Child Study: Effective Diagnostic Assessment of Place Value

This child study report delves into the critical concept of place value within elementary education, emphasizing the importance of diagnostic assessments to gauge student understanding and inform instruction. The report details the rationale behind effective diagnostic assessments, highlighting their role in understanding students' readiness, identifying misconceptions, and tailoring teaching strategies to meet diverse learning needs. It then explores the core aspects of place value, including number recognition, counting, addition, subtraction, and grouping, with an emphasis on the base-ten system. The report discusses various teaching methods and manipulatives, such as ten frames, 100 charts, and base-ten blocks, to visually represent and reinforce place value concepts. It also covers the significance of understanding place value for performing complex mathematical operations. Finally, the report examines the benefits of learning place value and the different modes of activities and manipulatives used to develop children's understanding.

Running head: CHILD STUDY 1
Child study
Name
Institution

CHILD STUDY 2
Tables of figures
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CHILD STUDY 3
Rationale for Effective Diagnostic Assessment
Research has indicated that performing a diagnostic assessment is extremely important
especially at the beginning of a given unit or academic year (Ontario, 2013). An interview
conducted with one elementary school teacher revealed that performing this activity enables the
teacher to gain a proper understanding of the student before the learning session starts. This
involves assessing a student’s readiness to receive information and skills that have been outlined
in the curriculum expectations. It aids in a comprehension of the misconceptions that the students
may have regarding a given topic. After gaining this information, the teacher is able to make
planning decisions that are informed and based on the feedback received concerning the students.
Another interview with another teacher showed that due to the different learning needs
identified in the students, the teacher is able to adjust accordingly and ensure that all the students
will benefit to the maximum. Therefore, the teacher’s professional judgement is the foundation
upon which a diagnostic assessment lies (Walkgroove, 2015). This ability of the teacher to
choose the assessment tools that are most appropriate as well as determine how frequently and
on what times to administrate, enables data collected to be accurate and sufficient for making
judgements in regards to the students during the period of the learning cycle.
This process of carrying out a diagnostic assessment aids in the achievement of the major
priorities that have been outlined by the ministry of education. These include; reduction of gaps
in the achievements by students and high achievement levels by the all students (Walkgroove,
2015).

CHILD STUDY 4
Child Study
Part A
Place value refers to the value that is assigned to every place in a given number under the
foundation of the system of the base of the number (National Center on Intensive Intervention,
2015). There are different aspects that should be used with students to ensure that they gain a
complete understanding of place values. These include; learning the names of the numbers and
using them to count. This brings in a familiarity due to continuous practice by the students in
reading and writing the numbers. This first step does not require the incorporation of place value,
it just involves getting to know the numbers (Pender et al., 2011).
The students are able to identify the things that have been grouped together either by
counting or by making use of patterns. Students therefore learn the names of different numbers
then count them to understand what each number name represents. This enables the students to
know for instance, that all teen values have a one in front of them (Fuata'i, 2008). They also get
to know that all the twenty and thirty numbers have a two and three in front of them respectively.
It is important for teachers and parents to teach their students how they should count and ensure
that they practice with different objects.
Another aspect involves the addition and subtraction of the numbers. This involves
simple calculations. These are calculations that can be easily learned by children and can be
performed fairly quickly with practice. It is very important for children to practice sufficiently in
order for them to become facile with addition of single digit numbers that have sums as high as
ten to eighteen (Richardon & Portman, 2014). Moreover, they should also practice enough in
order to be in a position to perform subtractions of single digit numbers that provide solutions of
single digit answers that involve minuends that range between ten and eighteen. This is

