With almost 50 members in attendance, it was encouraging to see the level of participation in this year's SPIN meeting in Louisville. Two suggestions came out of the meeting which will be implemented at next year's conference. First, the SPIN will sponsor a panel discussion on a topic (or topics) of our choice in developmental math. This will require identifying both topic(s) and panelists. In the fall, I will send out a survey requesting your input on this. In the meantime, if you have any thoughts, please send them along to me. The more input I receive, the better our choices will be. Topics suggested at the meeting include placement policies, distance education, equipping adjuncts, tracking students, using computers in teaching, and serving students with disabilities. Second, it was suggested that the SPIN continue sponsoring a poster session. Poster sessions give SPIN members the opportunity to share short, poster-type presentations about whatever they do. These sessions have been well received in the past.

Other highlights of the meeting included discussions of the SPIN web site and listserv. Over the past year, Daryl Stephens and Roberta Lacefield have done an outstanding job of developing these resources. If you haven't already done so, we encourage you to check out our web site at www.etsu.edu/devstudy/spin/. We also invite you to contribute your links or information to it. In addition, we hope to expand the listserv to include as many members as possible. If you are interested in joining, further information can be found on the following page.

Finally, I will make every effort to send out the SPIN directory by the end of April. If you do not receive a copy by the middle of May, please let me know. Thanks to all of you who made this year's meeting a productive one.

Tom Armington

(tmarmington@juno.com)
 

Speaking on math anxiety and barriers to student success in mathematics, Sheila Tobias' presentations at NADE 2001 examined both instructional and student issues in learning. According to Tobias, the predominant causes of math anxiety are environmental factors created by math teachers. These include pressures created by timed tests, an overemphasis on one right method and one right answer, humiliation of students at the blackboard, an atmosphere of competition, absence of discussion, and other related dynamics that typify the math classroom. For many students, these factors lead to destructive self-beliefs about the math abilities they possess, avoidance behavior, and an unwillingness to explore mathematical concepts in the classroom environment. Coupled with the negative influence of environmental factors is the belief that students who do well in math do so because of native ability, not effort. This misconception, propagated by teachers and society at large, only serves to reinforce negative student behaviors that lead to underperformance in mathematics.

Tobias also discussed what she identifies as a misfit between students' learning characteristics and instructors' teaching styles in mathematics. Only a small percentage of students are "math minded." The rest, she suggests, have learning style preferences or needs that do not fit traditional modes of math instruction. Specifically, students who are high verbal performers need discussion and choice, utilitarian learners need memorizable, predictable learning patterns, and underprepared students need periodic clarification with respect to weaknesses in prior content areas. The typical math class, however, tends to offer only a single, "math minded" approach to learning.

Tobias outlined various ways that college developmental math faculty can respond to these negative factors. First, she emphasized the importance of good diagnostic and placement procedures. This includes the need for colleges to consider the effect of time restrictions on placement testing and for students to be given the opportunity to prepare in advance for placement tests. It also includes the need for faculty to identify and understand the learning style needs and preferences of their students, and for accurate assessment of student disabilities where they exist. Second, instructional methods have to be altered to accommodate the learning characteristics of different kinds of students. For example, instructors should include more discussion and choice in the classroom and less focus on a single right way and right answer to solving problems. As students commonly conceptualize mathematical principles differently than their instructors, the instructor must also be willing to answer "their" questions rather than focusing only on his or her way of conceptualizing a particular principle. This can be accomplished simply by having students submit written questions each day as part of their homework assignment. Citing Philip Uri Treisman's research on the power of group interaction, Tobias emphasized the importance of having students work together with other students as well. Third, as student learning is driven by tests, college instructors need to be aware of certain testing issues. These include the impact of timed testing and test format on student performance. Instructors should experiment with testing by removing time restrictions and varying test types to include open-ended questions, problem solving, or even essay questions, as opposed to just "right answer/wrong answer" questions. Finally, "math clinics" can be useful in helping students deal with the effects of math anxiety or other student-related barriers to learning math. Tobias suggests that math instructors team together with a college counselor to offer voluntary sessions in which students can explore the various factors affecting their individual performance in math.
 
