In this section
I am going to discuss the findings of my action research on the effects
of different types of warm-ups on students in the classroom. This
finding will help and determine the usefulness of warm-ups in a
mathematics classroom.
Surveys were
completed after each unit to gather information on what the students
thought about each warm-up before they received their test grades so
that they were not influenced by their grade. I expected the students to
have increased motivation for the games and puzzle units while having
increased comprehension in reviewing the previous lessons material. I
hoped that reviewing previous mathematical concepts would aid in their
comprehension, but I did not know what to expect. In each unit the
question, what are your observations about the beginning of each class
(what happens?, what do you do while homework is getting checked?) was
asked. The students' comments were categorized into four categories.
They were not relating, doing something other than mathematics, working
on the warm-up, and working on mathematics not dealing with the warm-up.
Interesting trends I found when looking at the data are the more and
more warm-ups the students saw the more participation I received.
Along with that
the participation in others areas of mathematics besides the
mathematics in the warm-up decreased as the students' continued to be
expected to work on warm-ups. This follows the research which stated
that as students become more familiar with warm-ups their participation
in them will increase. This is exactly what I found. Also, looking at
the data, previous mathematical topics included in the warm-up have the
least amount of participation from the student's. This could have
happened because of many reasons but I believe the main one would be the
students already understood the review material really well so
therefore did not feel like the needed the review. Through my
observations the students became more familiar with the routine of
warm-ups and therefore their participation increased. Students did not
participate for two main reasons. They either did not know how to do the
mathematics in the warm-up or felt like they had a complete grasp of it
and therefore did not need the extra review and practice.
The next common
question I asked in each of unit's in which a warm-up was offered was
why or why not would you be more motivated to learn if this type of
warm-up was used in class? Again I expected students' motivation to
increase in the games and puzzles unit and decrease in all of the other
units because of the "extra" work the students were asked to do. Answers
were categorized as not relevant, increasing motivation because the
warm-up is helpful, increasing motivation because the warm-up is fun,
neutral, decreasing motivation because of the extra work, and decreasing
motivation because the time could have been used more productively. The
student's responses can be found in . I found that students, when
answering this question, thoroughly enjoyed the unit in which games and
puzzles were used. Outside of that unit it seemed students were
motivated if they thought the warm-up was helpful to them. A trend in
the responses was students are the surveys continued felt very strongly
about the effect of warm-ups on their motivation.
The rest of the
first unit's survey was used as a pre-survey into what the student's
expected from each warm-up and what they believed about warm-ups in
general. Results of the pre-survey can be found in the preceding
sections.
The "warm-ups
reviewing the previous lesson's" survey included the question did you
think going over the previous lesson at the beginning of the class was
beneficial to your understanding? (The warm-ups we started class with).
Students from the pre-survey thought going over the previous lesson's
material at the beginning of the class would be beneficial. After the
unit with warm-ups reviewing the previous lesson the students still were
of that same opinion. The students believed that these warm-ups indeed
aided their comprehension as reflected in their responses. During my
observations on this chapter I found that the students seemed to enjoy
that we spent time reviewing yesterday's lesson. I believe it also aided
in their comprehension because they got to see and try to understand
the information in a new day. I also found that students who believed
they already understood the material were off task for the majority of
the warm-up. Therefore I spent time trying to keep them on task while
working with the other students.
Included in the
warm-ups reviewing the previous lesson's survey was the question which
was more beneficial to your understanding of mathematics? Student
believed that having a warm-up over the previous lesson was more
beneficial than having no warm-up at all. This was the result I was
expecting.
Finally I
looked at the students' assessment over this unit and compared it to
their assessment scores on the first unit which was the unit that did
not include any warm-up. Like I mentioned above I used a paired t test
because the assessment scores were approximately Gaussian because the
Normal Probability Plot was approximately linear. The two-tailed P value
equals 0.6237 which is not statically significant. Also, a 95%
confidence interval of the difference between the mean of no warm-up and
a warm-up for the previous lesson is (-3.88 to 6.31). Since 0 is
included in this mean there was no difference in assessment grades. This
means warm-ups which included review of the previous lesson did not aid
or detract from the students' comprehension of the unit.
