R.+Garrity


 * Title of Project: ****
 * Usage of problem solving skills in technology education classes help students achieve a higher score on their Mathematics and NECAP testing ** **

** Problem Statement:  **** **The purpose of this study is to investigate the effects of problem solving in a technology education class on students Mathematics NECAP test scores.**

**** Significance of the Problem:  **** **NECAP testing is becoming of greater importance in high schools across Rhode Island. Soon, it will be mandated that all students pass the NECAP test as part of their graduation requirement. Technology education classes help to enforce basic and complex mathematical problem solving skills in order to construct projects. Through hands-on learning, students are becoming more effective problem solvers by incorporating math and science to the problems given in order to come up with creative ways to solve these problems. By applying the scientific method and the design process, the students are able to thoroughly break down a problem. The importance of teaching mathematics problem solving skills throughout the curriculum, and the various ways it can be used, helps underline the importance of a high school engineering course.** ** **  Definition of Terms:  **** **Problem Solving: The ability to identify the cause of a problem by applying mathematical and scientific reasoning in order to achieve a final conclusion through the process of experimentation and analysis.**
 * Technology Education: a class that applies math and science to real world situations using applied learning and hands-on skills in order to arrive at a concrete conclusion.**
 * NECAP: New England Common Assessment Program Test**
 * Mathematics NECAP: The NECAP test is divided into several sections, one of which is mathematics**
 * Test Scores: Results from the students NECAP testing mathematics**

**** Limitations:  **

** Review of Related Literature:  ** ** Introduction:  **** **Much mathematical problem solving is used in order to carry out the problem solving steps in every technology education classroom. In order to solve problems effectively, previous knowledge needs to be built upon and applied. This process is applied by all students in order to hypothesize about the task at hand.**
 * Many studies have shown that stronger problem solving skills lead to better grades on standardized tests. Student’s problem solving capabilities is often related to their level of mathematical achievement. By reinforcement of problem solving skills, the students bring their mathematical reasoning, no matter how strong or weak, into use in order to hypothesize. The students can then put their theories to work through an experimental phase in a hands-on manner, which helps them make conclusions about their theories.**
 * As we get deeper into the 21st century, mathematics is becoming more reliant on problem solving skills, than just mathematic computations. The importance of problem solving skills and how math is related to the real world and real world situations is seen by students in a technology education class. Applying the problem solving approach gives those who are visual learners a chance to understand things in which they wouldn't by just seeing it on paper.**