 

(Sheila Tobias is the author of 11 books, including Overcoming Math Anxiety, Succeed with Math, Breaking the Science Barrier, and They're not Dumb, They're Different. For further information, visit her web site at www.mathanxiety.net. She also requests that SPIN members with additional information on math anxiety please contact her at sheila@mathanxiety.net)/
 

Approximately 45 math presentations were given at the NADE 2001 Conference in Louisville. In an effort to share the conference with those unable to attend, we have collected the following summaries of presentations. SPIN members are invited to contact presenters for additional information. The newsletter thanks those who contributed to this effort.

Capturing Student Interest with Realistic Applications

 

"When will I ever use this math?" Have you ever heard this question in your class when teaching mathematics? NADE addresses this student concern in one of its goals, stating that developmental mathematics should "develop in each learner the skills and attitudes necessary for the attainment of academic, career and life goals." This question is also addressed in the Crossroads in Mathematics, Standards for Introductory College Mathematics (Standard for Pedagogy, P-3): "Mathematics faculty will actively involve students in meaningful mathematics problems that build upon their experiences, focus on broad mathematics themes, and build connections within branches of mathematics and between mathematics and other disciplines so that students will view mathematics as a connected whole relevant to their lives." This presentation was designed with these goals in mind to help math faculty answer this student's question.

The presenter discussed methods of researching topics of student interest in order to write realistic, real-world exercises on a developmental math level. This included studies of various business, science, and engineering texts, interviewing faculty from other disciplines, and internet searches on topics of interest. The presenter also illustrated a variety of exercises that may be assigned to students in lieu of the more traditional, non real-life exercises. For illustration purposes, the presenter chose the topic of radicals and rational exponents. Statistics on student performance and attitude were also presented.
 

Presenter: JoAnne Thomasson (jthomasson@pstcc.cc.tn.us)

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Basic Mathematics and Relativity Theory
 

This presentation illustrated how several implications of Albert Einstein's Theory of Relativity can be discussed naturally within the context of the Basic Mathematics curriculum. Examples were presented from astronomy, the famous equation E = mc², time dilation, geometry, and addition of velocities.

The astronomy example uses the vastness of the universe to derive very large numbers, thus motivating the need for scientific notation. During symbol manipulation, the equation E = mc² provides an opportunity to discuss nuclear fusion, which powers the sun. The simple radical sqrt(1 - beta²) is used to discuss the notion of time dilation in special relativity, where twins are shown to age differently. The geometry example examines general relativity based on non-Euclidean geometry - the geometry of curved surfaces, contrasting some of the differences between the surface of a sphere and plane Euclidean geometry. A complex fraction is used in the addition of velocities to give an example where
 

Presenter: Dr. John A. Maroli (jmaroli@uakron.edu)
 

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Patterns and Connections in Developmental Algebra
 

In 30 years of teaching, one of the presenter's main goals has been to link topics together. Instead of seeing courses as a list of many unrelated topics, his students see the topics as parts of a branching tree of patterns and procedures. He is particularly interested in linking together items that initially seem completely unrelated.

The presentation examined one of the strands that runs through the prealgebra and algebra classes. Simple sequences are used to get students started recognizing patterns. The sequences are also used to demonstrate inductive reasoning. From there, connections between sequences are examined, moving on to two dimensional patterns and fractals. The journey passes through Pascal's triangle, the Fibonacci sequence, and the Sierpinski triangle, ending with a surprising connection between chaotic functions and fractals.

By presenting courses this way, the presenter shares with his students the things that drew him to mathematics in the first place. He treats each class as if it were the last math class students will take. In addition to achieving higher level skills in algebra and critical thinking, students leave the class with an intuitive idea of the structure and beauty of mathematics.
 

Presenter: Pat McKeague (cpm@mckeague.com)

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Changing Mathematics Curriculum to Make Connections
 

This presentation focused on strengthening students' understanding of concepts through the use of comprehensive applications as capstone activities at the end of a learning unit. The presenters demonstrated the idea through a weight-loss problem involving a 150-pound person who loses 2 pounds per week for six weeks. Through a series of group questions about the weight-loss process, a full range of graphing concepts was discussed. These included independent and dependent variables, slope, coordinates, x and y intercepts, linear relationships, the equation of a line, functions, domain and range, and tabular representation of data.

