Are My Students REALLY thinking About Their Thinking? - PowerPoint Presentation

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Are My Students REALLY thinking About Their Thinking? - PPT Presentation

Assessing Metacognition in the Math Classroom Andrea Johnson Bellingham Technical College and am I really teaching them how to do that As teachers we can either Deliver content and expect students to absorb it ID: 803580

thinking section learning students section thinking students learning math door metacognition level understanding boudreaux initial confidence student research reflection

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Slide1

Are My Students REALLY thinking About Their Thinking? Assessing Metacognition in the Math ClassroomAndrea JohnsonBellingham Technical College

Slide2

… and am I really teaching them how to do that?

Slide3

As teachers, we can either…Deliver content and expect students to absorb it (focuses on content, not student learning)

orUse the content as a framework for understanding

(focuses on student learning)

Slide4

Outline

Background and motivation Building Expert Learners: Research in Metacognition in Math (STEM)

nstructional approach

for promoting

reflection

Analyzing students’ reflective

writing

Preliminary

data analysis

Slide5

Slide6

Taming the Math MonsterHorror

Panic

Frustration

Confusion

Intimidation

Slide7

Taming the Math MonsterEmpowerment

Clarity

Safety

Enthusiasm

Confidence

Slide8

Personal Math Log

Examination of self as a learner

A priori

attitudes about math

Set goals

Ongoing reflection throughout quarter

Slide9

Personal Math Log – Student Example

Slide10

Reading Apprenticeship Conceptual Framework

Slide11

“What’s All the Fuss About Metacognition?”(Alan Schoenfeld, Cognitive Science and Mathematics Education

, 1987)

To define “metacognition” more precisely, recent research has focused on three related but distinct categories of intellectual behavior:

Beliefs

and Intuitions

– building a mathematical framework from students’

beliefs, intuitions, and past experiences

in trying to understand and make sense of the world.

Knowledge About One’s Own Thought Processes

Expert learners

have a

strong sense of what they already know

and they

use it efficiently

* Expert Learners realistically

assess what they are capable of

learning

Self-Awareness or Self-Regulation

– awareness of one’s thinking

and one’s progress as they are learning or solving problems.

Slide12

Outline

Background and motivation Building Expert Learners: Research in Metacognition in Math (STEM)

nstructional approach

for promoting

reflection

Analyzing students’ reflective

writing

Preliminary

data analysis

Slide13

How People Learn: Key Findings (National Association of Science)Pertaining to becoming “Expert-Learners”

Slide14

“It’s not only what you know, but how you use it (if at all) that matters.”(Schoenfeld, 1987)

Slide15

Example of

the Absence of Self-Regulation (

choenfeld, 1987)

Slide16

Example of Self-Regulation

(Schoenfeld, 1987)

Slide17

How People Learn: Key Findings (NAS)Implications for Instruction

“The teaching of metacognitive skills should be integrated into the curriculum . . .

. . . instruction in metacognition must take place within discipline-specific content . . . ”

Slide18

but . . . can metacognition be fostered within the constraints of an otherwise traditional course?

and how can we determine the extent to which it was learned?

Slide19

Thinking about Students Thinking about Their Own Thinking

Slide20

Metacognition: Early foundations

Flavell

, 1979

Schoenfeld, 1987

Metamemory

, cognitive monitoring

Jean Piaget

Cognitive Structures (Schemas)

ot innate – can be learned

David Kember & Doris Leung, 2000

Development of a Questionnaire

to Measure the Level of Reflective Thinking

Slide21

Lipman Kung and Lindner, 2007

“Research on students

natural

in-context

metacognitive activity is rare.”

“One of the reappearing problems with metacognition research is the ‘fuzziness’ of the concept...

Veenman, 2012

“Whether a statement is simply cognition or metacognition

not straightforward to determine.”

Slide22

Metacognition is big, messy, and private

. . . and thus difficult to observe and study!

Slide23

Outline

Background and motivation Building Expert Learners: Research in Metacognition in Math (STEM)

nstructional approach

for promoting

reflection

Analyzing students’ reflective

writing

Preliminary

data analysis

Slide24

Developing Metacognitive Activities and Assessments for Introductory Physics*

North Dakota State Univ.

Nate Grosz

Alistair

McInerny

Mila

Kryjevskaia

(PI)

University of Maine

Thanh

Lê

MacKenzie

Stetzer

(PI)

Western Washington Univ.

