Active learningRevising class materials based on

formal and informal assessment of

students’ learning

Malgorzata Marciniak

LaGuardia Community College

CUNY IPDM, March 31, 2017

Abstract

Active learning is described as a process wherestudents engage actively in problem solving thatpromotes analysis and synthesis of the classtopics. In the light of recent findings andpublications, the active learning style of teachingis more efficient in STEM fields than the traditionallecturing style, where students listen passively.

Outline

The presentation will include sample worksheetsand description of methods of implementingthem in the classroom. The most important aspectof this study presents motivations and methods ofrevising the worksheets based on formal andinformal assessment of students’ learning.

Outline

My talk from last year was about assessment ofclass worksheets, but I presented mainly theworksheets. This year I will present mainly theassessment. Since the prompts in the assessmentaddress not only class worksheets, but all classmodules, I will present the assessment first andthen explain how it helped with designing andredesigning the class worksheets.

Motivation

Faculty who teach developmental math classesoften complain about students’ attitudes, mathanxiety, and poor study skills. Since the first twoissues have their roots deep within students’ pastand may be difficult to address in a multiculturaland heterogeneous classroom. I decided to focusmy first assessment on study skills.

Motivation

Believing that this quantitative as well asqualitative aspect of students’ accomplishmentswill create a topic for a sequence of reflectiveassignments that will support students’ success.At the same time, I hope that focusing on self-observation of study skills will distract students formsubconsciously feeding their anxiety.

Justification

In my understanding, anxiety can be formedwhen students repeatedly doubt their skills or givethemselves negative feedback. Unfortunately, thisis often the case when they study mathematics,since even a small distraction can causemathematical errors. Repetitive negativefeedback can then become a habit and disruptstudents’ long term learning.

Justification

An assessment that immediately follows theprocess of learning may modify any habit bygenerating another one that is more beneficialand certainly more encouraging. Thus instead ofrepeating in their heads “I am so terrible in math”students will make a list of topics they learned,then make a list of topics that they did not learnwell, and at the end make plans for reviewing.

Implementation

Study skills is a vast topic; thus narrowing it may be a goodidea. It is strongly suggested in literature that the firstassessment prepared by an inexperienced author shouldbe as simple as possible. Following this suggestion, Idecided to focus on immediate reflections after a lecture(class activity, etc.). Students are asked three basicquestions about what they learned, what they did notlearn, and what they should review. This assessment issupposed to direct students’ attention to the process oflearning; in particular, to help students find what parts ofthe instruction are unclear and must be revisited.

Implementation

The entire assignment fit on an index card and took onlyfew minutes from class time. I wanted it to be a naturalextension of the lecture, and not a new class module. Iwanted the assessment to be mathematical and focusedon the material that was just presented in class.

Choice of lesson: During previous assessment, manystudents identified fractions to be the most difficult topic.Thus, I decided to use that topic for the next assessmenthoping that the distinction between studentsunderstanding and misunderstanding will be clear.

Assessment

� What did you learn today during class? This is positive

thinking, and most students will feel good answering it, and this is the right place for

this question to ease into the next one.

� What parts of the presentation were less clearthan others? Which may be easily forgotten, or caused some confusion in

the past? These questions carry negative thinking and may be painful for some

students.

� What should you review? This question searches for solutions to

issues discovered in question 2, easing the negative feelings from the previous

question.

Assessment

The feeling of energy in this assessment is presented as follows:uplifting, down-falling and again uplifting. This design helpsstudents remain in balance with their energy. But it increasestheir awareness of what they are lacking. RIGHT BEFORE ANDDURING THE ASSESSMENT I emphasized the importance of thiswork, asked for complete English sentences and clear writing.RIGHT AFTER AND DURING THE FOLLOW UP I thanked studentsfor doing a good job with writing. Again, I indicated that Igained significant information from their work. DURING THEFOLLOW UP I pointed out how students’ writing changed myview of their learning.

Results and Benefits

The intention of this assessment is to draw students’

attention towards their state of knowledge after the

lesson. In particular, the celebrated “know what you don’t

know” is hidden here among two innocently looking

questions.

