Problem+Solving

Problem Solving


 * What Is Problem Solving? **[[image:smartoon-problem-solving.jpg width="362" height="316" align="right"]]

According to the Illinois State Board of Education (1997), > solving problems demands that students be able to read and listen, comprehend ideas, ask and answer questions, clearly convey their own ideas through written and oral means, and explain their reasoning. Comprehending reading materials and editing and revising writing are in themselves forms of complex problem solving. The ability to locate, acquire and organize information from various sources, print and electronic, is essential to solving problems involving research. In all fields—English language arts, mathematics, science, social studies, and others, the command of language is essential in stating and reasoning through problems and conveying results (para. 5).

In short, solving problems requires that students can search out information, process and clarify it, and then apply this knowledge to resolve a current situation.


 * How Does Web 2.0 Make Problem Solving Easier to Incorporate Into the Classroom? **

The interactive tools provided by Web 2.0 allow students to explore concepts from a constructivist standpoint without requiring the teacher to create these more involved and hands-on lessons on his or her own. That leads to the next obvious question, what does it mean to be constructivist? A constructivist education is one in which the learner generates meaning for themselves from experiences, rather than simply relying on being told important information. It is also sometimes used synonymously with problem-based learning or inquiry-based learning. If you would like more information on constructivist theory, click here.

The downfalls of constructivist learning include the time for prep and materials, and teacher not being well trained in creating appropriate lessons. Web 2.0 helps alleviate these issues because it allows for student-centered lessons without extensive setup and without the need to buy costly manipulatives for each classroom teacher. Examples of such tools are highlighted in the section below.

** Examples **

If explanations of Web 2.0 tools are needed, please visit the Web 2.0 Tools page. On this page are specific Web 2.0 tool examples relating to the Problem Solving standard.

**Applets** Since applets are interactive, they are easily incorporated into problem solving. Using these tools can be as easy as using the applets to present the problems themselves like a student would solve in a textbook, without the downsides of a textbook. These disadvantages are that the problems are limited due to space, unchanging across time and individual learners, lacking additional visuals to aid comprehension, and unable to provide feedback. Due to this, textbook problems allow students to do an entire set of problems incorrectly, which does not enhance true problem solving skills. Applets, on the other hand, can provide unlimited problems aimed at a certain skill and level for individual learners, as well as provide the necessary visuals and feedback to support the student in mastery of the concept of the problems (Kumar & Singhal, 2000).

Besides simply presenting problems for students to solve, other applets allow students to physically manipulate situations with a click or drag of the mouse (see the GeoGebra excerpt below). Following the constructivist view of education, these applets let students visualize changes and draw conclusions via experimentation. These particular types of applets can be useful tools in the mathematics classroom where many students miss concepts due to the abstract nature of the subject. With an applet, the student can see multiple representations of the same concept all on the same page, as well as change a variable and watch how all representations change simultaneously. This allows students to not only see how the representations (graphs, charts, tables, etc.) are all related, but also to build hypotheses about the effect of variables, test them, and draw conclusions. Douglas Clements (1999), author of 'Concrete' Manipulatives, Concrete Ideas, verified this by stating th at using these virtual manipulatives provided by applets can "provide control and flexibility to the learner...and assist the learner in making connections between various pieces and types of knowledge—in a word, serving as a catalyst for the growth of integrated-concrete knowledge," all of which is the purpose of the problem solving learning standard (as cited in Duebel, 2010, para. 5). For more on using applets in the mathematics classroom, read Uses of Java Applets in Mathematics Education.

> media type="youtube" key="rZnKMwicW_M" height="401" width="637" align="center" //GeoGebra offers both a full download, as well as a fully-functional applet for those who cannot download software to a computer. While it is titled after the applet, the site itself has its own discussion forum, wiki, and email list to maximize interactivity between users. Watch the video for a quick glance at what GeoGebra has to offer and// //visit the site for more details.//

**Blogs** The availability of blogs allows teachers to use both text and other media to pose questions that students need to search out more information about in order to answer. The blog also allows students to see other proposed answers and agree or disagree with others' solutions. Teachers have used them to propose issues on every academic subject from sports to space travel. Teachers have commented that, "the web interface was more connected to the students' experiences and provided excellent stimulus resulting in rich student conversations"(Chittleborough, Jobling, Hubber, & Calnin, 2008, p. 6).

For example, one teacher's blog has students provide responses to a question regarding a picture of an image showing mist above a lake, and the following are examples of two student responses. The first responded, "Obviously in this picture the water from the lake/sea is evaporating," and the following student replied, "I think that the water is evaporating even though it has not reached its boiling point [100 degrees] because some of the water molecules have just enough energy to become gaseous" (Chittleborough et al., 2008, p. 6). The first student ventured an answer to the problem based on the picture, and then the next student became even more specific from both looking at the picture and reading the previous response.

In the classroom, a student may not respond to this picture because they do not know what is happening and do not know where to begin. Many students will simply wait for the teacher to tell them what it is they are seeing. The simple use of a blog in this situation has students theorizing and about the science behind the picture without a teacher's intervention. They have been given a starting point by reading other student responses and an outlet to search for themselves and report their findings. This blog has students analyzing others' responses, investigating the topic, as well as actively participating in a discussion which are all higher order thinking skills required for problem solving (Chittleborough et al., 2008).