Therese Claire

Tija

Tippett

Andrew Boudreaux (PI)

Whatcom Community College

Sara Julin (PI)

*Supported by National Science Foundation, under collaborative research grants

DUE-1245313, DUE-1245699, DUE-1245993, and DUE-1245999.

Slide25

Scaffolded activity in which students reflect on own learning pathways

Elicit (Engage students with issues known through research to be challenging)

Confront

(A key observation or question that leads students to recognize need for new ways of understanding the issue)

Refine

and Resolve

(Scaffolded instruction that guides students through the necessary thinking)

Reflect

{

Andrew Boudreaux-WWU

Slide26

Components of Reflective Thinking:Retracing the learning pathwayAndrew Boudreaux-WWU

Identify problematic and productive aspects of my

initial

reasoning

Diagnose my underlying learning difficulty.

Describe specific differences in my thinking

then

compared to

now

Retrace my

learning pathway

How did I come to know what I know?

Slide27

Narrative Reflection(Andrew Boudreaux-WWU)

An informal, written “learning commentary” in which students discuss how their understanding of specific concepts has

changed.

Slide28

Lab HW: Narrative ReflectionAndrew Boudreaux-WWU

An early version:

Slide29

Lab HW: Narrative ReflectionAndrew Boudreaux-WWU

broader scope of reflection

Early versions

of assignment

increasing levels of scaffolding

Slide30

Lab HW: Narrative ReflectionAndrew Boudreaux-WWU

Current Version:

Slide31

Lab HW: Narrative ReflectionAndrew Boudreaux-WWU

increasing levels of scaffolding

broader scope of reflection

Current

version

Early versions

of assignment

Slide32

Metacognitive Elements Rubric

A reliable measure of the amount, depth and quality of student reflection.

Response:

Iterative development of a scheme for coding student writing.

Need:

Slide33

Metacognitive elements rubric(Andrew Boudreaux – WWU)

Start “top down” with components of reflective thinking. Modifications based on analysis of student writing.

Identify problematic/productive aspects of initial reasoning.

Diagnose underlying learning difficulty.

Describe differences in thinking

then

compared to

now

Retrace my learning pathway:

How did I come to know what I know?

Slide34

Metacognitive elements rubricAndrew Boudreaux-WWU

13 codes in 4 code groups:

Cognition

(Codes 1-4)

Reflection on initial ideas

(Codes 5-7)

Reflection on current ideas

(Codes 8-10

)

Metacognition

(Codes 11-13)

Ini

tial

reliability checks promising

Slide35

When answering the prelab, I reasoned that I would want to have a super bouncy ball rather than a sticky lump of clay because the bouncy ball [BB] would have a greater change in velocity and therefore transfer a greater magnitude of momentum to the door. My answer was incomplete

because I did not mention the impulse that the ball gives the door and I did not describe how the BB delivers a greater impulse. The prelab was difficult to answer because when I first thought about the situation it seemed the clay would be a better choice because it sticks to the door and moves with the door to close, while the BB rebounds.

So I first thought that since the BB would have a negative velocity, it would take away from momentum transferred to the door,

which is actually opposite of what happens.

By clarifying with my lab partners, it now makes sense to me why the BB delivers a greater impulse to the door than the sticky clay. Because momentum is conserved, the final momentum of the system must be equal to the initial momentum.

The system consists of the ball and the door. Initial momentum of the system is the momentum of the ball (its m X v) and this momentum must stay constant throughout the collision. The BB has an initial positive velocity towards the door and then turns around. The clay has an initial positive velocity and then collides and sticks to the door and continues forward but with a decreased velocity. In both cases the door gains velocity in the forward

direciton

but since the BB rebounds, the door it collides with must have a greater velocity to make up for the BB’s velocity in the opposite direction.

When the clay sticks to the door and moves with it, the clay loses a great amount of velocity and the door only gains a little because they are both traveling in the same direction and the momentum of the system must stay the same.

It made a lot more sense when the lab TA explained how with the conservation of momentum, the BB is traveling the opposite

of the door so the door has a greater velocity to keep momentum constant.

The clay is moving in the same direction as the door so it has a smaller change in velocity and so the door does not gain as much momentum as it does with the BB.

5,6

Slide36

Slide37

“I learned a lot . . .”“I don’t have any questions . . .”“There isn’t anything I’m confused about . . .

”“My answer to question 2.b was wrong . . .”