Students answers contain particular mathematical topics

and skills. Students use mathematical terminology in

complete English sentences and at the same time are

revisiting recent topics in their minds without getting into

details of mathematical procedures. They only revisit “the

feeling” of being more fluent or less fluent.

Results and Benefits

I observed in class that after this assessment wasprovided in writing and repeated informally inspeech, students began to communicatewillingly and clearly about what they do notunderstand. It helped me direct the lecture intothe topics that are particularly challenging for allstudents, not only those that speak up about it.

Summary

The assessment helped me with revisions of the class

assignments and can’t resist an impression that having it in

class significantly improved the energy of the relationship

among student and myself. It convinced students that I do

care not only about the subject but about them. The

assessment improved communication among students

and myself, since students began pointing out unclear

aspects of the presentation willingly and precisely.

MAT99 FRACTIONS

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4. Use prime factorization to simplify to

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NAME______________________

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8. Find the LCM of the given

numbers:

a) LCM(12,20)=

b) LCM(15,35)=

c) LCM(36,48)=

9. Which fraction is greater?

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what did you learn today (provide specific topics)

1 adding and subtracting fractions

2 how to add and subtract fractions

3 adding and subtracting fractions

4 how to add fractions

5 reciprocals

6 adding fractions

7 how to convert improper fractions to mixed numbers

8 easier way to simplify fractions

9 I learned how to deal with fractions

10 simplify fractions, add and subtract

11 multiply and divide fractions

12 learned how to solve some kind of fraction as +- x

13 divide fractions, addition fractions, subtract fraction, mixed number

14 how to solve few fractions

15 how to find LCM when adding and subtracting fractions

16 I learned that I remember simplifying fractions

17 reciprocal

18 fractions, LCM

19 I learned that my teacher doesn't really explain the equation or how to solve them

20 when dividing fractions, we need to keep, change, and flip

21 different way to solve fractions

22 fractions, we don't really focus on one topic

what was difficult (provide specific topics)

converting improper fractions to mixed numbers

nothing

LCM

different denominators and signs

converting improper fractions to mixed numbers

subtracting fractions

remembering the formulas for /+-x, knowing when to do what

Finding the LCM

substract or add fractions withdifferent denominators

how to multiply with whole numbers

adding fraction was kind of difficult

everythinh was easy

staying focused

I got stuck when adding and subtractiong fractions with different denominators

adding and subtracting fractions

not difficult, just takes practice

convert improper to mixed, addition and subtraction

figure out the correct formulas to use for a problem

adding and subtracting fractions

adding and subtraction

What would you like to review (be as specific as possible)

review converting improper fractions to mixed numbers

more of adding and subtracting fractions

LCM

review subtracting and adding fractions

everything to get better knowledge

I will review what I need help on

full fraction practice

nothing

which fractions are greater or less than others

nothing in spesific

everything was clear

I do not teed to review anything

everything was clear to me

rules of operations

nothing

fractions

we can go over the topic again

adding and subtracting fractions

adding and subtraction

review everything to pass this class

MAT99 FRACTIONS

1. Simplify the following proper fractions:

a) −��

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b) ��

��=

2. Convert the improper fractions to

mixed numbers:

a) −��

�=

b) ��

�=

3. Convert mixed numbers to improper

fractions

a) 3�

=

b) −2�

�=

4. Use prime factorization to simplify to

lowest terms

a) −� �

����=

b) ���

�� =

NAME______________________

5. Multiply the following fractions,

simplify your answers to lowest terms:

a) �

�∙��

�=

b) �

��∙��

�=

c) �

��∙���

�=

6. Find the reciprocal of the given fraction

a) Reciprocal of −�

�� is _______

b) Reciprocal of �

�� is _______

7. Perform division and simply your

answer

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�÷ 2 =

b) 11 ÷��

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c) ��

�÷

��

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d) �

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��

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e) ��

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8. Find the LCM of the given

numbers:

a) LCM(12,20)=

b) LCM(15,35)=

c) LCM(36,48)=

9. Which fraction is greater?

Circle the correct sign

a) �

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b) −�

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c) −�

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d) �

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10. Add or subtract the fractions:

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