Constructivism is ideal in most subject areas as the main courses in every grade level are either skill based (math and language/reading) or an application of those subjects (science, social studies, etc.). This means that application is natural to the learning environment.
Constructivism relies on an artifact, proof, learning evolved and applied. Orey explains that we are in a constant struggle for equilibrium in learning. We are constantly given new information that we are required to sort into some kind of schema, or heaven forbid, we are required to create a new "file folder" based on the new information. (Laureate Education, Inc. , 2008)
Constructivism naturally requires a person to create hypotheses upon applying and cultivating a new skill. Decision making, problem solving, and experimental inquiry are natural to my subject area, mathematics. These are 3 of the six tasks listed in Using Technology with Classroom Instruction That Works (pg. 203). Quite often students are asked a question (real world math problems) that require them to make an educated guess as to what methods or courses of action make sense to investigate the given problem. I love math particularly because there is often more than one way to answer a question. Math affords a great ability to be adapted into many inquiry and research based investigations for this very reason.
I found that the website listed on page 214 of our textbook, "Using Technology" was a great example of incorporating numbers and operations into a science question, such as an investigation as to how the water cycle works. It requires students to make assumptions, revise or completely change these assumptions based on new information. This sounds a lot like the basic theories Piaget outlined.
If you are asking, what about an artifact? Constructivism asks for proof, for investigation through construction. The number one way to incorporate math using a technological artifact is Microsoft Excel or any other spreadsheet program. I myself have used Excel to have students investigate rainfall in rainforests, while including math topics such as average, adding and subtracting decimals, comparing and ordering numbers, and other sixth grade math concepts.
Be prepared to sacrifice time for constructivism.
But keep in mind, what is better, skimming through and only reaching the short term memory experience, or creating, applying, and reaching a long-term connection? (Laureate, 2008).
Glazer, E. (2001). Problem Based Instruction. In M. Orey (Ed.), Emerging perspectives on learning, teaching, and technology. Retrieved 3/23/2010 from http://projects.coe.uga.edu/epltt/
Laureate Education, Inc. (Executive Producer). (2008). Program 1: Understanding the Brain. [Educational video]. Baltimore: Author.
Pitler, H., Hubbell, E., Kuhn, M., & Malenoski, K. (2007). Using technology with classroom instruction that works. Alexandria, VA: ASCD.