Contextualized vs. Integrated: What is the Difference?

In June, Algebra 1 in Manufacturing Processes, Entrepreneurship and Design (AMPED for short), a 2-year curriculum development project will be complete with 2 years of pilot behind us.  The AMPED IMG_0531 (1)program will be launching in other middle and high schools next fall. The course is as much integrated as it is contextualized.  Herein lies the question, “What is the difference between integrated and contextualized learning and does it matter?”.

Before we attempt to answer the question, here is a little history about the programs at Loveland High School.  The Geometry in Construction curriculum was first piloted in 2005-06 and began showing immediate success with increased state test scores and with improved attitudes in mathematics.   Our district liked what they saw.  Fast forward to October 2013.  We were approached to create “a contextualized/integrated” program similar to the Geometry in Construction curriculum but for Algebra 1.   Why?  The failure rate in our school’s Algebra 1 was too high.   In most U.S. schools Algebra 1 is the most failed course which when failed dramatically increases student drop out potential.  As we began to write the AMPED course we realized that AMPED was much more integrated and less contextualized than Geometry in Construction.

So, how do 2 everyday teachers develop a working definition for contextualized learning and for integrated learning and more importantly how are they different?  Can positive student outcomes be expected from an integrated course?  Will students respond favorably?

Our working definition of integrated/contextualized learning: Can the CTE concept be done without the math….if so it is integrated. If the math is required to do the CTE concept, it is contextualized. It is contextualized if one must know the math to complete the task. This definition creates a fuzzy zone. For example, do you need to know the Pythagorean theorem to “square” a foundation? Technically no. Someone must know the 3-4-5 combination but not the theorem. We do take the definition of contextualization one more step.   Does someone in the process/career path need to know the Pythagorean theorem? Our answer is “yes”.   Someone on the work crew (engineering, architects, framing, concrete, excavators, etc.) must know about the Pythagorean theorem in order to design the foundation.

To explain, in concrete terms, we refer to 2 math activities. The first lesson is the math problem found in this month’s newsletter (Create a Tool). This lesson is contextualized in that someone needed to know how to create the tool that is used in sheet metal fabrication. The second lesson is integrated. It is the Trajectory Launcher, which uses the engineering design cycle. Access this lesson by visiting   and scroll down 4 lessons.  In this lesson, the math is not required to build a launcher. We do it for an engineering lesson using kinesthetic and visual learning.

With this working definition, we set out to create AMPED. It is based on the running of a REAL business. This business is primarily the printing of t-shirts and engraving of materials. Of course, the question that surfaces is “Does it matter to students if it is integrated vs. contextualized?  Student enthusiasm tells us probably not as much as we thought. Being an engaged learner may be just as important. A study done by the Colorado Department of Education in 1999 encourages us with the following:

The retention rate for how students learn is as follows:

5% Lecture

10% Reading

20% Audiovisual

30% Demonstration

50% Discussion

75% Practice by doing

90% Teaching others

We see this as a “learning engagement scale” and therefore, we set out to focus on “practice by doing” and by “teaching others” if the math was not naturally occurring in CTE. Our students report back:

“Teachers expect us to be active learners not just to sit.

The class is more interesting and fun because of the things we do.

Running a real business gives meaning/usefulness to the algebra.

Gives me a way to make sense (something I can relate to) of the new material.”

In summary, our students are active learners. We are happy with our student’s outcomes and their success. The bottom line is that our students are passing algebra and their attitude towards math is improving.