BEYOND CROSSROADS TNMATYC

AMATYC
BEYOND CROSSROADS
TNMATYC
KNOXVILLE
MARCH 24, 2017
PRESENTED BY:
Mary Beth Orrange
SUNY Distinguished Professor, emeritus
orrange@ecc.edu
This presentation can be found at slideshare.net
https://www.slideshare.net/orrange/beyond-crossroads-tnmatyc

AMATYC STANDARDS
Crossroads in Mathematics: Standards for Introductory College
Mathematics Before Calculus (1995)1
http://www.amatyc.org/?page=GuidelineCrossroads
Beyond Crossroads: Implementing Mathematics Standards in the First
Two Years of College (2006)2
http://beyondcrossroads.matyc.org/
AMATYC IMPACT (Improving Mathematical Prowess and
College Teaching) ( coming in 2017)

CROSSROADS IN MATHEMATICS GOALS
Improve Mathematics Education at two-year colleges
and at the lower division of four year colleges and
universities.
Encourage more students to study mathematics.
Crossroads, as it is commonly referred to, emphasized desired modes
of student thinking and guidelines for selecting content and
instructional strategies. When published in 1995 it was considered
groundbreaking in content. Standards were written for intellectual
development, content, and pedagogy

BEYOND CROSSROADS GOAL
Stimulate faculty, departments, and institutions to examine, assess, and
improve every component of mathematics education in the first two
years of college.
Beyond Crossroads provided a set of standards designed for
implementation of the three standards in Crossroads focusing on
student learning and the learning environment; assessment of student
learning, curriculum and program development; instruction, and
professionalism.

AMATYC IMPACT GOALS
AMATYC IMPACT updates the original two standards
documents providing clear ideas about how to make an
impact on our students, colleagues, department,
college, state, and nation.
IMPACT is still being written and is expected to be
approved by AMATYC’s Delegate Assembly in San Diego
in November.

TODAY’S WORKSHOP
• Four topics:
• Teaching Problem Solving
• Using Group Methods
• Building a Department Team
• Assessing Student Learning
• Workshop style:
• Interactive and activity based.
• Will primarily, but not exclusively, use “think/pair/share” activity
• Will model the standards.

TEACHING PROBLEM SOLVING
“Problem solving is a major part of mathematics. It is the sum and
substance of our discipline and to reduce the discipline to a set of
exercises and skills devoid of problem solving is misrepresenting
mathematics as a discipline and shortchanging the students.”3

CROSSROADS -PROBLEM SOLVING
Standard I-1:
“Students will engage in substantial mathematical problem solving.
Students will use problem-solving strategies that require persistence,
the ability to recognize inappropriate assumptions, and intellectual risk
taking rather than simple procedural approaches. These strategies
should include posing questions; organizing information; drawing
diagrams; analyzing situations through trial and error, graphing, and
modeling; and drawing conclusions by translating, illustrating, and
verifying results. The students should be able to communicate ad
interpret their results.”1

WHAT IS PROBLEM SOLVING?
• Beyond Crossroads does not expand what “Problem Solving” really means other
than it would be good to use it.
• “Traditional content and instructional approaches should be balanced with inquiry,
problem solving, modeling, use of technology, and collaborative learning.” (page 5)
• “Students will engage in substantial mathematical problem solving.” (page 7)
• And so on ..
• Today’s definition: Problem Solving is using math to solve a problem – not just how
to follow an algorithm but how actually to apply math in a specific situation. Could
be a simple problem such as “how far/how long,” draw a diagram or full semester
projects.

IS THIS WHAT WE
MEAN BY PROBLEM
SOLVING?
First we need to
establish our end
product – what do
we want our students
to be able to do?