Two strengths of the activity were its effectiveness in drawing a full range of graphing concepts together into a single problem and its usefulness in connecting mathematical concepts and terminology to an everyday example with which students can easily identify. The presenters emphasized the importance of active learning, visualization of concepts, making connections, and discussion. Capstone activities such as the one demonstrated also help students gain in-depth understanding of mathematical concepts through interaction and communication with each other.
 

Presenters: Carolyn Curley (curley@ecc.edu)
Trish Shuart (shuart@polk.cc.fl.us)
Patricia Pacitti (pacitti@oswego.edu)
 

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Algebra Labs: Possible Key to Success in College Algebra?
 

In an effort to increase students' success in College Algebra, the Learning Support Department offered a 1-hour algebra lab course for students to take concurrently with the College Algebra course. The lab provided further instruction and assistance on topics students found difficult. It was institutional policy that any student earning less than a C grade in College Algebra would be required to take the lab when re-enrolling in College Algebra.

Initially, the lab course was plagued by complaints of students and instructors. Over time, adjustments were made to lessen the complaints and make the course more beneficial to students and instructors. During the Spring Semester 2000, labs linked to the same algebra class were piloted. All of the students had previously attempted College Algebra one or more times. As a result of the linked labs, student needs were better met and more students successfully completed the class. Benefits of linking the lab to an algebra class included better opportunity for the lab instructor to communicate with the course instructor about lessons, better environment for group work since all students were from the same class, extra opportunities for students to learn to use the TI-83 calculator, and greater development of student confidence.

The presenters provided data from almost 3700 students comparing student performance in the linked-lab courses to that of students in College Algebra who did not take the lab. Approximately 53% of those taking the lab earned grades of C or better as compared to 43% of those in the traditional classes. The number of students receiving A or B grades was also higher. The students in the linked-lab algebra classes were all repeaters, none of whom had been successful in algebra in the past. It is also interesting to note that few students withdrew from the linked class. For the first time, these students felt that they had a good chance of passing.
 

Presenters: Don Brown (dbrown@gsvms2.cc.gasou.edu)
Donna Saye (dbsaye@gsvms2.cc.gasou.edu)
 

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Using Graphics in Mathematics Papers and Web Pages
 

Mathematics teachers have had a growing need for graphic representations both on paper and on the Internet. This presentation provided an overview of graphic types and basic manipulation of those types. Participants were given information on how to obtain free or cheap utilities that will enable the user to reduce, enlarge or view the graphics, as well as make some basic adjustments to the graphic itself.

In addition to manipulation of graphics, teachers were shown software that is applicable to their teaching. Some of the free software utilities that were demonstrated include Graphmatica (www.pair.com/ksoft/), which will display graphs of mathematical equations, and Curve Expert (www.ebicom.net/~dhyams/cvxpt.htm), which assists in the plotting of points with minor regression analysis. A free fractals program, Fractals (www.arosmagic.com), was also demonstrated to generate interest in the beauty of mathematics.
 

Presenter: Mary Susan Hall (mhall@gpc.peachnet.edu)
 

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Relationship of Students' Attitude toward Mathematics and Their Improvement in Developmental Math
 

One of the greatest frustrations that developmental math instructors face may be that some students simply do not reach the levels of achievement that the instructor might anticipate. A question one might ask is "Do these students share some common characteristics?" This study focused on the relationship between student attitude towards mathematics and improvement in developmental math classes. In conducting this research, pre- and post-test scores were used to measure improvement. Student attitudes were measured using six of the attitude scales from the Fennema-Sherman Mathematics Attitude Scales. The subscales included attitude toward learning mathematics, math anxiety, effectance motivation, and beliefs about the usefulness of math.

The data were analyzed for the entire group and for subgroups consisting of male and female students, and traditional and non-traditional students. No significant relationship was found to exist between student attitude toward mathematics and improvement. There was, however, a significant difference in the improvement scores of traditional and non-traditional students. Analysis also revealed that a significant difference existed in both confidence in learning mathematics and math anxiety scores of males and females. The presentation concluded with discussion of further research possibilities in this area.
 

