1. Mathematics in Context vs. Glencoe
Linda A.G. Gantz & Hana Oh
EDIT 732
Objective: We will compare and contrast the technology supported learning environments of Mathematics in Context Online and Glencoe Online.

2. Getting to know our technology supported learning environments.
Constructivist Objectivist
Mathematics Glencoe
in Context

3. We will compare and contrast the following
The Learner
The Teacher
The Learning Context
The Learning Activity
The Content
Assessment
 APPLICATION OF THE CONSTRUCTIVIST CHECKLIST

4. Mathematics in Context
The Learner
Constructivist
Mathematics in Context
Objectivist
Glencoe
Develop mathematical models and strategies to solve problems (Learner control )
Use numbers, symbols, diagrams, and words to describe the world around them (Multiple perspectives 
Student-directed goals  )
Become cognitively ready for high level problem solving (Metacognition )
Expected to master the topic looking at the extended examples (Focus on results)
Expected to memorize steps in order to solve equations (rote memory)
The examples and additional practice items are fixed (pdf file!)
Available resources are designed for students to work independently

5. Mathematics In Context
The Teacher
Constructivist
Mathematics In Context
Objectivist
Glencoe
The teacher is both facilitator and guide in the teaching and learning process. (Teachers as coaches  )
Teachers need to embrace the mathematics, collaborate with others, and reflect on their understanding of the concepts.
Transmission
Teacher Centered
Lecture supported environment.
Materials and lesson ideas provided.

6. Mathematics in Context
“We no longer teach, but rather we coach- we have moved from the sage on the stage to the guide on the side. The coach provides the scaffolding for the learner. (Duffy & Cunningham, 1996, p.184)

7. Mathematics in Context
The Learning Context
Constructivist
Mathematics in Context
Objectivist
Glencoe
Problems are real-life application (everyday) problems that helps students to make connections as to why it is important in learning the topic (Authentic contexts  )
Most practice problems are word problems for students to understand the context through scaffolding (Scaffolding )
Interactive problems/manipulatives are available for students to play around and generate answers (dynamic) (Experiential)
Take home projects are available with historical background and relevance to why the topic is important and they allow students to reflect on the findings to help them understand the context (Knowledge construction  )
Provide project using calculator for students to follow each step without making connections to context (busy work, Learn by doing)
Available interactive movie and questions for students to try but connections are not made and includes wrong solutions!!! (static)

8. Mathematics In Context
The Learning Activity
Constructivist
Mathematics In Context
Objectivist
Glencoe
In developing each strand (Number, Algebra, Geometry, and Statistics and Probability) the developmental question was “ How can we design a set of activities over the 4 years (Grades 5-8) that would provide students an opportunity to progress from informal notions in that strand toward using formal mathematical reasoning and representations to model and solve routine problems.”
(Senk, 2003)
Web Quest Project
USA TODAY® Related Activities
Brain Pops
Teacher created, not necessarily curriculum driven.

9. Mathematics In Context
The Learning Activity
Constructivist
Mathematics In Context
Objectivist
Glencoe
Authentic activities 
Interaction is essential for learning mathematics.
Collaborative for teacher & student
Self-regulated
Teacher’s pace

10. Mathematics in Context
  MiC Lesson Video
Student page

11. Mathematics in Context
“Here the task of the designer are two-fold:
To instruct the student on how to construct meaning, as well as how to effectively monitor, evaluate, and update these constructions; and
to align and design experiences for the learner so that authentic, relevent contexts can be experienced(Ertmer & Newby,1993, p.66).”

12. Glencoe Brain Pops Web Quest Project
“ …directed learning environments reflect an objectivist epistemology, in which the learner is driven by externally generated objectives ( objectives generated independently of the learner) and by explicit activities and practice, with the goal of transmitting a discrete and well defined body of knowledge.”(Dabbagh & Bannan-Ritland, 2005, p.4)

13. USA TODAY® Related Activities USA TODAY Related Activities provides activities related to the
concept of the lesson as well as up-to-date Snapshot data.
Internet Activity
I Love the City!
Materials: calculator Work alone or in a group of two or three. The table shows the population of each of the ten largest cities
in the U.S. according to the results of the 2000 census.
The population of each city for 1950 is also given.
Rank and City
Population in 2000
Population in 1950
New York, NY
8,008,278
7,891,957
Los Angeles, CA
3,694,820
1,970,358
Chicago, IL
2,896,016
3,620,962
Houston, TX
1,953,631
596,163
Philadelphia, PA
1,517,550
2,071,605

14. “In essence, constructivist pedagogy is applied to attain traditional goals, and the environment becomes an instance … “domesticated constructivism” ( Jonassen & Land, 2000, p.16).”
“…modeling is a more efficient way of learning than trial and error. Jonassen (1999) discussed two types of modeling, behavioral and cogitive modeling. The former is the one most people are familiar with, as it is arguably the easiest way to teach a psychomotor skill and involves imitation of the demonstrated act ( Dennen, p.813)

15. Mathematics in Context
The Content
Constructivist
Mathematics in Context
Objectivist
Glencoe
Problems are real-life application (everyday) problems that helps students to make connections as to why it is important in learning the topic (Previous knowledge constructions , Problem solving )
The content is easy to manipulate and draws students in by including stories to help students understand the relevance (Conceptual interrelatedness  )
External links provide students with other websites that provide similar structure of problems in interactive setting (Alternative viewpoints )
Aligned with state and national standards
Content laid out in a fixed format.
Unable to explore ideas on their own and most activities and lessons are done by memorizing the steps and mastering

16. Mathematics In Context
Assessment
Constructivist
Mathematics In Context
Objectivist
Glencoe
Assessments looks at students’ thought processes and their development by using some form of rubric.
(Senk, 2003)
?Authentic assessment 
Tests that emphasize the one correct answer.
Computation driven.
Standardized practice.

17. Mathematics in Context

18. Algebra 1
 Self-Check Quizzes—SOL
   
Chapter 3
1.  Solve x + 5 = -7. A. -2 B.
-12 C. 35 D. 2
Hint
2.  Solve 23 - x = 142.
119
165
-165
-119
3.  Fifteen minus a number is thirty-two. Find the number. 47
-17
-47 17

19. Mathematics In Context
Mathematics In Context
Glencoe
Are technologies used to keep students…..  
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