ACTIVITY – WHY LEARN MATH?
• On your own: Write down in your notebook why you think it is
important to learn math. (Think)
• With your partner: Use your two answers decide what do we should
expect our students to be able to do at the end of their last math
class at a community college. What is the take-away for our
students? (Pair)
• Share your ideas with another pair: Decide how we as a math
department can make this happen. How does what we do in our
course help them get there? (Share)

PROBLEM SOLVING USING PROJECTS
Teaching problem solving is not easy. Creating materials is not simple; for
example do you want one-solution or an open ended solution problem?
Do you give them all the needed information?
What is an open-ended assignment?
Numeric skills examples are easier to find than algebra-based examples.
As we use more software and programs to teach we should find ways to
engage the students in applied problems. Erie Community College’s title III
grant:
https://facultypages.ecc.edu/title3/Projects/Interdiscipl.htm4

PROBLEM SOLVING USING PROJECTS
Project assignments should include the aspects identified
in standard 1:
• A relevant problem
• Student questions about the assignment – identify the given,
assumptions and what the problem is
• Use a diagram to visualize the situation
• Work though a solution by trial and error
• Graph the solution
• Model the solution
• Express the solution in words –a summary paragraph or two

ACTIVITY - PROJECTS
• On your own: Do you use projects as a problem solving activity? If so,
pick one and describe the class you use it in, the topic you use it to
teach, how long do the students have to solve the problem, and what
the project is. Write your answers down in your notebook.(Think)
• With your partner: Describe your projects to each other and find one
improvement to what each of you do. If one or both are single
solution assignments discuss how they could be expanded to an
open-ended project. (Pair)
• Whole group discussion: How can open-ended projects be made less
onerous to grade/assess? (As a group)

PROBLEM SOLVING AS A DAILY ACTIVITY
• Principles for teaching problem solving
• Model a useful problem-solving method (show them what you want)
• Teach within a specific context (keep it real!)
• Help students understand the problem (it’s not natural for all students)
• Take enough time
• Ask questions and make suggestions (keep them moving along without doing
the work for them)
• Link errors to misconceptions (we learn from our mistakes)5
• Some advice for using a structured solution process:
• https://uwaterloo.ca/centre-for-teaching-excellence/teaching-
resources/teaching-tips/developing-assignments/cross-discipline-
skills/teaching-problem-solving-skills 5

PROBLEM SOLVING AS A DAILY ACTIVITY
• One problem solving model
• Define the problem (with specifics)
• Think about it (they will need to ponder)
• Plan a solution (consider all methods of solutions and chose the best strategy)
• Carry out the plan (be patient and consistent)
• Look back (does it make sense? Have I answered the question)5
• Some advice for using a structured solution process:
• https://uwaterloo.ca/centre-for-teaching-excellence/teaching-
skills/teaching-problem-solving-skills 5

ACTIVITY – TEXTBOOK PROBLEMS
• On your own: Those problems in your text book – you know #93, 94 and
95 in the problem set. How do you use them? Think about the best way
to incorporate those problems into your course.
• With your partner: With your partner decide on one improvement to the
way you use those problems.
• Whole group: List the way to use them
• (Do you assign them? Do you have them submit the solutions? Do you include
the on your assessments - tests? Craft projects out of them?)

ACTIVITY – TODAY’S STUDENT
With your partner: List the changes you have seen in the last few years
in your students and their skills. Now prioritize the ways they have
changed in how the affects on your classroom and the problems you
assign.
Share your ideas with another pair: As a group, discuss how best to
adapt and adjust your classroom teaching and problem assignments to
the changes in the students.
Share with us all.

PROBLEM SOLVING RESOURCE
Beyond Crossroads gives us some examples of Teaching in Context:
http://beyondcrossroads.matyc.org/MVID/What_is_TIC.html
Ten free activities:
http://www.makeitreallearning.com/
https://www.teachingchannel.org/videos/real-world-math-examples
Next steps -
http://beyondcrossroads.matyc.org/MVID/Next_Step_TIC.html
Whole group discussion: What site do you use for problem solving?

ADVICE FROM MARY BETH
• Start with something manageable for both you and your students
• Build on what they know
• Make it real – use data from the newspaper; it just might be relevant
• Build it into the regular process of your class – not just once in a while
activity.
• Don’t be afraid of manipulatives – use that closet reserved for the
“Math for Teachers” course
• Borrow what you can – expand and use. It takes a lot of time to
develop materials on your won.