Presenter: Mrs. Lawanna Fisher (lfisher@mtsu.edu)
 

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Introducing a Computer Component into the Developmental Algebra Curriculum
 

Two of the basic principles in Crossroads in Mathematics, Standards for Introductory College Mathematics are that "mathematics must be taught as a laboratory discipline" and that "the use of technology is an essential part of an up-to-date curriculum." One goal of NADE is to "maintain academic standards by enabling learners to acquire competencies needed for success in mainstream college courses." Toward this end, the presenter's college encouraged faculty to include a computer component in the developmental algebra curriculum in order to better prepare students for their subsequent college math courses. This presentation focused on the results of doing so.

In instituting a computer lab for developmental algebra, a variety of activities suitable for the course were obtained. These included orientation activities to initiate student use of the computer, web sites that could be visited by students, and exercise sets suitable for the course. The presenter described the activities used, and also discussed some unexpected benefits of the computer lab that enhanced the interaction among students, and between the instructor and students.

To measure the impact of the computer lab on student attitudes, a questionnaire was administered at the beginning and conclusion of the course. Results of this survey were also presented.
 

Presenter: Bob Pesut (bpesut@pstcc.cc.tn.us)
 

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How Do I Love Thee Math? Let Me Count The Ways
 

There is a basic assumption among many math educators that the attitude of students toward math affects their grade. This study looked at data of success and attrition rates in developmental mathematics courses and attempted to find correlations between attitudes toward math, students' ages, and their grades. Data was gathered using subjects from over four semesters with 1506 valid subjects. The questionnaire asked for students' feelings toward mathematics, and their age as nontraditional (25 or older) or traditional (younger than 25). Grades at the end of the semester were noted. Passing grades included A to C, attrition included F and W. The grade of D was not given. Data analysis included descriptive, correlational, ANOVA, and multiple regression. Data from those with neutral feelings were not used in the correlational analyses.

59% of the students responded with neutral feelings, 33% with negative feelings, and 18% with positive feelings. In all categories of feeling, passing rates were higher than attrition rates. Nontraditional students appeared to feel less negatively toward math than traditional students. However, passing rates were about the same for both. Very weak, but significant, correlations were found between feeling and grade (r = 0.089, = .05), and between age and feeling (r = 0.213, =.01). No correlation was found between age and grade. Nonetheless, based upon multiple regression analysis, the best indicators for passing would be traditional students who like mathematics.

The correlation coefficients obtained were so low that prejudging a student's grade based on feelings or age may not be practical. Instructors should not equate bad attitude toward math as a route to failure. Advisement should include dispelling student self-prophecies that they cannot do math. Pedagogy should include techniques to ease the pain of those who hate math, but are required to take it. Further studies might examine how underprepared students should be advised with respect to math, how past student experiences affect attitudes and success, and how pedagogy can relate math to student experiences in real life.
 

Presenter: Y Wacek (wacek@mwsc.edu)
 

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Teaching Online Mathematics Courses
 

As distance learning has expanded, so has the use of the Internet. More and more, we are seeing the expansion of course material to the Internet. What are the issues for teaching course material on the Internet? What students will benefit from such opportunities? These are some of the issues addressed in creating an online developmental math course and other math courses.

This presentation provided both resources and methods for teaching a course on the Internet, as well as an emphasis on the new technologies becoming available. Several online mathematics courses were used to demonstrate some of the basic forms of communication and evaluation that are necessary for a course to be successful.
 

Presenter: Mary Susan Hall (mhall@gpc.peachnet.edu)
 

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Developmental Math Post-test Results: An Item Analysis
 

Developmental math faculty at the presenters' university are held accountable for student learning in three courses: basic mathematics, elementary algebra, and intermediate algebra. One indicator of student learning is data from multiple-choice post-tests given to each student as a final exam. These post-tests have been used by the Developmental Studies Department for several years, yet there had been no rigorous analysis to determine if the test results indicated that course goals and objectives were being met. The researchers believed that an extensive item analysis of the test results could be used to improve instruction, and possibly revise curriculum, to better meet the course goals and objectives mandated by the state Board of Regents.