“The lab didn’t help me . . .”

“I got all of the prelab questions right . . .”

Non-Codes

Andrew Boudreaux-WWU

Slide38

Outline

Background and motivation Building Expert Learners: Research in Metacognition in Math (STEM)

nstructional approach

for promoting

reflection

Analyzing students’ reflective

writing

Preliminary

data analysis

Slide39

Peer Initials

Section

Completed

Graded

Response Questions Completed

Explanation/ Plan for Incomplete Work

_____

3.1

_________

3.2

_________

________ ________

__________

______________________________________

_____

Summary Exercises

_________

3.3

_________

________ ________

__________

______________________________________

_____

3.4

_________

________ ________

__________

______________________________________

Packet

Slide40

Section

Response Questions – HW 3

3.1

1) What did I do in this section?

2) What problems did I encounter using my

initial

understanding of this concept?

3) Identify ideas/skills that I have learned or that I am now more comfortable with after completing this section.

4) Evaluate how effective my thinking process was regarding this section (For example, “I originally thought…, but now I know….”)

3.2

1) What did I do in this section?

2) What problems did I encounter using my

initial

understanding of this concept?

3) Identify ideas/skills that I have learned or that I am now more comfortable with after completing this section.

4) Evaluate how effective my thinking process was regarding this section (For example, “I originally thought…, but now I know….”)

3.3

1) What did I do in this section?

2) What problems did I encounter using my

initial

understanding of this concept?

3) Identify ideas/skills that I have learned or that I am now more comfortable with after completing this section.

4) Evaluate how effective my thinking process was regarding this section (For example, “I originally thought…, but now I know….”)

Slide41

Revised Version of HW Response Questions

Section

Response Questions – HW 5

5.1

1) What did I do in this section?

2) On a scale of 1-5 (1 = lowest confidence level, 5 = highest confidence level), how confident am I about this material before starting this section?

3) After completing this section, was my confidence level correct. Were there any areas that I struggled with that I didn’t anticipate. If so, what? Give details.

5.6

1) What did I do in this section?

2) On a scale of 1-5 (1 = lowest confidence level, 5 = highest confidence level), how confident am I about this material before starting this section?

3) After completing this section, was my confidence level correct. Were there any areas that I struggled with that I didn’t anticipate. If so, what? Give details.

5.7

1) What did I do in this section?

2) On a scale of 1-5 (1 = lowest confidence level, 5 = highest confidence level), how confident am I about this material before starting this section?

3) After completing this section, was my confidence level correct. Were there any areas that I struggled with that I didn’t anticipate. If so, what? Give details.

5.8

1) What did I do in this section?

2) On a scale of 1-5 (1 = lowest confidence level, 5 = highest confidence level), how confident am I about this material before starting this section?

3) After completing this section, was my confidence level correct. Were there any areas that I struggled with that I didn’t anticipate. If so, what? Give details.

REQUIRED

Choose one section from this chapter or one concept that was difficult for you. Describe your INITIAL understanding and compare it to your CURRENT understanding. Use examples from your homework to describe HOW you came to a better understanding or mastery

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Slide42

Response QuestionsStudent Sample – Sustained High Scores (100.5% to 99%)

Slide43

Response QuestionsStudent Sample – Remained Low (64% to 66%)

Slide44

Response QuestionsStudent Sample – Raised Score (51% to 67%)

Slide45

Response QuestionsStudent Sample – Scores Dropped (70% to 38%) Example of “Non-Codes “

Slide46

Chapter ReviewsNo Metacognitive Questions

Metacognitive Questions

9) Simplify

the following problem,

according to the steps provided

pproaching

the Problem

What

type of problem is this? __________________________________________.

What word(s) in the directions are meaningful? What is it asking you to do, specifically? ____________________________________________________________________________________________________________________________________.

What skills do

you already know

that might help you to work this problem?

____________________________________________________________________________________________________________________________________.

What

tools

have you learned that might help you to solve this problem? __________________________________________________________________

__________________________________________________________________.

Solving the Problem

Thoughts/Steps

Used While Solving

Reflecting on the Problem

Does my answer make sense? Explain. ___________________________________

___________________________________________________________________.

While working this problem, did you remember/discover an idea that caused you to change how you solved this problem? Explain. ___________________________

___________________________________________________________________

___________________________________________________________________.

Is there an idea/skill/concept that is still confusing to you? If so, explain. _______

______________________________________________________________________________________________________________________________________.