CHILD STUDY 5
important because whenever you regroup for subtraction, there is always a need to subtract
numbers between ten and eighteen. It is important for children to gain enough practice in this
field so that this sort of subtraction becomes easy and automatic for them.
Grouping is another concept that students are taught that is very important in enhancing a
better understanding of place values. This is because grouping items into groups of say, twos,
threes, five, or ten basically involves multiplication of the items per group and the number of
groups to gain the total amounts (Iksan & Effandi, 2009). Grouping items by tens is a prelude to
comprehending the aspects of arithmetic that is based on tens.
The National Council of Mathematics teachers provides that children who are in
kindergarten up to the second grade should be taught place value and the base ten number system
by the use of different models (Ministry of education, 2012). This will ensure that when children
go to the following grades they have a proper understanding of the structure of place value and
the base ten system. This in turn ensures that they are able to compare decimals and whole
numbers.
One way of teaching is by the use of the numeration system. This is a method of learning
that uses symbols to represent numbers. Every number needs to be represented by the use of a
different symbol to avoid confusion on what the intended number was. The numeration system
for place value has very few digits which are then repeated in the creation of larger numbers. The
base of a system refers to the number of times that one can count without repeating a digit
(Garlikov, 2017). The number of digits that are contained in the system of place value
numeration is similar to the base and it has to have a place holder. The value of any given
number is therefore determined by its position. The base number thus shows how the numbers
have been grouped (Mabott & Bisanz, 2008).

CHILD STUDY 6
Universally, the base ten numeration system is what is used. It has been said that this is
because humans have ten fingers which are used to count. This numeration system has ten digits.
These are the numbers from zero to nine. Zero is used to serve as a placeholder. It is sued to hold
a position when there is no other number to be placed in that position (Richardon & Portman,
2014). Using this system, the value of any numeral is identified by multiplication.
This begins from the right. Every single position to the right of the decimal point is 1/10th
position towards the right. Incidentally, for the number 520.9, the two in the second position to
the left of the decimal point is (10 x 2, meaning it has a value of 20. Additionally, in the number
520.67, the seven which is in the second positon towards the right of the decimal point has a
value of (7/100) which is 0.07 (Hiebert, 2012). The principle that has been employed here is
referred to as the multiplicative principle. The numbers that have been determined using the base
ten system are added together to provide the total value of the number by making use of the
additive principle. That is; (100 x 5) +(10 x 6) +(1 x 5) = 564.
A lack of proper understanding of the base ten system of numbers can make students fail
to develop counting strategies that are sophisticated. This may cause students to count by one as
opposed to counting by groups of thousands, hundreds, or tens. It may also make complex
mathematics such as traditional algorithm that involves long division very much more difficult
for the students (Garlikov, 2017). For instance, if a student fails to grasp that 4 in 456 represents
400, the student can encounter many different problems in advanced mathematics.
Teaching Place Values
One way that teachers use to teach place values and base ten number systems is by the
use of ten frames. This is a method that enables the students to visually see and keep track of
what makes a ten and then view what remains.

CHILD STUDY 7
Figure 1
In the above figure students can see that there exists two groups of tens and there are
three ones. This aids students in addition and subtraction. This is because an increase of another
tens column will cause the number to increase to 33. Conversely, removal of one tens frame will
lead to a remainder of 13 counters.
Another method that can help students to have a better understanding of the base ten
system is by the use of a 100 chart. This is shown below.
Figure 2

CHILD STUDY 8
This chart contains of a flat block for the one hundred value, a long block for the tens
value and a unit for the ones. By making use of the base-ten blocks, students can be able to see
the grouping visually. Form the base ten blocks above, it is easy to see that there is one hundred
(100), four tens (40), and seven ones (7) (Lee, 2008). It is also clear that the final number (147)
is formed by addition of all the group values together. Therefore, base ten blocks help students to
comprehend the concepts of composing and decomposing (PDST, 2016). Composing involves
carrying and is used in addition while decomposing involves borrowing and is used in
subtraction.
Composing occurs because there exists an over-abundance more than ten in one position.
This brings in the need to trade the groups of tens for one unit of the next grouping order in a
correspondence of one to one (Boucher, 2012). Incidentally, if Jane had nine cakes and then
received six more, she would trade the ones that are now ten for one block position of ten, as
shown below;
Figure 3
This is just like in traditional algorithm where you put one over a spot of tens.