REFLECTION
Take a moment and write down at least two ideas you learned in this
part of the workshop about problem solving and how you might
incorporate these ideas in your classroom.
USING GROUP METHODS

CROSSROADS –COLLABORATIVE LEARNING
Standard P-2:
“Mathematics faculty will foster interactive learning through student
writing, reading, speaking, and collaborative activities so that
students can learn to work effectively in groups and communication
about mathematics both orally and in writing.”1

COLLABORATIVE LEARNING
• Collaborative learning is strictly defined as an unstructured process in
which participants define problems, develop procedures, and
produce socially constructed knowledge.
• Cooperative learning is a structured, systematic instructional strategy
in which groups work toward a common goal.
• In reality, most group learning activities are a mix of cooperative and
collaborative learning.
• The goal of both collaborative and cooperative learning is for students
to be actively involved in learning activities.2
USING GROUP METHODS

COLLABORATIVE LEARNING
What is Cooperative Learning?
http://beyondcrossroads.matyc.org/MVID/What_is_CL.html
Benefits of Cooperative Learning:
http://beyondcrossroads.matyc.org/MVID/benefitCL/benefitCL.html
When students collaborate, they learn more math and gain social skills
at the same time!7
USING GROUP METHODS

WHY WORK IN GROUPS?
When students are working with others to understand mathematics
they:
• Students clarify their own thinking,
• Articulate ideas to others who can extend the reasoning or point out
misconceptions,
• Consider different ways of thinking about or solving a problem,
• Explain strategies used and justify solutions offered,
• Compare solution strategies for accuracy and utility,
• Relate to previous problems and topics to make connections;
• and the learning becomes “learner centered” rather than “teacher
centered”6
USING GROUP METHODS

DECISIONS
• When to work alone? Working alone gives time for students to think,
plan, and reflect.
• When to use pairs? Using pairs maximizes the number of students
who get to talk and explain.
• When to use groups? Using groups exposes students to a larger
number of ideas and strategies than pairs.
• When to use whole classroom discussion? Whole class discussions
make for quick brainstorming sessions or when groups are stumbling
at the same point in an activity.
USING GROUP METHODS

ACTIVITY: WHEN TO USE GROUP TYPES
• With your partner: List two specific types of problems or situations in
which you would utilize each of the four strategies listed above: ones
that would be suitable for individual work, pairs, groups or whole
class discussions. Provide justifications for your answers.
• Discuss your findings with the whole group.
USING GROUP METHODS

STRATEGIES FOR FORMING GROUPS
• How to form groups
• Self-selected
• Random
• Teacher selected
• How often to change groups
• Daily
• Weekly
• By chapter
• Never
• How and when to assign roles in groups – accountability
• Roles
• http://beyondcrossroads.matyc.org/MVID/individualCL/individualCL.html
• Jigsaw
USING GROUP METHODS

IN THE BEGINNING OF THE SEMESTER
• Establish norms in the beginning of the semester
• Students need to come prepared, to respect each other, participate in the solution of
the assignment, and be responsible for their own learning.
• First assignment should “set the stage”
• It should be a meaningful assignment
• Every student needs to contribute to the solution
• It should require students to talk to each other
• It should include individual thought, pair, group and whole group interaction
• The instructor must make sure all students have access to all relevant
materials and understand the task – it is not the responsibility of the
students to teach the other students but to learn with them.
USING GROUP METHODS

THE GOAL:
IN A PRODUCTIVE GROUP THE MEMBERS
• Work to understand what each member is saying
• Ask for evidence (Why do you think that? Can you show me on the
graph where that happens? How does your response answer the
question?)
• Search for limitations (When is it not true? What if the number is
zero?)
• Builds solutions on previous ideas or what was previously said in class
USING GROUP METHODS

OVER TIME
Student should need less intervention as the semester progresses.
Groups should have more sophisticated solution methods.
Group learning is not always natural for all students.
Whole group discussion 1: Why are some students reluctant to
participate in group learning tasks?
Whole group discussion 2: How can we as teachers help our students
overcome these obstacles?
USING GROUP METHODS

