Upload
hoangkhue
View
217
Download
1
Embed Size (px)
Citation preview
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
1. Simplify the following proper fractions:
a) −��
��=
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
a) ��
�÷ 2 =
b) 11 ÷��
�=
c) ��
�÷
��
�=
d) �
��÷
��
�=
e) ��
��÷
���
�=
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) �
�><
�
�
b) −�
�>< −
�
�
c) −�
�>< −
�
�
d) �
�><
�
�
10. Add or subtract the fractions:
a) �
��+
��=
b) −�
+
�
=
c) −�
�−
�
�=
d) 1 +��
�=
e) −2 +�
�=
f) −2 −
�=
g) �
�+
�
=
h) −�
+
�
�=
i) −�
�−
�
�=
j) �
��−
�
�=
k) −�
��+
�
�=
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) −��
��=
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
a) ��
�÷ 2 =
b) 11 ÷��
�=
c) ��
�÷
��
�=
d) �
��÷
��
�=
e) ��
��÷
���
�=
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) �
�><
�
�
b) −�
�>< −
�
�
c) −�
�>< −
�
�
d) �
�><
�
�
10. Add or subtract the fractions:
a) �
��+
��=
b) −�
+
�
=
c) −�
�−
�
�=
d) 1 +��
�=
e) −2 +�
�=
f) −2 −
�=
g) �
�+
�
=
h) −�
+
�
�=
i) −�
�−
�
�=
j) �
��−
�
�=
k) −�
��+
�
�=