CHILD STUDY 9
Conversely, if jane had 15 cakes and gave 7 to Ann, she would have to break the tens into
ones so as to give Ann 7 cakes. This is just like borrowing in traditional algorithm. It is shown
below.
Figure 4
Students receive practice and exposure with the base ten system by making use of the
national library of virtual manipulatives. This assists students in addition and subtraction practice
by making use of the virtual base ten blocks and it also aids in developing their comprehension
of the decimal system.
A lot of the frustration and confusion that students face in higher elementary grades in
relation to Math is due to a lack of proper comprehension of the base ten system. If students were
provided with proper exposure of manipulatives in base ten in lower grades, the low
understanding levels can be reduced in higher grades.
Importance of Learning Place Values
Learning about place value is important to children because it enables them to determine
the value of different numbers. Since the number system only contains values from zero to nine,
place value is the tool that aids in showing numbers that are greater than nine. Having a proper

CHILD STUDY 10
understanding of place value also enables students to know how to carry out addition and
subtraction of numbers that involve carrying and borrowing respectively (Omari & Chen, 2016).
When students understand what every part of a whole number represents, they are also able to
break numbers apart, reform those numbers, and understand better how multiplication and
divisions work.
Activities and Manipulatives Used in Learning Place Values
There are three modes of activities that are used in developing children’s understanding
of place value and the base ten system (Leslie, 2017). These include; the iconic mode that uses
images, the symbolic mode that incorporates symbols and language, and the enactive mode that
involves actions. Manipulatives refer to practical apparatus used in the place value learning
process. These include; place value counters, there are sticks used in class that have been cut into
ten sections that are all equal, place value cards, digit cards, hundred squares, dominoes, and dice
among others. These manipulatives are accompanied by actions on the part of the students as
they practice on how to use them. Symbolic mode of learning is incorporated by the teachers in
theory as they teach the students. For instance, they may use a certain letter to refer to a certain
number without repetition. Finally, images used in learning place value are mainly in the use of
charts that have different images for different place values.
Difficulties Encountered in Learning Place Values
The main difficulties inherent with learning about place values for students include; lack
of the ability to recognize 3,7, and 10 as countable or composite unite (Songs, 2014). This is
depicted mainly by students being unable to count collections that are large in an efficient
manner. Students may also fail to recognize the structural foundation upon which two digit
numbers are recorded. Incidentally, a student may read 87 as ‘eighty-seven’ but thinks of the

CHILD STUDY 11
eight and the seven as 80 and 4. However, the student may not recognize the importance of the 8
as a count of tens though they may say how many tens have been placed in the tens place.
Finally, the students may fail to have a sense of numbers that are greater than ten.
Misconceptions Among Students
Some of the common misconceptions that children hold in regards to place value include;
some students believe that a number that has three digits must be bigger than the number that has
two digits. In such an incidence, a student might believe that 6.89 is bigger than 8.8. some
students also have a belief that whenever two numbers are multiplied, the result is greater than
both original numbers (Partin, 2012). Moreover, some believe that to multiply a number by 10,
you just need to add a zero at the end.
Conceptual Understanding of Place Value
Conceptual understanding therefore means that students are able to identify the key ideas
by receiving assistance to draw conclusions about them, and they are also able to gain the
heuristic value associated with these ideas (Wiggins, 2014). This means that the students are in a
position to use these ideas strategically in problem solving-mainly with problems that are not
routine-and they are able to avoid having common misunderstandings (Van de Walle, 2007).
This is better as opposed to simply relying to procedures whereby the students simply know the
definitions and rules relating to the issue.

CHILD STUDY 12
Part B
Summary of Diagnostic Interview Conducted with Boris.
Boris is a young boy from a school in the neighborhood. His parents accepted that he can
be involved in this study. This activity involves an evaluation of his level of understanding place
values and how well he can apply the concepts when working with different mathematical
operations appropriate to his age. An initial teaching plan was developed that was continually
expended as Boris’ level of knowledge increased.
The diagnostic interview that was conducted with him indicated that he was good at
naming the place values of numbers but he did not understand conceptually what the place
values meant. An oral test further revealed that he was not very well able to identify which
decimal system numbers were larger than others. Incidentally, when I asked him which number
is larger between 0.015 and 0.05, he argued that 0.015 was larger because it had 15 while the
other one had only 5.
Another concept that Boris was struggling with was the process of decomposing. In his
calculations, during his written test, whenever a question required him to perform a composition
activity, he had no difficulty. However, when he was required to perform a subtraction
calculation that involved borrowing, he became frustrated because he was unable to continue
with the calculation after that point. Moreover, when he was required to organize numbers either
in ascending or descending order he faced difficulties if the numbers consisted of a fraction. For
instance, when provided with; 0.5, 1/3, 0.99 and required to arrange the numbers from the
largest, he was unable to come up with the answer. Finally, he was unable to form parts from the
whole number or use the place values of the numbers to form one complete number. For