This article, “Latent class analysis of children with math difficulties and/or math learning disabilities: Are there cognitive differences?”, was co-written by H. Lee Swanson, Andres F. Olide, and Jennifer E. Kong. It was published in the Journal of Educational Psychology in October 2018. The focus of this article was on the study of children with math difficulties (MD) as well as math learning disabilities (MLD). This article had two main questions, the first being if there is a hidden class of children at risk for MD and MLD and if that classification can be recognized within a diverse sampling of students when their performance in reading, intelligence, as well as math is measured and incorporated in this investigation. The second question is if cognitive measures will be able to foresee if a child will be a part of these latent classes of learners. An analysis was done on 447 children in grade three, as well as “at-risk children” in grades two through five using three specific models. This study produced four important results. One of these which included finding a distinct latent class of children with either MD of MLD when cutting of scores at respective percentiles. Secondly, testing produced a high level of probability of finding children who have MD or MLD with reading problems while also having a underlying class of low problem solvers with average reading and calculation scores. Also, they discovered children defined as MD but not MLD produced high-level “effect sizes” on reading, but not cognitive measures. Finally, it was found that the understanding of problem-solving component processes, estimation, and the most important component of working memory were both distinctive and significant within study-classified MD and MLD students.
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The research problem, in this case, was that a considerable number of children in school displayed characteristics of MD, with estimations of this fraction being between 6.4 and ten percent. This is particularly trouble-some knowing that math skills have been shown to have a substantial impact on being employable. The purpose of this study was to identify if there was a latent class of children with either math difficulties (MD) or math learning disabilities (MLD) as well as to see if there were ways to predict if incoming children would belong in either of these categories. The hypothesis of this study was not stated clearly, instead, I assumed they hypothesized that this hidden class of students would be identifiable and that there were ways to determine if children were at risk of belonging to either of these two camps. My critique of this research problem is that the problem is clearly stated, as well and the purpose of this study. However, the purpose was stated time and time again in different approaches which make it difficult to understand the exact reason(s) behind this purpose. Their hypothesis was not clearly stated either, instead, they listed previous studies and evidence that can make the reader believe they will be able to find these latent MD and MLD groups of students and be able to discover a way to identify markers students may have to pre-categorize them into either camp.
This study included a multitude of sources cited properly and placed appropriately within the paper. These sources dates range from 1976 to 2016 which is understandable seeing this was first submitted February of 2017. This paper also included varying viewpoints from respected researchers and opposing evidence from different studies whose emission was like that of their study as well as using this information to expand upon their research. I could not find any evidence of bias or perspectives that would be inappropriate in an empirical research article.
The parent population of this study was children from grade three drawn from a longitudinal study that also included “at-risk children” in both grade two through grade five. The reason as to why third graders were chosen was due to it having the largest number of children and the focus of classroom instruction had both math word problems as well as calculations. The total sample consisted of 447 children in the third grade of which there were 222 males 225 females. These children selected from six Southwest public schools. The sample consisted of 199 Caucasians, 133 Hispanics, twenty African Americans, twenty-three Asians, twenty-four children who were identified as Native American or Vietnamese and forty children showed mixed ethnicity. The sample was primarily low to middle socioeconomic status.
Ten graduate students who were trained in test administration tested all participants in their schools. There was a group testing session as well as an individual testing session. During the group testing session, data was acquired from the problem-solving process (components) booklets, Test of Reading Comprehension, Test of Mathematical Ability, and the Visual Matrix task. The residual tests were given separately. Fluid intelligence was assessed by administering the Colored Progressive Matrices test which was measured numerically. Calculation and Problem-Solving Skills were assessed using the arithmetic computation subtest for the Wide Range Achievement Test-Third Edition and the numerical operations subtest for the Wechsler Individual Achievement Test which was measured numerically. Word problem-solving accuracy was evaluated using four measures: The Story Problem subtest of the Test of Math Ability, The Story Problem-Solving subtest from the Comprehensive Mathematical Abilities, The KeyMath Revised Diagnostic, the Wechsler Intelligence Scale for Children, Third Edition. Reading comprehension was assessed by the Passage Comprehension subtest from the Test of Reading Comprehension-Third and word recognition was assessed by the reading measure decoding subtest of the Wide Range Achievement Test, third edition. Cognitive ability was measured for determining working memory included a phonological loop, central executive and visual-spatial sketchpad. Other tests involved measuring assumed to find the relationship between working memory and math, word problem-solving components, estimation, magnitude comparisons, naming speeds and finally inhibition. These tests were administered using various adaptations from similar studies that were reliable and appropriate. The study was observational – a graduate student observing a specific small-group of individuals from the parent population as well as one-on-one observations.
The data collected was quantitative. To evaluate the best model fit also seeing as latent class analysis (LCA) is an exploratory analysis, a sequence of models were fit, altering the number of latent classes between one and six. A mixture of both statistical markers and substantial theory were used to calculate the model with the best fit. Models with different numbers were compared using information criteria. Given the evidence, the three-class model provided an the best fit to the data and was chosen where the first latent class was labeled as average achievers across all variables, the second class was labeled as those at risk for MD, and latent class 3 was characterized as those who were poor math problem solvers. There was no mention of statistical software. Tables were used in displaying all the data collected from the various tested used. I believe that the tables were useful to me, although seeing as I was a bio-chemical major for three years, and a mathematics major for two years at the University of Minnesota I think I do not reflect the average reader when it comes to the overall population. I think using bar-graphs would have made understanding the data simpler instead of using tables to convey the differences and similarities in the three aforementioned categories. None of the tables were misleading, just difficult to comprehend.
This study concluded that within a heterogeneous sample of third-grade learners there is an identifiable group of children with MD which was measured at the 25th percentile. These results offer empirical evidence for the generally used “25th percentile” score for determining risk. Also, it was found that the probability of locating a latent class of children with MD or MLD that was completely autonomous from reading problems is quite low. These findings were consistent with many other studies which found that math difficulties are indeed comorbid with reading difficulties, and therefore share comparable processing shortfalls.
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The author’s adequality addressed the limitations of their studies, which were limitations due to the size of their sample consisting of less than 500 students all of which came from the same state in the United States. I think this is the biggest limitation when it comes to this study and is uncertain given these limitations the conclusions were justified. However, I do think that when they were citing their conclusion that it is somewhat justified since they did not make any independent conclusions, instead they used their findings to support other studies. I think it is widely known that some many students and educators believe some students struggle specifically with maths so I believe the message of this study to is strong.
I chose this study because I plan on being a STEM educator in secondary education which focuses on mathematics and physics. This article contradicted my thinking about teaching math because I do not believe in the concept of someone not being a “math person”. The reason I believe this is due to this concept being very gendered and appearing strongly among girls in junior high. It made me rethink my views on this topic because this research has shown that from an early age, there a student that specifically struggle in math and no other subjects.
However, with that being said, I still believe that with enough work and with the right education almost everyone can succeed in math. My goal is to inspire a love and thirst for math which I feel is lacking among the students I have tutored in my four years as a tutor at college campuses and as my work as a teaching assistant.
- Swanson, H. L., Olide, A. F., & Kong, J. E. (2018). Latent class analysis of children with math difficulties and/or math learning disabilities: Are there cognitive differences? Journal of Educational Psychology, 110(7), 931–951. doi: 10.1037/edu0000252
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