International Critical Issues:

Increasing Rigor and Cognitive Demand

Pamela R. H. Bailey

George Mason University

 

 

 

 

 

 

 

 

 

 

 

 

International Critical Issues:

Increasing Rigor and Cognitive Demand

Cognitive Demand PowerPoint to be used to guide the presentation.

Who: NCTM Regional Conference Participants

Where:  Baltimore, MD

When: November, 2010

How and What:  Increasing rigor in the mathematics secondary classroom and developing rich tasks high in cognitive demand.

Objective for the session: 

·         Participants will define rigor and if it is increased when lesson is taught conceptually or is it as a skill.

·         Define and recognize levels of cognitive demand.

·         Create a rich task that is high in rigor and cognitive demand given a standard textbook question.

·         Experience activities high in cognitive demand and rigor based on the function approach to teaching algebra (reform approach).   

How is the topic important to improving math teaching and learning?

With the technological advances in the world, mathematical needs by employers and society are very different from the past and are changing rapidly every day.  Mathematics instruction however has not progressed at the same pace.  A majority of teachers around the world are still focusing on procedures versus the conceptual understanding therefore inhibiting students in their growth to become productive citizens.  The critical issue is why school systems around the world have not insisted on a standards-based approach to mathematics.

 Tasks that engage students in making connections within and between concepts and to real-world situations require a higher level of thinking in order for them to successfully solve and analyze (Stein, Smith, Henningsen, & Silver, 2000).  This implies that teachers need to increase their understanding of student thinking so that there will be a change in instructional practices that are based on the National Council of Teachers of Mathematics (NCTM) Process Standards (Cwikla, 2002).  If we do not engage students, expect exact answers with no consideration for thinking processes, and demand that students just sit and get concepts then our society will decline.  Changes in curriculum need to be examined from various stakeholder viewpoints with regard to the intended, written, and implemented programs according to Kulm and Li (2009).  China and the United States approach curriculum and instruction issues with different lenses.  When considering the culture and society of both countries with respect to education we also need to look at the history of the each country as well as the expectation of academics.  Change is effected by the culture of the area which may embrace new ideas or stand firm with past actions.  China has a national curriculum which provides the structure within their culture to promote change to more inquiry, problem solving, and instruction that is student-centered.  The United States educational system is a culture where the schools are controlled by administrators, are textbook driven, and have teachers that are lone rangers within their classrooms.  Parents of children in China and the United States in general have very different values.  Our students do not value their education so we, as educators, need to find ways that will encourage them to do so.  With technology and various types of internet and video games commonplace in most homes, students are used to immediate gratification.  It will take time for educators to encourage the students to think.

 

 

Professional Learning Session:

I.                   Opening problem – Participants need to determine the answer using two different methods.

What is 2/3 of 3/4?

II.                Rigor in Conceptual Understanding and Skill Efficiency

Materials:  Handout

                  Item on cards for wall

Handout contains a table with a list of activities or actions for participants to check off if each of the line items is representative of student’s learning conceptually or with a focus on skill efficiency.

Participants will be handed a card with one of the items from the handout written on it.  They are to put it on the wall under the heading of conceptual understanding or skill efficiency.

Take turns sharing why they placed their card under the heading.  Illicit comments from other participants regarding the placement.  Goal is to have participants discuss student effort, challenges, thinking, and problem solving involved with each of the items.

Discuss each item to determine the rigor involved using Bloom’s taxonomy.

Questions:

What makes a problem rigorous?

Does a rigorous problem also increase conceptual understanding?  Does a rigorous problem also increase skill efficiency?

Does a lesson that is based on conceptual understanding (or skill efficiency) also increase rigor?

III.             Levels of Cognitive Demand

Materials:  Manila envelopes with problems

                  Handout to record levels

Pass out manila envelopes and handout to small groups.  Their task is to read each question and determine if they believe it is low or high cognitive demand and WHY.

As groups go over each question they should focus on justifying responses.

Questions:

What makes a problem high/low in cognitive demand?

What can destroy the cognitive demand of a problem?

What can a teacher do in order to maintain a high cognitive demand?

IV.             Relate rigor and cognitive demand to the opening activity and the importance for increasing student expectations.  Bring up the concept of the function approach or a standards-based approach to teaching and learning algebra.

Given a typical question from a textbook have students create a rich task that is high in cognitive demand.  Have on the screen what makes a rich task.  Share out.  

What were the responses from the attendees?

At the end of the session we had a question and answer period.  Below are some of the main questions and comments.

How do teachers implement lessons higher in rigor and cognitive demand?  I was able to share with the group how our school district changed the curriculum maps in algebra so that there is a focus on the Rule of 5, the NCTM Process Standards, and the 5E’s.  Teachers have also had the opportunity to attend professional learning sessions on these ideas, were involved in the development of the maps, and follow up sessions where example lessons were shared and discussed. 

Did all of the teachers accept the change?  Some of the teachers expressed concern as should be expected.  It was stressed that change will take time and a total turnaround is not expected.  Balance is the key; a balance between conceptual understanding and skill efficiency and between teacher-centered and student-centered lessons and activities.  Discussed 21st century teaching and learning and the expectations in our society for problem solving, representations, and being able to communicate knowledge and justification of thinking processes and mathematical manipulations.  Support was provided quarterly where teachers could share ideas across the schools and in collaborative sessions within the schools.  Central office mathematics support personnel and mathematics specialists are also available to assist in planning, modeling, and coaching teachers.    

Could an example of a unit of study be given?  The overall flow of a quarter was shared for Algebra I and then one of the big topics was discussed in more detail.  Talk centered on the cognitive demand expectations of the unit, “if” the teacher chose to implement the unit with a more standards-based approach. 

Participants expressed a concern for administrator’s reactions to assessments and end of course tests.  Discussion ensued about teaching to a higher cognitive demand leads to increased rigor and conceptual understanding.  Students will not be memorizing material which is easily forgotten and instead will experience the mathematics from multiple representations.        

 

 

References

Cwikla, J.  (2002).  An interview analysis of teachers' reactions to mathematics reform professional development.  Presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA.

Kulm, G., & Li, Y.  (2009). Curriculum research to improve teaching and learning:  National

and cross-national studies.  ZDM Mathematics Education.  41, 709-715.

Stein, M., Smith, M., Henningsen, M., & Silver, E.  (2000).  Implementing standards-based

mathematics instruction: A casebook for professional development.  New York: Teachers College Press.