**** Students with difficulty in mathematics:  **** **"Many students cannot solve challenging mathematical problems. The lack of problem solving strategies greatly concerns educators, researchers, and even students. Oftentimes, students do not have the training to solve complex, real life mathematical problems. The strategies necessary for the solution to complex, real life mathematical problems may not be addressed adequately by text resources." (Improving Student Achievement through Inclusion of Problem Solving in the Math Curriculum, Page 15) The techniques of learning by doing are often forgotten in a math class. At no fault to the teachers, the majority of class time is devoted to preparation for standardized tests, which brings us to what math classes have become. "According to Knuth & Jones (1991), much of mathematical instruction is devoted to drill and practice on math facts and computations and other low-level math skills." (Improving Students Achievement through Inclusion of Problem Solving in the Math Curriculum, Page 15) Applying these math skills to real world situations through a problem solving approach would make for much more productive learning. When students are able to see the relevance of a problem, they are more apt to understand how to apply it in the necessary places. "Teachers often focus on memorization and recall instead of critical thinking skills and reasoning necessary for problem solving.” Today's teachers need to include problem solving and the necessary strategies throughout the entire curriculum in order to prepare students for a successful future." (Improving Students Achievement through Inclusion of Problem Solving in the Math Curriculum, Page 15)** **Much research conducted shows that students with learning disabilities have a greater difficulty at mathematics than students without learning disabilities. This is because, "the curriculums that most students with learning disabilities are exposed to are ineffective because little emphasis is put on the everyday application of mathematics in their lives."(Teaching Math to Students with Learning Disabilities) Students who are considered gifted or upper level students are able to grasp the ideas of problem application much easier than students with learning disabilities. Research shows that, "teaching different strategies to children helped them learn and retain not only higher order concepts and problems, but also basic mathematics facts."(Teaching Math to Students with Learning Disabilities) Many of these different strategies are used in order to solve technical problems. Individual as well as group work helps students become more of an active problem solver, and helps the students see several ways of solving a problem, rather than finding themselves stuck with not knowing the next step.**
 * There is a tremendous disconnect in mathematical problem solving between higher and lower achieving students in all grade levels. The dissection of a problem and how we solve it is relevant in both mathematical reasoning and hands-on technology, but mathematics is more theory in calculations than the application itself. Word problems in mathematics can help put a "real world" situation to the test as something that a student can understand the relevance of, "much of the evidence indicates that word problem performance improves as children gain greater ability in (a) understanding underlying arithmetic operations (e.g., Rasmussen & Bisanz, 2005), (b) distinguishing between types of word problems on a basis of mathematical operations (e.g., Fayol, Abdi, & Gombert, 1987; Rittle-Johnson, Siegler, & Alibali, 2001), and (c)an effective use of strategies (e.g., Geary, Hoard, Byrd-Craven, & Desoto, 2004;** ** ** S **** iegler, 1988)." (Growth in Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties, Page 343) This idea of problem dissection and application is something seen on a daily basis in an technology education class. Real world problems are initiated by the teacher with the students beginning by breaking down the problem. After the problem is broken down, research may be needed. After deciding on the best result for the problem, math and science is applied in the experimentation phase of the project. After a concrete result is established, the students are to reflect on their projects. ** **
 * A group named The National Council of Teachers of Mathematics (NCTM) was set up in order to help all students in math achieve success. "The NCTM believed that in all areas of life, math helps people solve problems and make good decisions." (Strengthening the Third "R" Helping Students with Disabilities Achieve in Math, Page 1) The standards for teaching math were revised in the 1997 Amendments to the Individuals with Disabilities Education Act. This act raised the bar on what students with disabilities were to learn, due to a much more technologically driven society than before. The need for, "conceptual understanding and problem solving rather than procedural knowledge or rule-driven computation" (Strengthening the Third "R" Helping Students with Disabilities Achieve in Math, Page 1), became the primary focus of the NCTM Standards.**
 * The same research explains Montague's Solve it Approach, which helps to define problem solving from a mathematical as well as technical perspective. Montague's approach contains the following steps: reading the problem (understanding the problem), paraphrasing (putting the problem into their own words), visualization (make a mental image of the problem), hypothesizing (about possible solutions), estimating an answer (staying focused on the problem and making educated guesses), computing (how to recall the correct procedures for working through the algorithms and necessary math facts for accuracy), and checking the problem (how to check the mathematical problem solving process to ensure the problems accuracy and correctness. Montague's Solve it Approach in math is much like the steps used in a traditional technology education classroom. In conclusion, following this process should help lead to greater improvement in mathematics test scores.**

**** Application of Science, Math, and Technology in Problem Solving:  **** **A student’s ability to learn does not stop at the classroom. Outside influences, such as a students job, where a student lives, peers, clubs, and organizations a student may belong to, tutoring, and interactions with teachers outside the classroom influence the way a student thinks and this can lead to the way in which the student solves a problem.**
 * "Mathematics is commonly referred to as “the language of science” and we typically require our physics students to take mathematics as prerequisites to their study of physics. As instructors, we are often surprised by how little math our students seem to know, despite successful performances in their math classes. When students appear to have trouble with math in our physics classes, we might ask them to “study more math.” But using math in science (and particularly in physics) is not just doing math. It has a different purpose – representing meaning about physical systems rather than expressing abstract relationships – and it even has a distinct semiotics – the way meaning is put into symbols – from pure mathematics." (Problem Solving and the Use of Math in Physics Courses, Page 1) Technology education is the process of applying science and math, to real world applications, situations. Much math is involved in physics, and through application in a hands-on setting, students of all levels are able to understand the concepts in a much more efficient way.**
 * "Average ability individuals may have the ideas that they need in an applied mathematical problem solving situation but may be unable to use them because they lack certain processes which would allow them to "fit" their knowledge systems to the problems situation." (Applied Mathematical Problem Solving, Page 237) This is where technology education shows its relevance and importance. "Students do not first learn an idea, then learn to solve problems using the idea, and finally learn to solve applied problems. There is a dynamic interaction between basic mathematical concepts and important applied problem solving processes." (Applied Mathematical Problem Solving, Page 236)**