What is your plan to clear up the confusion? __________________________________________________________________

Simplify the following problem.

10) Write

and solve a mathematical sentence, using the appropriate operation(s) to solve the following problem.

One kind of cereal has 220 calories per serving. Another kind has 110 calories in each serving. During a month with 31 days, how many calories would you save by eating the second kind of cereal each morning for breakfast?

Slide47

Ch. 1 Review - Student Example

Slide48

Chapter 2 Review - Student Example

Slide49

Narrative Reflection LetterMath 90 - Narrative ReflectionName: ______________________Date: _______________________

Your task in this assignment is to write an informal letter to a peer, a friend, or to me that includes the following information (Be sure to write your letter in paragraph style rather than as a list):

Choose one of the

learning targets

(specific concept) that you have struggled with so far in the quarter, but one that you have made the most significant gains in your understanding. Make sure to state the target in your letter.

Consider your

initial

understanding.

Rank your initial understanding 1-5 (1=not well, 5=very well).

Tell your friend/peer/me what specifically you understood about the concept prior to learning more. What was unclear or misunderstood?

Cite evidence

from your homework or notes.

Summarize your

current

understanding of the learning target. In your letter, share how your current understanding differs from your initial understanding.

Cite evidence

from your homework or notes.

Learning Pathway: Explain in your letter what specific activities – working a homework problem, fixing a mistake, working an example, etc. helped to change your ideas.

Be more specific than just listing activities

Slide50

Narrative letter - Student Example (82% to 43%)

The chapter that I struggled most on was all of section 4, which was all about fractions; adding, subtracting, dividing, solving equations, and a mix of other things involving fractions. Fractions are something that I have never been very fluent in, and according to my classmates I am not the only one who feels that way. There was a lot to cover in this section, and there were times where the homework did get overwhelming, and times where I got frustrated for not being able to understand the material. Aside from my struggles, I felt especially confident in 1.1 to 1.8, and sections 2.1 to 2.5. I felt confident in these sections because it felt like

review

for me from the last math class I was in, I felt like it was extra practice that strengthened what I already knew, and I feel like those skills are now solid.

Prior to doing well in sections 1.1 to 1.8 and 2.1 to 2.5, I was able to recall all the material since I’ve spent time with it during my last math class, which I felt I really benefited from because I had some knowledge rather just jumping into something completely new. I felt prepared and ready to do the work! I remember when we spent some time with PEMDAS and I was able to grasp the steps, how to do each one with accuracy. There were times where I may have stumbled across an obstacle, I made sure to ask questions, get help, and ask my peers for help as well.

In essence, I feel that the math class I was previously in prepared me very well before entering Math90, I feel like I can really succeed in this class because the instructor is so great at explaining material in ways her students can understand, she makes sure everyone understands the material before moving on, and encourages asking any questions that may come up that we have along the way.

What helped me the most was the note packets we got at

the beginning of a new chapter/section, what also helped me a lot was going through examples with the whole class, seeing how it is done and listing the steps. It really helped me when I had notes handy, that I could use to help me work through all the problems.

In conclusion, this honestly has been the best math experience I have ever had, and I’m not just saying that. When a teacher is willing to do everything that they can to help you succeed, they are doing their job right. So Mrs

. Johnson

, I would like to thank you for everything that you’ve done to help me succeed this quarter, you really made a difference in my learning career, and as a student as well. Thank you for helping me get one more step closer to my dream career.

Sincerely

Student

Slide51

Narrative letter Student Example – (104% to 98%)

Slide52

Key Terms-Vocabulary Toolkit

Section

Key Term

Vocabulary/Objective

How well did I already know this?

Rank 1-5 (1=not well, 5=well)

What does it mean to me now?

Explain how you know.

Show proof (give an

example

in context)

Key Terms/Vocabulary

Use this chart for key terms/vocabulary that you struggle to understand.

This information can be transferred to your exam toolkits

Slide53

Now It’s Your Turn! 

Slide54

Outline

Background and motivation Building Expert Learners: Research in Metacognition in Math (STEM)

nstructional approach

for promoting

reflection

Analyzing students’ reflective

writing

Preliminary

data analysis

Slide55

Is There Proof in the Pudding?

