen, despite these external inducements and sanctions (p. 15).” Purchasing IMP is not an answer to promoting student achievement. Student achievement lies in the hands of the teacher, his or her content knowledge and pedagogical content knowledge. But even if change is acceptable, is IMP the answer to a standards-based approach as seen by criteria for analysis by Stein, Remillard, and Smith (2007).

None of the studies presented in this paper covered all of the questions or items of analysis mentioned by Stein, Remillard, and Smith (2007). Some of the studies even covered items not brought up such as cost and the affective results of implementing IMP. When we combine the concerns and weaknesses found in the program and its implementation along with the bias of who paid for the studies, we may begin to question the effectiveness of IMP. In conclusion, our world is constantly changing. We need to encourage students to become problem solvers and appreciate mathematics. Our traditional method of teaching mathematics is doing the opposite, leading more students to stop taking mathematics instead of taking more courses. IMP is interesting to students. Its flaws may lie more in the facilitator versus the program.

References

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standards-based mathematics curricula. Phi Delta Kappan, 7, 503-506.

Clarke, D., Breed, M., & Fraser, S. (2004). The consequences of a problem-based mathematics

curriculum. The Mathematics Educator, 14(2), 7-16.

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