KNOWING HOW TO TEACH WITH GROUPS IS A
LEARNED SKILL
• Go slowly the first semester
• Suggestions for classroom orientation and manipulatives:
• Desks vs tables
• Dry erase boards around the room
• Individual dry erase boards
• One calculator per group / one handout /
folders with problems
USING GROUP METHODS

ACTIVITY: TEACHER CONTRIBUTIONS
With your partner: Identify what the instructor should do when your
students are working in their groups. Do your activities vary with the
time of the semester or quarter?
With another pair to form a group: Discuss how the teacher’s behavior
might be different based on the math topic, the timing or some other
variable.
Whole group discussion of ideas generated.
USING GROUP METHODS

ACTIVITY: REFLECTION
On your own: Take a minute to think about your own feelings about
collaboration. Are you comfortable collaborating or would you rather
“go alone?” Is your answer different for learning and for working?
With your partner: Share your personal experiences in your learning or
working collaboratively. Do you think your students will have the same
challenges? And if so how could you help them overcome the
challenges?
USING GROUP METHODS

SOME TECHNIQUES
• Think – Pair – share
• Jigsaw
http://beyondcrossroads.matyc.org/MVID/jigs
awCL/jigsawCL.html
• Paired Boardwork Traveling (Maria Anderson)
https://youtu.be/D3Rhc9dIl8U
• Pass the problem
• Barkley, Elizabeth F., K. Patricia Cross, and
Claire H. Major. Collaborative learning
techniques: A handbook for college faculty.
(2014)
USING GROUP METHODS

MORE REFLECTION
part of the workshop and how you might incorporate these ideas in
your classroom.
Think about the ways group method techniques were modeled in this
session and determine if they would be helpful in your daily worklife.
USING GROUP METHODS

BUILDING A DEPARTMENT TEAM
Have you ever played on a sports team?
Common goal easy to identify in sports world.
Team works best with common goals….
Businesses have goals – production goals, sales
goals, stock price goals. Education …. hmmm
Does the sports team analogy work in your
department? Does a new faculty member
know what your department values? How
about your adjunct faculty members? Do you?

MISSION STATEMENT
A mission statement is a one-sentence statement describing
what the organization does. Niki – “"To bring inspiration and
innovation to every athlete in the world." or McDonalds “to
be our customers' favorite place and way to eat.” but what
you want your department to be known for.11

ACTIVITY: CRAFT A MISSION STATEMENT
On your own: Craft a short mission statement; not be a corny poster
but something that expresses what you want your department to be
known for.
With your partner: Discuss how you would get your entire department
to embrace the idea in your mission statement. Once you have
determined how you would establish consensus craft a plan as to what
your department would actually do with or use the mission statement
– otherwise it is just an academic activity.

BASIC DEPARTMENT TEAMBUILDING
Each department member must have what they need – access to
computers, calculators, the internet, manipulatives for their courses,
and so on. If they don’t have access to the basics they won’t be a
functioning part of the team. This goes for part-time or adjunct faculty
also.
Just as students need to be taught how to work
collaboratively, so do faculty. Not an easy task –
if it can’t be done within the department solicit
someone from outside the department to help.

BASIC DEPARTMENT TEAMBUILDING
Team-building is not a one-time activity but needs to be scaffolded
from the bottom up. Perhaps begin with a social activity, work through
mission, goals, plans and assessment in a non-threatening way.
Use team-work for department projects. We tend to call them
committees but that lacks the punch of a team. Technology team
conveys a different concept than technology committee. Embed team
language within your department for maximum effect.

ACTIVITY: GOAL -SETTING
A mission statement describes what your organization does; who you
are right now. A goal statement is where you want to be and the plan
is the steps taken to achieve the goal. A goal statement is an action
statement that is measurable.
On your own: Create one goal that would be realistic and appropriate
for your department. Write it down.
With your partner: Determine if you have one goal between you or two
different goals. Use your combined expertise to refine the language of
the one or two goals.
Whole group discussion: Discus the implementation phase within your
department. Determine obstacles for achievement and support for
success.