Data on Section 1 (MC) and Section 2 (Traditional)

Section 1

Section 2

Exam 1

(averages)

84.13

79.6

Exam

(averages

)

64.33

53.84

Pre-Assessment 13%

14%

Post-Assessment 47%

52%

Growth_ _________________34%_____________________38%_____________

Data Between 2 MC Classes (Class 1 – Andrea’s, Class 2 – Linda’s)

Class

Exam 1

(averages)

84.13

73.5

Exam 2

(averages)

64.33

67.9

Pre-Assessment

16%

Post-Assessment 47% 56%

Growth 34% 40%______________

Slide56

Summary of ResultsNo significant difference in test scores between MC and traditional classes -Time frame

- Data in metacognitive research tells a different story (Suzanne

Brahmia

- Rutgers University)

- To

become an expert learner (in any

discipline) takes

time.

- This

is an ongoing journey – just the beginning!

Consistent monitoring of student learning through

reflective responses

leads to

metacognitive practices

, which eventually lead to becoming

expert learners

. This leads to

higher test scores

Slide57

Assessment-Centered Classroom“Formative assessments – ongoing assessments designed to make students’ thinking visible to both teachers and students – are essential. They permit the teacher to grasp the students’ preconceptions, understand where the students are in the “developmental corridor” from informal to formal thinking, and design instruction accordingly. In the assessment-centered classroom environment, formative assessments help both teachers and students monitor progress.” (Key Findings, NAS

)

Slide58

Shifting GearsFrom technical tools to classroom community…..

Slide59

A Community-Centered Approach“Learning is influenced in fundamental ways by the context in which it takes place. A community-centered approach requires the development of norms for the classroom and school, as well as connections to the outside world, that support core learning values.”(Key Findings, NAS

)

Slide60

Fixed Mindset:

Achievement stems from innate ability Setbacks confirms inferiority

Failure and challenge lead to reduced effort

Growth Mindset:

Ability (including intelligence) is expandable

Failure and challenge are opportunities for growth

Slide61

What Makes a Great Teacher(Mindset – Carol Dweck)

“Great teachers believe in the

growth

of the intellect and talent, and they are fascinated with the process of learning.”

Set high standards for ALL students

(not just one’s who are capable or who are already achieving) and then

give students the tools

to reach them.

“… you must help me to help you. … Success is not coming to you, you must come to it.” (Marva Collins)

reate an atmosphere of trust, not judgement. (Benjamin Bloom)

Slide62

The BoxSara Julin

del of “Think Space”

Slide63

Sara Julin’s Classroom

Focuses on Relationships

- Starts on day 1

Focuses on the “Big Ideas

”

- Starts on Day 1

- Models from Day 1

Promotes Intellectual

amaraderie

- Mistakes – come up to board and show how to get

the

‘wrong

’

answer

- Ask each other questions to reach solution

Alternative Assessment Activities

- Score own papers, reflecting on what they “did” say as opposed to what they “meant” to say.

- Students wear “hat”

(

authority of right or wrong)

- Students engage in internal dialogue at a higher level

- Helps students to value reflective thinking more, since it is valued in the

classroom.

Slide64

In ConclusionAre My Students Really Thinking About Their Thinking?By providing the tools and creating an atmosphere that nurtures inquiry and self-assessment, as well as one that encourages an internal dialogue at a higher level, the students will learn to construct their own understanding…… and then, yes, they will really be thinking about their thinking!

Slide65

References

Andrew Boudreaux Professor of Physics –

WWU

Andrew.Boudreaux@wwu.edu

Sara Julin

Professor of Physics

Whatcom Community College

sjulin@Whatcom.ctc.edu

Linda Hegeberg

Math Instructor

Bellingham Technical College

lhegeberg@btc.edu

Andrea Johnson

Math Instructor

Bellingham Technical College

ajohnson@btc.edu

Slide66

Chapter 2: Key Findings of the National Resource Council’s

How People Learn, available for free download at http://www.nap.edu/catalog/9457/how-people-learn-bridging-research-and-practiceThis is an essential discussion of the research base on MC, and implications for instruction.

Chapter 8: Education and Mathematics,

What’s All the Fuss About Metacognition?

Alan H. Schoenfeld

Campbell

, R. L. (2002).

Jean Piaget's Genetic Epistemology: Appreciation and Critique

Retrieved from the World Wide Web September 21, 2003 from http://hubcap.clemson.edu/~campber/piaget.html

Harley, 1995

Guenther, 1998

Merriam & Caffarella, 1991

http

://