The presenters were awarded an Instructional Evaluation Development Grant to study the post-test results for Spring, Summer, and Fall 1999. The results of their study included an item analysis of each of the intermediate and elementary algebra post-tests. Emphasis during the session discussion was given to items on each test that were most frequently missed. The results indicated whether, and to what extent, course goals and objectives were being met. During the discussion, session participants also shared testing procedures from their various campuses, as well as teaching strategies.
 

Presenters: Dr. Jennifer L. Dooley (jdooley@mtsu.edu)
Linda M. Clark (lclark@mtsu.edu)
 
 
 

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Implementation Models for Interactive Multimedia

Software in Developmental Mathematics
 

Interactive multimedia software is being incorporated into a variety of models to deliver developmental mathematics instruction. The software: a) provides thorough explanations of concepts and skills using multimedia, b) imbeds items requiring student interaction within the instruction, c) provides immediate feedback, including detailed solutions, and d) includes provisions for the development of skills. Four implementation models incorporating interactive multimedia software are the following:

1. Full implementation model. Students meet in a computer lab and follow a set schedule. The software presents the content while the instructor provides individual assistance.

2. Hybrid model. During the direct instruction part of class, the instructor may answer homework questions or lead whole class discussions. During the computer-mediated component, students work with the software to learn new content.

3. Open labs supported by instructional staff. Students use an open lab at times that best fit their schedule. The open lab allows them to use the software, ask questions, and take exams.

4. Distance learning. In this model, the interactive multimedia software provides the presentation of content, practice with skills, and feedback. A web platform, such as WebCT or Blackboard, is used to facilitate communication, but not as a mechanism for the instructor to present lessons.

Presenter: Dr. Patrick Kinney (kinne002@tc.umn.edu)
 
 
 

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Writing to Learn in Developmental Mathematics
 

This session introduced a format for incorporating writing assignments into developmental math courses. Each writing assignment, called a Mathematics Learning Log, focuses on a problem chosen either by the student or the instructor. Students document their work on the problem in three parts - introduction, mathematical process, and conclusion. A five point rubric is used to evaluate the learning log.

Samples of student work were shared with participants of the session. Each demonstrated one of the following benefits of integrating writing and mathematics: a) writing can help students to effectively use mathematical language, b) writing can help students become more comfortable with mathematical concepts, c) writing can help students make connections among mathematical ideas, and better understand relationships, and d) writing can help students explore mathematical situations, learn from mistakes, and develop strategies.

Participants also discussed how mathematics learning logs could meet the goal of "writing across the curriculum."
 

Presenter: Laura Smith Kinney (LKinney@northland.edu)
 

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Factors Affecting the Selection of a Developmental Math Textbook
 

This presentation examined three categories of factors that should be considered when selecting a developmental mathematics textbook. These include 1) curricular guidelines as established by the school, governmental agencies, and professional organizations, 2) evaluation of textbooks and supplementary materials, and the department selection process, and 3) post-selection assessment procedures. Some of the curricular guidelines include prerequisites for sequential developmental mathematics courses, prerequisites for subsequent mathematics courses, departmental pretests and posttests, mandates at the national, state, and local levels, and suggestions from mathematics organizations. The evaluation of textbooks and supplementary materials involves ranking textbooks based upon size, cost, type of textbook, topics included, organization, and the availability and quality of supplementary materials.

The textbook selection process should encourage the involvement of the entire faculty. Consideration should also be given to the working relationship with textbook representatives. Once a textbook has been selected, assessment procedures should include both student and instructor input. Students could voice opinions through web sites, math labs, instructors, evaluation instruments, counselors and departmental chairs. Instructors could voice opinions through textbook selection committees and department chairs. Pretest and posttest instruments could be used to test the effectiveness of the textbook.

The above list of factors used in selecting a developmental mathematics textbook should not be considered comprehensive, rather as a guideline for choosing a textbook.
 

Presenters: Dr. Terrence R. Sundeen (tsundeen@mtsu.edu)
Mrs. Lawanna Fisher (lfisher@mtsu.edu)
 

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Functional Innumeracy among Developmental Math Students

This presentation explored the results of a qualitative study that won the NADE proposed research award for the year 2000. Functionally innumerate developmental math students have more difficulty with concepts than with algorithms. They may not understand place value problems or how to correctly order numbers or switch between number forms. Of these difficulties, writing numbers as percents or percents as numbers and using percents caused the most uncertainty. By contrast, these same students successfully perform complicated algorithmic calculations, such as order of operations or addition of fractions.

