Wednesday, September 28, 2011

Constructivism in Practice

As a math teacher, it can sometimes be difficult to think of ways for students to generate and test their hypothesis.  In the book entitled Using Technology with Classroom Instruction that Works, one of the recommendations mentioned was problem solving (Pitler, Hubbell, Kuhn, Malenoski, 2007).  In math, my department consistently incorporates problem solving in every lesson.  This can be in the form of solving algebraic skill problems or solving real world word problems. 

My students are currently learning the rules of exponent as well as how to simplify problems containing exponents.  With the knowledge they gain while learning basic exponent rules, students may have a better understanding of the skill once we begin lessons on square roots.  For instance, students will devise a list of integers that are raised to the power of two (or squared).  Then, students will work backwards to devise a list of square roots.  Students will generate and test a hypothesis as to what the actual outcome would be by estimating each problem.  They will test their hypothesis by actually working the problem to see how close the actual answer was to their hypothesized answer. 

In order to enhance students’ learning, technology could easily be utilized.  According to Dr. Orey (Laureate, 2011), students should be engaged in learning and the process of creating an artifact to share with others to follow the theory of constructionism (Laureate Education, Inc., 2011).  For this particular lesson involving exponents and square roots, students could create a spreadsheet via Microsoft Excel.  Students could design a table with the problem in one column, their hypothesis in the next column, the actual answer in another column, and the last column would involve the difference from their hypothesized answer and the actual answer.  Then, students could create a line graph that represents the difference from their hypothesis and the actual answer.  This way, students can visually see how off or how close they were to generating the correct answer for each problem.  After generating their graph, students can share their findings with their collaborative groups.  Students can compare their differences and distinguish which problem(s) the majority of students were missing.  Finally, collaborative groups can work together in order to formulate a plan for determining the correct solution to those problems which had the most errors. 


Laureate Education, Inc. (Producer). (2011). Program five: Cognitive learning theory [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from

Pitler, H., Hubbell, E., Kuhn, M., & Malenoski, K. (2007). Using technology with classroom         instruction that works. Alexandria, VA: ASCD.

Wednesday, September 21, 2011

Cognitivism in Practice

        The sensory memory holds information for only a very brief moment.  We must capture students’ attention by using cues, questioning, using different colors (stimuli), and even using gestures and fluctuating our voices.  In order to move information from short term memory to long term memory, teachers can make information meaningful and relevant to students’ lives.  In today’s society, students are surrounded with various means of technology in their everyday lives. Perhaps by integrating an assortment of technology into our lessons, students will be better able to determine the purpose of the assignment, the relevance of the topic, and the context of the material. 
      Researchers Pitler, Hubbell, Kuhn, and Malenoski (2007) discussed how cues, questions, and advance organizers enhances "students' ability to retrieve, use, and organize information" (p. 73).  I apply all of these instructional strategies in my own classroom in order to teach- and check - for understanding.  As Pitler et al. (2007) noted, cues are hints for what the students are getting ready to learn, while questions help to trigger memories.  In addition, "advance organizers help students focus their learning" (p. 73).  

     I do not always have to check for students' understanding via a formal assessment.  I do not only check understanding of the topic, concept, or skill by means of a quiz or test.  Cuing and questioning helps me to see what the students already know.  

I use graphic organizers to assist students with the placement of an abundance of information.  I have utilized Word and Inspiration software to create graphic organizers that help students to compile information into a more defined space.  I feel that this helps most students "see" the information.   This is also another way to check for understanding based on the placement of the information. 

       Additional instructional strategies include summarizing and note taking which "focuses on enhancing students' ability to synthesize information and distill it into a concise new form" (Pitler et al., 2007, p. 119).  I can check for student's understanding of the day's essential question (pertaining to the lesson) by having students answer the question on a chart that I have created in Word.  The chart includes the Essential questions throughout the entire chapter, along with a space for students to write a short, concise response.  Here, I can quickly see if the student understood the lesson.  

   I have also used graphic organizers as a form of note taking, especially when covering a multitude of topics that students will later compare and contrast.  This way, students can divide the information into categories and see the bigger picture.  I also have had students utilize the Inspiration program in order to collect their thoughts into web.  This strategy has the students taking ownership of their understanding of the context.  


Pitler H., Hubbell, E., Kuhn, M., & Malenoski, K. (2007). Using technology with classroom instruction that works. Alexandria, VA: ASCD.

Wednesday, September 14, 2011

Behaviorism in Practice

Pitler, Hubbell, Kuhn, and Malenoksi (2007) suggested that effort has a direct influence on student achievement and that reinforcing effort enhances students’ understanding of that relationship.  Teachers must express to their students how important effort is and that the amount of effort that they put forth will ultimately affect their overall academic performance.  It would help to have a matrix designed for students in order to examine what exactly constitutes effort. 
One researcher, Edward L. Thorndike, stated that “responses were strengthened or weakened by the consequences of behavior” (Smith, 1999).  Dr. Orley (Laureate, 2010) also stated that “reinforcement is more powerful than punishment.”  According to the behaviorist learning theory, Dr. Orey (Laureate, 2010) recommended reinforcement of desirable behaviors.  James Hartely noted that positive reinforcements should be used more than negative, as positive reinforcements serve as a motivator for success (Smith, 1999).  Teachers can praise and reinforce quality effort from their students by giving appropriate feedback.  Meanwhile, undesirable efforts should be punished, primarily in the area of attention as off task behaviors generally warrant punishment.  Punishment for a lack of effort may also include point deductions based on missing homework assignments, or skipped answers. 
Homework and practice is yet another instructional strategy that relates to the behaviorist theory.  After students learn the concept, they now have the opportunity to apply their skills on their own.  Pitler et al. (2007) explained, “Having students practice a skill or concept enhances their ability to reach the expected level of proficiency” (p. 188).  They go on to say, “Multiple exposures to material help students deepen their understanding of content and become proficient with skills” (Pitler, et al., 2007, p. 188).  Therefore, students’ skill level may be strengthened or weakened depending on the amount of practice, or homework.  Meanwhile, teachers need to give feedback to the students fairly quickly as students tend to make careless errors at times while practicing a new concept.  We do not want our students to continue making those errors, even if they are completing their homework and practicing daily.  Therefore, it is important for teachers  to reinforce practice and accuracy at the same time.    


Laureate Education, Inc. (Producer). (2011). Program four: Behaviorist learning theory [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from

Pitler, H., Hubbell, E., Kuhn, M., & Malenoski, K. (2007). Using technology with classroom instruction that works. Alexandria, VA: ASCD.

Smith, K. (1999). The behaviourist orientation to learning. In The encyclopedia of informal education. Retrieved from