The warm-ups
reviewing previous mathematical topics taught in other mathematics
subjects included the question: Did you think going over the previous
lesson at the beginning of the class was beneficial to your
understanding? (The warm-ups we started class with). Students from the
pre-survey thought that this type of warm-up would be helpful for their
understanding but not as helpful reviewing the previous lesson. After
the chapter the students seem to still be of the same opinion they
started with. Most of the student thought that this type of warm-up
aided their comprehension but not as much as the warm-up reviewing the
previous knowledge. 6% strongly disagreed and 13% were neutral on their
reviewing previous mathematical topics warm-up and all agreed or
strongly agreed on the warm-up over the previous lesson. Some of my
observations from this unit were students for all of the warm-ups did
not see the relevancy making it hard to motivate them to work diligently
on it. This type of warm-up cut down on the reviewing during the
teaching part of the lesson because the students for the most part
already understood the previous mathematics included and therefore could
concentrate on the new mathematics. I found this type of warm-up did
not aid so much in the comprehension of the actual lesson but allowed me
to work through the lesson more quickly because we had already reviewed
and therefore the students had less questions during instruction.
Included in the
warm-ups reviewing previous mathematical topics was the question which
was more beneficial to your understanding of mathematics? I found the
result to be what I expected because the students desired to spend more
time on what they viewed as being on the test. Students could not always
find the correlation between the warm-up reviewing previous
mathematical concepts and the day's lesson. This caused them not to see
in some instances the benefits of the warm-up to improving their test
grade. Students did see a direct correlation between the warm-up over
the previous lesson and their test grades. So therefore they desired the
warm-up over the previous lesson the most.
Finally I
looked at the student's assessment over this unit and compared it to
their assessment scores on the first unit which did not include any
warm-ups. As I mentioned above I used a paired t test because the
assessment scores were approximately Gaussian because the Normal
Probability Plot was approximately linear. The two-tailed P value equals
0.7317 which is not statically significant. Also, a 95% confidence
interval of the difference between the mean of no warm-up and a warm-up
reviewing previous mathematical concepts is (-5.3 to 7.4). Since 0 is
included in this mean there was no difference in assessment grades.
Which means warm-ups over previous mathematical concepts did not
positively or negatively affect a student's comprehension.
Warm-ups which
included games and Sudoku puzzles by my observations were the warm-ups
that the students' enjoyed the most. Warm-ups over games and puzzles
also included the question did: you think going over the previous lesson
at the beginning of the class was beneficial to your understanding?
(The warm-ups we started class with). Students did not know if games and
puzzles would prepare them for the day's lesson because their opinions
were split between strongly agree, agree, and strongly disagree for the
most part. After this unit the students believed that games and puzzles
warm-ups were beneficial to their learning. This opinion was similar to
what they thought for all of the units before this. 88% of the students
believed that games and puzzles were beneficial to their understanding
of this unit. My observations for this unit's warm-ups were very
surprising to me. Some of the students were incapable of playing the
addition and multiplication games without the use of their calculator.
Therefore from my observations I believe for some student's the games
were beneficial in the review of basic addition and multiplication facts
but for other students the games only affected their motivation and not
their comprehension. The Sudoku games I believe aided the students in
activating their brain for the day's so therefore aided comprehension in
this unit.
Included in the
warm-ups which involved games and puzzles was the question which was
more beneficial to your understanding of mathematics? I expected student
to remain of the opinion that reviewing the previous lesson was the
most beneficial warm-up in aiding their comprehension. I found this to
be the case. I also found that some students believed that games and
puzzles were the most beneficial which was a very surprising result.
Finally I
looked at the student's assessment over this unit and compared it to
their assessment scores on the first unit which was the unit that did
not include any warm-up. The two-tailed P value equals 0.0467 which is
statically significant. Also, a 95% confidence interval of the
difference between the mean of no warm-up and a warm-up reviewing
previous mathematical concepts is (0.08 to 9.81). Since 0 is included in
the 95% confidence interval we can conclude that warm-ups which
included games and puzzles were detrimental to the student
understanding.
The final item
which was asked in the surveys was the effect of each of the warm-ups on
students' motivation in a mathematics classroom. Warm-up over the
previous lesson's material and warm-ups involving games and puzzles both
had positive responses from the students. This can be found in table 16
and 18 respectively. Many students were neutral about review warm-ups
and their effect on motivation (59%) but almost none (6%) found it
detrimental to their understanding. Many more students had an opinion
about games and puzzles and their effect on their motivation. 70% found
games and puzzle warm-ups to increase their motivation and 44% found
games and puzzle warm-ups to decrease their motivation. The only warm-up
in which the students' motivation was negatively affected by the
warm-up was the unit involving warm-ups over previous mathematical
knowledge. Again, many of the students were neutral (44%) but 51% found
it detrimental and 6% found it to be helpful.
- Students' achievement was not affected by warm-ups.
- Students' motivation was positively influenced by warm-ups.
- I found many benefits of warm-ups such as setting up the classroom while the students were engaged in learning.
- As warm-ups were increasingly used student's enjoyed them more and understood the expectations of them.
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