STANDARDIZATION
The more standard common practices used in a department the closer
to a team the department will become.
When a course sequence and department use common routines for
learning practices, there are many advantages for students and
instructors:
• Students do not have to navigate different expectations in each course.
• A smaller investment is required from instructors and students in developing
norms and routines.
• Little time is required to prepare students for activities.
• New students entering the sequence can learn from the existing
knowledgeable core.

ACTIVITY: COMMON PRACTICES
Hold a department discussion to create a plan to either identify worthy
practices or to spread a practice across the department. Remember –
in a brainstorming session there are no bad ideas.
On your own: Create a list of commonalities among all the math
classes at your institution.
With your partner: Share your list of commonalities. Now craft a wish
list of potential and appropriate routines that you would like to see
used across courses in your department.
With another pair to form a group: What strategies do you think would
help promote the widespread use of these routines? What obstacles
would prevent the establishment of such routines? What could you
implement at the minimum?

ACTIVITY: PERSONAL GOALS
Align personal goals with department goals. Embrace
self-interest; folks cooperate better if they see some
value in it for them.12
On your own: Identify two areas you are working on
this year/semester/quarter in your professional life.
How will you know when you have achieved these
goals? That is how will you measure your own
success?
With your partner: Share your goals. How would you
realistically help your partner achieve their goals if
they worked with you? Would this strategy work in
your department? Why or why not?

TEAM PITFALLS
“The leading causes of team failure are absence of trust, fear of conflict,
lack of commitment, avoidance of accountability, and inattention to
results. Teams need to find ways to avoid these dysfunctions.” 13
• Fear of conflict—Although most people don’t enjoy conflict, it is important to acknowledge that
conflict is required sometimes to get through an issue. To deal with conflict effectively, the team
needs to discuss each member’s conflict styles and to establish ground rules at the beginning for
how the team will work through conflict.
• Lack of commitment—Review each team member’s responsibilities at the end of each meeting
and ensure that all team members are aligned.
• Avoidance of accountability—State explicitly what the team’s goals are going to be; regularly
discuss progress toward those goals; and continually emphasize as a group how important it is to
meet these goals for the success of the project and the satisfaction of the team.
• Inattention to results—Keep the team focused on tangible goals and reward individuals on
successes.

REFLECTION
On your own: Take a minute to think about your own feelings about
your department as a team. What did you discover in this workshop
that could you use to help turn your department into a team?
The team-building process can help create a productive environment in
which team members speak openly and honestly, deal with problems
professionally, share expertise, and feel like they contributed.13

ASSESSING STUDENT LEARNING
Is assessing more than testing? …. Begin with the premise that
student assessment should improve performance, not just audit it.

SACS
Southern Association of Colleges and Schools (SACS) Commission on
Colleges (SACS.org)
CORE REQUIREMENT 2.12 (2011 Principles of Accreditation SACS) The
institution has developed an acceptable Quality Enhancement Plan
(QEP) that includes an institutional process for identifying key issues
emerging from institutional assessment and focuses on learning
outcomes and/or the environment supporting student learning and
accomplishing the mission of the institution. (Quality Enhancement
Plan)15

THE FIVE QUESTIONS OF ASSESSMENT
SACS
1. What are you assessing? Learning goals.
2. What tools will you use to gather the information? Assessment
methods.
3. From whom and how will you gather the information? Assessment
plan.
4. How will you analyze the results? Assessment data review process.
5. How will you use the results of assessment to improve student
learning? Closing the loop. 14

TENNESSEE BOARD OF REGENTS (TBR)
• https://www.tbr.edu/cc/tennessee-higher-education-higher-
standards
• https://www.tbr.edu/sites/tbr.edu/files/media/2015/02/CCA-
Remediation-final%2092.pdf
• https://www.tbr.edu/sites/tbr.edu/files/media/2015/02/Readiness%2
0Facts%20-%20Higher%20Ed.pdf
TBR - another level

STUDENT LEARNING ASSESSMENT
• We must demonstrate that our students are learning what we say
they are.
• So … how do you know they are learning?
• Assessment is an ongoing process aimed at understanding and
improving student learning.
• Improvement is really the heart of assessment.

