Journal 4
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Jan 9, 2024
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Uploaded by MatePorcupine4041
Nathalie Fernanda Cuevas
EDST 2005
Journal 4: Computational Procedures
After reading Chapter 4 in classroom discussions, answer the following questions. Remember:
you don’t have to use evidence – I want to hear your voice, ideas, opinions…….
1.
Explain the two categories of conceptual procedures in your own words.
Within the classroom, teachers educate students on how to solve problems with
speed and accuracy to move onto the next question quickly. There are two categories of
conceptual procedures, which are computational algorithms and strategies.
Computational Algorithms are steps that is taught in class on how to solve a problem as
the butterfly method or Keep, Switch, Flip when dividing fractions. These are steps that
the students memorize and repeat without having a strong conceptual understanding of
the reason why the students must do these steps. In elementary school, I remember
memorizing and repeating steps to solve problems and move one. The focus in my math
classes were to get the most correct answers possible and achieve the highest grade. The
focus of math conceptual understanding was obsolete and as a student intern, I am happy
to see a shift from math algorithms to strategies. However, teachers presently
continuously to enforce the algorithm after teaching strategies. Conceptual strategies are
students using their previous understandings to manipulate the numbers to effectively
solve the problem. I understand conceptual strategies as the use of number sense because
there is no definite strategy to solve a problem. The students can use a variety of
strategies such as making a ten, counting on, and partitioning to find the answer. With
strategies, the students are not learning steps but are working to use mental math and
critical reasoning to get to the answer. Both conceptual procedures are important in the
classroom because they have developed the essence of education and the need for change.
2.
Suggestion 1: Use Whole Class Discussion to Teach Computational Procedures.
a.
Explain this suggestion in your own words.
The use of whole class discussion to teach computational procedures is
essential because students explore together the ins and outs of mathematical
properties. By having a strong understanding of conceptual procedures, students
will be adept in using these procedures to create strategies for speed and accuracy.
Within the discussion, the students are working together to understand the why of
the mathematical properties being talked about. Therefore, the teacher facilitates
the discussion by aligning the conversation with the instructional goals to include
all students and learn how to participate. As a future teacher, I will use whole
group discussion to enable learning in the classroom because I can easily assess
my students and their knowledge. The opportunity to talk about math and using
math language will reinforce the importance of math, critical thinking, and
establishing a strong foundation for future math concepts.
Watch video clip 4B and answer the following questions:
i.
When Ms. Powers asks students to turn and talk with their partners about
the next step in the computational procedure, many immediately call out
“minus two!” yet some students in the clip struggle to explain why this
step makes sense. What might this indicate about their understanding of
subtraction and decomposition?
In the video, all students understood the first part of
decomposition, where you had to subtract six to get to twenty. In the
second part of decomposition, some students understood that the next step
must be to subtract two because six plus two is eight. Other students do
not understand as quickly because it means that they do not have a strong
understanding of addition and its inverse relationship with subtraction.
The students are confused with the strategy of decomposition where 8 was
broken down into two number when added together will be eight.
Therefore, this indicates that the students need a stronger reinforcement in
understanding the meaning of decomposition to subtract single digits from
double digits. Their weakness in decomposition as well demonstrates their
limited understanding in place value because it is used in regrouping for
subtraction. Place value is important for subtraction because students
understand the why beyond memorization and repetition.
ii.
Pick a student to watch throughout the video clip. What clues are given
that enable you to decide if he or she understands the strategy or is
confused by the strategy?
The student that I picked was Liam because he demonstrates a lack
of understanding with the strategy being taught. He tried to repeat and
understand Teddy’s response, but it was difficult for him, which lead him
to answer that it was an easier way to solve the problem. Liam is correct
because using decomposition is an easier method to solve subtraction
problems. On the other hand, the teacher made Liam repeat what Teddy
said, which does not prove of true understanding of the strategy. He had a
hesitant face throughout his conversation with the teacher and the students
because he did not know if he was right or wrong. Liam did try his best to
understand, but he needs more practice with decomposition. Additionally,
the teacher in this conversation did not dig for knowledge but accepted
that Liam could repeat what Teddy said. Therefore, she would not know if
Liam needed help strengthening his understanding. As a student, I have
been in Liam’s position, and I can feel his nervousness through his
expressions. As a future teacher, I would have probed for deeper
understanding and make him understand that it is normal to not know
everything.
3.
Suggestion 2: Use Whole Class Discussion to Connect Computational Procedures to
Concepts.
a.
Explain this suggestion in your own words.