In the study, fifteen developmental math students, who had exhibited some or all of the described difficulties, participated in an interview process. They described similar backgrounds and educational experiences. The majority had limited numerical experiences outside of an educational setting. Furthermore, many had disrupted or stressful experiences in math courses.

Results of the study have implications for adult developmental mathematics.
 

Presenter: Jo Fitzsimmons Warner (jo.warner@emich.edu)

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Quarter to Semester Conversion: Revising Mathematics Courses and Sequences
 

The presenters' university converted from quarter to semester system in Fall 1998. Throughout the planning period, faculty revised courses and sequences or eliminated them and developed new ones. The Mathematics Department's decisions to drop basic college algebra and revise precalculus meant the Developmental Studies (DS) mathematics curriculum had to prepare DS students for precalculus and cover more material in less time, so students could still complete the program in a reasonable amount of time. These factors influenced DS decisions to a) change from individualized, self-paced instruction to lecture classes, covering more material in a more directive manner; b) replace the two-quarter arithmetic sequence with one semester of prealgebra; c) collapse the two-quarter basic algebra course (8 quarter hours) into one 3-hour semester course; d) require the previously optional intermediate algebra; e) add a required 1-hour class lab, in addition to the required 1-hour computer lab, for more instruction time; and f) give tests in class on scheduled dates instead of individually in a Test Center.

After two years on the semester system, pass rates for students in the first DS mathematics courses have improved, going from 50% passing arithmetic to 60% passing prealgebra, a significant difference in the proportions passing (Z = 2.401, p < .05). The change in content and more structured approach of the semester system seem to have allowed more beginning students to successfully complete the basic mathematics material. At the same time, pass rates for students in basic algebra have remained stable, with 47% passing under the quarter system and 46% passing under the semester system, a nonsignificant difference (Z = 0.344). DS faculty had serious reservations about requiring students to cover more material in less time, but performance data indicate the semester revisions have had a positive effect for prealgebra students and have not been detrimental to basic algebra students.
 

Presenters:

Dorothy C. Mollise (dmollise@jaguar1.usouthal.edu)
Charlotte T. Matthews (cmatthew@jaguar1.usouthal.edu)
 

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Internet Searches and Electrical Circuits: It's Set Theory
 

Teaching the topic of compound inequalities offers the opportunity for introducing students to some interesting applications of Boolean algebra while making connections that students may never have guessed existed between real world situations and math. The set of electrical switches having the values 1 for closed (on) and 0 for open (off), and having parallel circuits and series circuits as operations, forms a Boolean algebra. This application, presented through diagrams of parallel and series circuits, is a good, intuitive way to emphasize the difference in the use of <and> and <or> in mathematics. The theorems of Boolean algebra can be used to simplify systems of electrical circuits. The subsets of a particular set, and the operations <union> and <intersection> form a Boolean algebra, as do a set of logical propositions having only values <true> or <false> and the operations <or> and <and>.

Alluding to these examples gives students a glimpse of the bigger picture of the applications of what they are studying, while leading into the topic of solving compound inequalities. The presenter also examined the use of Boolean connectives in Internet searches.
 

Presenter: Annette Williams (awilliam@mtsu.edu)

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Setting the Pace in Developmental Mathematics with Graphing Calculators
 

Employers expect their workers to be literate in the use of technology. NADE has recognized this need "to develop in each learner the skills and attitudes necessary for the attainment of academic, career and life goals." Many college math programs address this goal by using graphing calculators in their instruction. In order to prepare the developmental student with the skills needed in their courses of study, as well as in their chosen professions, developmental math instructors must use graphing calculators in their instruction as well. This further supports the NADE goal "to maintain academic standards by enabling learners to acquire competencies needed for success in mainstream college courses."