COURSE-EMBEDDED ASSESSMENT
Course-embedded assessment refers to techniques used in the
classroom (one class period, several or over the duration of the course)
to assess students' learning, as individuals and in groups.
Course-embedded assessment is common sense, and it can enable an
institution to move from having a fragmented hodge-podge of courses
focused on delivering instruction to having an integrated, coherent
framework centering on student learning—thus helping students to
overcome the compartmentalization and fragmentation of writing (and
other) knowledge that occurs when skills are not transferred across
years and courses.16

COURSE-EMBEDDED ASSESSMENT
• POLL: Does your department / institution
have a process of course embedded
assessment? Via Program review or
systematic assessment?
• Whole group discussion: What does it
mean to you and your department?

CLASSROOM ASSESSMENT TECHNIQUES (CAT)
POLL: How many of you are familiar with Cross and Angelo’s work on
Classroom Assessment Techniques? (CAT) 17
POLL: How many of you use CATs on a regular basis?
Classroom Assessment Techniques (CATs) are a set of specific activities
that instructors can use to quickly gauge students’ comprehension.
They are generally used to assess students’ understanding of material
in the current course, but with minor modifications they can also be
used to gauge students’ knowledge coming into a course or program.

CLASSROOM ASSESSMENT TECHNIQUES
• CATs are meant to provide immediate
feedback about the entire class’s level of
understanding, not individual students’. The
instructor can use this feedback to inform
instruction, such as speeding up or slowing
the pace of a lecture or explicitly addressing
areas of confusion.
• As with group or collaborative learning there
is a set of specific language and specific
techniques.

• Minute Paper: Have students identify the most significant things they
have learned from a given lecture, discussion, or assignment. Give
students one to two minutes to write a response on an index card or
paper. Collect their responses and look them over quickly. Their
answers can help you to determine if they are successfully identifying
what you view as most important. Or have them keep their
summaries in their notebooks.
• Muddiest Point: This is similar to the Minute Paper but focuses on
areas of confusion rather than summary. Ask your students, “What
was the muddiest point in… (today’s class, the problem set, the
homework)?” Give them one to two minutes to write and collect their
responses.

• Problem Recognition Tasks: Identify a set of problems that can be
solved most effectively by only one of a few methods that you are
teaching in the class. Ask students to identify by name which methods
best fit which problems without actually solving the problems. This task
works best when only one method can be used for each problem.
• Background Knowledge Probe: Assessing prior knowledge helps
teachers to determine the most effective starting point for a given
lesson and the appropriate level at which to begin the instruction.
http://beyondcrossroads.matyc.org/MVID/interview4a/interview4a.html

ACTIVITY: MUDDIEST POINT
• On your own: Write down what is the most confusing part of this
section so far.
• With your partner: Turn to your partner and share your muddies
point. Then, to the best of your ability, clear up your partner’s
muddiest point.

ACTIVITY: PROBLEM RECOGNITION TASKS
• With your partner: List as many situations that you can think of when
you would use Problem Recognition Tasks technique.
• With another pair: Compare lists, and elaborate on the details. How
would you incorporate this into an online class or one with extensive
reliance on a learning management system?

A FEW WORDS OF CAUTION
• If CAT is against your intuition – don’t use it!
• Don’t make CAT into a chore or a burden.
• Don’t have your students do something you have not tried yourself.
• Allow for more time than you think is necessary.
• Make sure you “close the loop” – give them feedback on the
information.

ACTIVITY: ONLINE ENVIRONMENT
Learning has moved beyond the classroom and into an online
environment. Classroom Assessment has moved to Learning
Assessment.
• On your own: How would you incorporate the minute paper into an
online class or one that makes extensive use of a course management
system?
• With your partner and another pair: Share your ideas and write out
two specific examples – and the course content in which it is based.
Then provide examples of appropriate student responses.

ACTIVITY: ASSESSING LEARNING IN GROUPS
• POLL: How many of you have used group activities for grades?
• Whole group discussion: What have you used and how has it worked
for you?
• Examples:
• Teambuilding activity , make the review day count as 10% on test
• Have one or two test problems that require problem solving be completed in
pairs or groups the day before the test
• Use the grade on the test problem as part of the test or include parts of the
group problem on the assessment.