Students do not need to be of a certain age to benefit from a blog. To see a teacher/student blog in action with young students, click here.

In order to work on problem solving skills, an instructor of a literature seminar utilized a wiki so students could thoroughly investigate texts outside of the classroom. When portions of the text were posted on the wiki, the students were required to highlight either a word or phrase and clarify it. Then students are asked to read the other responses and reply to those interpretations and invoke a conversation about them (Columbia University, n.d.). In other instances, creating and editing wiki pages related to a specific course are assigned for students to learn how to investigate a topic individually and collect those resources into a public page for all to see. No matter what subject is being taught, a wiki can expand a student's abilities to research and apply their findings in a means that is understandable to others - essentials to problem solving.
 * Wikis **[[image:New_Picture_(3).jpg width="582" height="356" align="right" caption="A student wiki for an Educational Psychology class at the University of Illinois. Click on the picture to visit the wiki." link="@http://wik.ed.uiuc.edu/index.php/Psychology_of_Classroom_Learning_and_Management"]]


 * What Does This Mean for Education? **

The move towards using Web 2.0 tools to help teach student problem solving skills helps transition the classroom from a teacher-centered place into a student-centered atmosphere. When a classroom is student-centered, the teacher becomes a facilitator who's focus is "empowering the students to think for themselves, incorporating strategies to promote life long learning and academic optimism" (Chittleborough et al., 2008, p. 3). The benefit of a teacher being a facilitator is that instead of imparting knowledge in a more traditional lecture form, the teacher helps students question themselves and follow up on their questions. As the students are asked to reflect on their own experiences, they "find their ideas gaining in complexity and power, and they develop increasingly strong abilities to integrate new information" (Thirteen Ed Online, 2004, para. 4). A descriptive summary of the differences between a teacher in the traditional sense and a teacher-facilitator follows. > A teacher tells, a facilitator asks; a teacher lectures from the front, a facilitator supports from the back; a teacher gives answers according to a set curriculum, a facilitator provides guideline and creates the environment for the learner to arrive at his or her own conclusions; a teacher mostly gives a monologue, a facilitator is in continuous dialogue with the learners. ("Constructivism," n.d., The Role of the Instructor section, para. 1).

Thus, when the teacher acts as a facilitator, the students are constantly searching for answers which is a very important aspect of learning to problem solving. This type of learning is also often referred to as teaching students how to learn. This is the educational direction of a classroom with students who are active problem solvers, and since Web 2.0 is by nature constructivist, it is aiding teachers in achievement of this inquiry-based route.

The change from traditional lecture methods to student-centered methods utilizing Web 2.0 tools may seem overwhelming to some. Simply using a Web 2.0 tool does not automatically increase problem solving skills, as they are not one size fits all solutions to teaching troubles. Web 2.0 must be integrated into the curriculum with purposeful intent and thoughtful consideration. Advice from teachers involved in the study presented by Chittleborough et al. (2008) who have found success in using Web 2.0 for problem solving and other higher-level thinking skills include changing the pedagogical methods to include: > The suggestions above are just ways to get started implementing Web 2.0 in the classroom, but are by no means the only way to utilize these tools to improve problem solving. Web 2.0 adds new tools consistently, so it is important to continue to research what new tools have arrived on the educational scene and how they can fit into a classroom's curriculum.
 * Blogs and wikis to help stimulate student thoughts and discussion of problems outside of class.
 * Podcasts and other audio/visual stimulus to provoke thought.
 * Tools that allow access to current data to propose relevant problems.
 * Interactive games for instant feedback.
 * Offering multiple tools to approach the curriculum; student choice fosters ownership.


 * References **

Chittleborough, G., Jobling, W., Hubber, P., & Calnin, G. (2008). //The use of web 2.0 technologies to promote higher order thinking skills.// Retrieved from @http://www.aare.edu.au/08pap/chi08664.pdf.

Columbia University. (n.d.) //E-learning: Higher learning in a web 2.0 world.// Retrieved from @http://www.columbia.edu/cu/tat/pdfs/e-learning.pdf.

Constructivism. (n.d.). Retrieved from Wikipedia: @http://en.wikipedia.org/wiki/Constructivism_%28learning_theory%29

Deubel, P. (2010). Math manipulatives. //Computing Technology for Math Excellence//. Retrieved from @http://www.ct4me.net/math_manipulatives.htm

Illinois State Board of Education. (1997). //Illinois learning standards.// Retrieved from @http://www.isbe.state.il.us/ils/ela/standards.htm.

Kumar, A. & Singhal, N. (2000). //Using Java to Help Students Practice Problem-Solving.// Retrieved from phobos.ramapo.edu/~amruth/r/c/pajava/paper.pdf

Thirteen Ed Online. (2004). Constructivism as a paradigm for teaching and learning//.// //Concept to Classroom//. Retrieved from @http://www.thirteen.org/edonline/concept2class/constructivism/index.html.