The purpose of this workshop was twofold - to provide basic orientation to graphing calculator features for instructors who have not routinely taught with them, and to suggest activities which exploit the features of the calculator in the classroom. The first part of the session acquainted attendees with the TI-83 calculator features necessary for the classroom. Graphing calculators incorporate advanced technology in their design, and it is important for instructors to be familiar with all the quirks and tricks. Topics included Getting started, Data entry, Alpha keys, Lists, Pull down menus, Tables, Graphs, Analyzing graphs, and Function notation. The second part of the session stressed the calculator's potential for diverse approaches such as modeling and discovery. Emphasis was placed on using the calculator to solve real-world problems numerically and graphically. Several modeling activities were presented to illustrate how the curriculum can be enriched. Applications included Movements of dinosaurs, Tracking fireworks, Break-even analysis, Calculator options for applying the ac-method of factoring, Real-world applications involving rational functions, Discovering rules of mathematics, Solving equations and inequalities numerically and graphically, and Recognizing equations and inequalities that have many solutions or no solutions.
 

Presenters: Bob Pesut (bpesut@pstcc.cc.tn.us)
JoAnne Thomasson (jthomasson@pstcc.cc.tn.us)

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Tools of the Trade: Linking Problem-Solving to Math Applications
 

"Oh NO, not story problems," a familiar lament heard often in math classrooms and learning centers. The ability to transfer problem-solving strategies and skills from instructors and tutors to students in large classrooms and tutoring centers has always posed a special challenge for those involved. This presentation used the idea of a construction company and construction tools to emphasize the building blocks for forming the foundations to support mathematical problem solving. The goal is to construct the four steps in Polya's plan to solve word problems with more confidence.

The construction tools that help build problem-solving skills are as follows: 1) Patience, like the blueprint, provides order and timeliness to reach the end product, 2) Observation, like protective eyewear, allows one to see the details, 3) Past experience, like the hammering of nails into boards, allows for practice to perfect one's techniques, 4) Reasoning, like a level, helps balance one's thinking, 5) Questioning, like a saw, allows one to view the components of the structure being built, and 6) Critical thinking, like the hard hat, symbolizes analysis.

Polya's four-step problem solving process uses all of these tools. To facilitate the proper use of the tools, it becomes the job of the math instructor or tutor to ask questions that draw the student into deeper thinking. Listening goes hand in hand with the questioning. As construction supervisors, math instructors and tutors must model problem solving. This is accomplished through questioning techniques that fit the four-step process of understanding the problem, devising the plan of solution, carrying out the plan and looking back at the final product. Probing questions that engage students help build a foundation of confidence in their own problem solving abilities. Teachers can use these questioning techniques in lecture and assessment, while tutors can do the same when assisting students.
 

Presenters: Darlene Kohrman (dkohrman@kvcc.edu)
Apryl Clay (aprylclay@yahoo.com)
 
 

The first year of college is often disconcerting for students. New housing, new format of classes, new friends, and new freedom can all be overwhelming. How can you encourage your students to start the semester off on the proverbial right foot? Here are a few suggestions that may seem simple, but to many students they are not obvious.
 

1. Encourage your students to make appointments to speak with all of their teachers during the first week of classes to discuss expectations for the class and grading policies. Encourage them to ask questions such as "If you were taking this class, how would you prepare?" or "What is the single most important thing that I can do to ensure my success in this class?" Later in the semester, encourage them to make appointments to discuss their progress and find out ways to finish up the semester strongly.
2. Encourage students to come to every class and be prepared to learn and share. Instruct them to bring their textbooks, notebooks, and pencils or pens. Insist that they read or scan assignments ahead of time to better understand the material.
3. Suggest that they work on homework for each class everyday, keeping the material fresh in their memory.
4. Have a positive attitude. If you have one, your students will too!
5. Encourage students to get enough rest.
6. Instruct students to make daily schedules including dedicated study time. The schedules should allow more time to complete assignments than is anticipated. Tell students to complete all assignments at least one day early. This allows for unexpected problems and extra polishing on papers and projects.
7. Repeatedly encourage students to seek help early and often. Many students think they are bothering you in your office hours. You must dispel this myth!
8. Advise students to take advantage of all extra credit and retest opportunities even if they feel they do not need the points. They may wish they had those points on another assignment.
9. Advocate making at least one friend in each class to share notes and studying.
10. Advise students to keep all assignment and university deadlines.

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