**** Math Assessments for students:  **** **In order to see how the concepts of math are truly understood, some schools have converted to a Performance based Assessment. When defining mathematics as an educational course, the idea of what is to be expected of this course varies depending on location. The curriculum is stated to be rather "shallow," (Mathematics Performance Assessment in the Classroom: Effects on Teacher Planning and Student Problem Solving, Page 610) in that most time is usually spent on "routine problem solutions." The society in which we reside is technologically driven. The demand for skilled workers has dramatically increased since the boom of technology throughout the late 20th century to the present day. In order for workers to become "technologically sophisticated," we need them to not only know the math concepts in which they will encounter, but they must be susceptible to using these skills in problem solving, where they will occur to them in the real world.**
 * The relationship between problems students will encounter in the real world and how the skills they acquire in a mathematics class will help them to solve these problems is something that needs to be addressed in every situation possible. "Unfortunately, in contrast to the reform movement's focus on authentic, integrated knowledge application, traditional achievement tests sample isolated items of factual and basic information with multiple-choice response formats (Linn, 1993; Smith, 1991a, 1991b; Wilson, 1992). The result is that traditional tests prompt teachers to emphasize basic, factual information and to provide few opportunities for students to learn how to apply knowledge (Darling-Hammond, 1990; Wilson, 1992)." (Mathematics Performance Assessment in the Classroom: Effects on Teacher Planning and Student Problem Solving, Page 611) This is where Technology Education and the need for a higher order of thinking dealing with problem solving come into play. In technology class, students are given complex problems that involve thinking through the scientific method in order to process the information needed, to come to a conclusion.**
 * The need for assessing not only what a student learns in a math class, but how they apply it has started to show its importance. As teachers are teaching to the test in mathematics classes in order to help their students succeed on their tests, the knowledge of application is lost. Through Performance Assessment, students retention is put to use in a useful manor, by having them apply what they learn, rather than just rehearse repetitive knowledge.**
 * The problem in most educational institutions is the lack of performance assessment. There is much talk about applying real world situations to mathematical problem solving, but there is still a great disconnect. Getting the students involved in problem solving that they can see firsthand, and use to solve a problem in front of them, rather than just placing calculations on a paper is a much more valuable experience.**

**** Hypothesis:  ** There will be a slight, but noticeable increase in all students NECAP Mathematics grades as a result of taking a technology education class.


 * Ethical Issues and Considerations:**


 * The Research Participants:**


 * Instruments:**


 * Design:**


 * Data Analysis:**

** Time Schedule: **

** Objective and Essential for Cause of Research:  ** The main objective of this research is to prove that students in various levels of math are able to apply problem solving to real life situations, and therefore, their development in problem solving is helping them achieve a higher score on their mathematics standardized tests than those students in their math classes who are not enrolled in a technology education class. The information collected from other sources shows that students with greater problem solving skills achieve a higher score on standardized tests. Students with greater problem solving skills tend to be students who are in the upper level math classes. The students in the lower level math classes tend to have a much greater difficulty at applying mathematical reasoning in problem solving. Hands-on projects that students undertake in a high school technology class exhibit basic problem solving skills and their relationship to mathematics. As the students start to apply mathematical reasoning to these projects, they are able to understand how to become greater problem solvers and understand how to think through problems in order to achieve desired results. As we look into the industry which encompasses our job market, we are able to see much more of a need for skilled work than ever before. A mathematical reform was set in place to help the technologically driven society in which we reside to become better problem solvers. Unfortunately, due to the struggles of many students on standardized tests, the mathematics teacher’s jobs focus around teaching to the test. The repetitive knowledge that students gain is usually no more than wrote memorization, and by having the students at all levels apply the principles in which they learn in math to real world situations helps them relate what they are doing to something they find significant in the real world. Many students ask why they are studying specific things, or explain that they will never use it in the real world, and without understanding the relevance of the math they use, they are more likely to forget the knowledge then retain it.