ACTIVITY: BEYOND TESTING
• POLL: How many of you use something other than testing for grades?
• Whole group discussion: What have you used and how has it worked
for you?
• Does this take away from verification that students have learned the
course objectives?
• Whole group discussion: how can you translate this into the first part
of this section – how to include this learning assessment into your
department’s “report” of direct evidence of student learning?(Course
competencies, learning objectives, department goals …)

LEARNING ASSESSMENT TECHNIQUE
• Identify Learning Goals
• Implement effective learning activities
• Analyze report upon outcomes18

REFLECTION
part of the workshop about assessing student learning and how you
might incorporate these ideas in your class.
This presentation can be found at slideshare.net
https://www.slideshare.net/orrange/beyond-crossroads-tnmatyc
PRESENTED BY:
Mary Beth Orrange
SUNY Distinguished Professor, emeritus
orrange@ecc.edu

REFERENCES
1 American Mathematical Association of Two-Year Colleges. (1995).
Crossroads in Mathematics: Standards for introductory college
mathematics before calculus. Memphis, TN: Author.
2 American Mathematical Association of Two-Year Colleges. (2006).
Beyond Crossroads: Implementing Mathematics Standards in the First
Two Years of College. Retrieved from
http://beyondcrossroads.matyc.org/doc/PDFs/BCAll.pdf
3 http://jwilson.coe.uga.edu/emt725/PSsyn/PSsyn.html
4https://facultypages.ecc.edu/title3/Projects/Interdiscipl.htm
5https://uwaterloo.ca/centre-for-teaching-excellence/teaching-
skills/teaching-problem-solving-skills
REFERENCES

REFERENCES
REFERENCES
6 Blumenfeld, Phyllis C., Toni M. Kempler, and Joseph S.
Krajcik. Motivation and cognitive engagement in learning
environments. na, 2006.
7 Cabrera, Alberto F; Nora, Amaury; Crissman, Jennifer L; Terenzini,
Patrick T; et al. Collaborative learning: Its impact on college students'
development and diversity, Journal of College Student Development;
Baltimore43.1 (Jan/Feb 2002): 20.
8 Webb, Noreen M. "The teacher's role in promoting collaborative
dialogue in the classroom." British Journal of Educational
Psychology 79.1 (2009): 1-28.

REFERENCES
9 Springer, Leonard, Mary Elizabeth Stanne, and Samuel S. Donovan.
"Effects of small-group learning on undergraduates in science,
mathematics, engineering, and technology: A meta-analysis." Review of
educational research 69.1 (1999): 21-51.
10 Barkley, Elizabeth F., K. Patricia Cross, and Claire H. Major.
Collaborative learning techniques: A handbook for college faculty. John
Wiley & Sons, 2014.
11: Building a Collegial, Cooperative Department by Robert Kelly,
Faculty focus 10/18/12:
12: Masterclassmanagement.com 2/17/17:
13 “A Purposeful Approach to Team Work.” Academic Leader 21(6) (June
2005): 1, 7.
REFERENCES

REFERENCES
REFERENCES
14 http://sacscoc.org/staff/mjohnson/Jackson-Johnson-SCI.pdf
15 http://www.sacscoc.org/pdf/2012PrinciplesOfAcreditation.pdf; page
21
16 C Nelson - 2009 - secondlanguagewriting.com
17 Angelo, Thomas A., & Cross, K. Patricia. (1993). Classroom
Assessment Techniques: A Handbook for College Teachers. San
Francisco: Jossey-Bass.
18 Barkley, Elizabeth F., & Major, Clair H. (2016). Learning Assessment
Techniques: A Handbook for College Faculty. San Francisco: Josey-Bass.

BEYOND CROSSROADS TNMATYC

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (20)

Similar to BEYOND CROSSROADS TNMATYC

Similar to BEYOND CROSSROADS TNMATYC (20)

More from orrange

More from orrange (7)

Recently uploaded

Recently uploaded (20)

BEYOND CROSSROADS TNMATYC