The comprehending the connection between computational procedures
and concepts is essential for providing meaning for the students. Consequently,
the students can develop automaticity quickly because they understand that math
is not a set of meaningless rules and steps but are woven together. Using whole
class discussion, the teacher can informally measure the students’ knowledge and
assess their weakness to create a strong conceptual understanding. For conceptual
understanding to develop, the students to understand the concept and know the
procedure, which promotes a deeper understanding of the mathematical
properties. This connection is needed for the students not to be codependent on
rote memorization to understand math.
b.
Watch video clip 4C and answer the following questions:
i.
As Ms. Powers talks with Bryn, she presses him for reasoning to help him
clarify his thinking. What do we learn about Bryn’s understanding of
decomposition and subtraction because of Ms. Power’s questions?
We learned about Bryn’s understanding of decomposition and
subtraction is strong because of Ms. Power’s questions. Bryn clarifies his
answer by explaining what the easier number is and went more in depth on
how the problem was solved. He explained how powers and multiples of
tens are friendly numbers because they are easy to subtract and add from.
With the questions, Bryn went in depth with his vocabulary and what they
meant for everyone in the classroom to understand. Therefore, Bryn has a
strong understanding of subtraction and its relationship with addition.
Consequently, he assimilated the concept of place value as we can see
with how quickly he can separate and subtract the ones and tens.
ii.
When does Ms. Powers use turn and talk? Which of the four steps toward
productive talk does this talk move support in this discussion?
Ms. Powers uses turn and talk after she asks the class a complex
question to discuss and break down together. She pushes her students to
work together to understand each part of the strategy; she only facilitates
the conversation. Then, Ms. Powers brings the class to answer the question
after they have practice what they wanted to say and how they will say it
to everyone. The students are thinking on their own, which helps them to
deepen their knowledge and engage with other’s reasoning. Turn and Talk
supports the third step toward productive talk, which is helping students
deepen their reasoning. This makes the class discussion academically
productive because Ms. Powers is pressing the students for reasoning and
evidence. She is motivating the students to work together and feel that
their ideas are important for the discussion. Therefore, the students are
applying their reasoning to the ideas of others by agreeing and disagreeing
to create the connection between conceptual and procedural knowledge.
4.
Suggestion 3:
Use Whole Class Discussion to Build Number Sense Skills.
a.
Explain this suggestion in your own words.
Whole class discussion is used to build number sense skills by learning
how to use and manipulate computational procedures for different problems.
Students together are learning that computational procedures do not provide the
one size fits all model to solve problems. On the other hand, computational
procedures do help students develop number sense by making decisions on what
to do. The format of whole class discussion is necessary because all the students
are working at the same pace with the same information. The synthesis of the
concept and development of number sense needs to be fostered together for
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students to see that understanding math takes time. Teaching number sense must
be deliberate for the students to see how they can develop their math abilities.
b.
Read through example 4.3.2 and then watch video clip 4D and answer the
following questions:
i.
What fraction skills and strategies do students use to complete this fraction
number line task?
The students work together by creating a number line from 0 to 1, then the
teacher separates them into groups to solve the problem. Using
benchmarks, the students place fractions to finally chose 7/8
th
as the
location marked A on the number line.The decision for 7/8
th
was made by
partitioning the number line and understanding how 7/8
th
is 1/8
th
away
from 1. Even though 7/8
th
does not have an equivalent fraction in fourths,
it continues to fit on the number line when partitioned in eights. Another
way to solve this problem was using equivalent fractions, where the
students turned the fractions into eights. The students knew that fourths
can be converted into eighths by multiplying the denominator and
numerator by two. The students have strong sense in ordering fractions
because of their applied strategy of place value.
ii.
Mrs. Rowan calls on Jaehun to repeat Milo’s explanation of how he
converted seven-eighths to a percent. Compare Jaehun’s repetition with
Milo’s original explanation. What do you notice? How might Jaehun’s
repetition help other students make sense of Milo’s thinking?
Milo converted the fraction into percents because it was easier for him to
divide then to figure out the ordering of the fractions. Milo was solving the
question with speed and accuracy, where he understood that fractions and
percentages have the same quantity. On the other hand, his response was a
bit confusing to follow through because of the way he worded his
thoughts. Therefore, Jaehun’s repetition of Milo’s original explanation
demonstrates that she has truly synthesized how to order fractions and
solve the problem. She used 3/4
th
as her fraction to figure out the location
marked A on the number line. When you triple the fraction, she knew that
it will between 7/8
th
and 3/5
th
. She measured the distance between the
fourths, and it made Milo’s explanation more understandable by working
with fractions that students are comfortable. Jaehun easily converted the
fraction into percentage, which lead her to easily figure out the answer by
subtracting from 100%. Jaehun did not repeat Milo’s answer but provided
her own analysis of the problem and how she was able to solve it.