Independent Variable: Successful work in problem solving

Dependent Variable: Higher Math NECAP Scores

Cause: Problem solving skills taught in a technology education class

Effect: Higher NECAP Scores in Mathematics

** Sources  **

1. Swanson, H. Lee ; Jerman, Olga (2008) __Growth in Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties.__ Journal of Educational Psychology Copyright 2008 by the American Psychological Association, Vol. 100, No. 2, 343–379

2. Obudo, Francis (2008) __Teaching Mathematics to Students with Learning Disabilities: A Review of Literature__

3. Redish, Edwards F. (2005) __Problem Solving and the Use of Math in Physics Courses.__ University of Maryland, Department of Physics

4. Warger Envy & Associates (2002) __ Stengthening the Third R: Helping students with Disabilities improve in Mathematics. __ Research Connections in Special Education; n11 Fall 2002

5. Millard, Elizabeth S.; Oaks, Teresa L.; & Sanders, Therese M. (2002) __Improving Student Achievement through Inclusion of // Problem Solving // in the // Math // Curriculum.__ Saint Xavier University and Skylight Professional Development Field Based Master’s Program. Master of Arts Action Research Project (64p.)

6. Strauss, Linda C.; Terenzini, Patrick T.(2005) __Engineering Learning: Multiple Influences on the Development of Analytical and Group Skills.__ Association for Institutional Research, June 2005, San Diego, CA.

7. Fuchs, Lynn S.; Fuchs, Douglas; Karns, Kathy; Hamlett, Carol L.; & Katzaroff, Michelle (Autumn, 1999) __ Mathematics Performance Assessment in the Classroom: Effects on Teacher Planning and Student Problem Solving. __ American Educational Research Journal, Vol. 36, No. 3, pp. 609-646

8. Lesh, Richard (May, 1981) __Applied Mathematical Problem Solving.__ Educational Studies in Mathematics, Vol. 12, No. 2, pp. 235-264

** Sources WebPages  **

Growth in Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties: 

[|**http://0-ft.csa.com.helin.uri.edu/ids70/resolver.php?sessid=vmf1lhf2a3iokjagn3ugkkdj12&server=www-ca2.csa.com&check=92d569fdb0bc0d7e4c2764bb2b14dfb7&db=psycarticles-set-c&key=EDU%2F100%2Fedu_100_2_343&mode=pdf**]

Teaching Mathematics to Students with Learning Disabilities: A Review of Literature:

http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/3d/11/80.pdf

Problem Solving and the Use of Math in Physics Courses: 

[|**http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/29/00/97.pdf**]

Strengthening the Third R: Helping students with Disabilities improve in Mathematics: 

[|**http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/1a/a8/70.pdf**]

Improving Student Achievement through Inclusion of // Problem Solving // in the // Math // Curriculum: 

[|**http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/1a/6e/ac.pdf**]

Engineering Learning: Multiple Influences on the Development of Analytical and Group Skills:

[|**http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/28/ff/ce.pdf**]

Mathematics Performance Assessment in the Classroom: Effects on Teacher Planning and Student Problem Solving:

[|**http://0-www.jstor.org.helin.uri.edu/stable/pdfplus/1163552.pdf**]

Applied Mathematical Problem Solving: 

[|**http://0-www.jstor.org.helin.uri.edu/stable/pdfplus/3482367.pdf**]