Much like the runways of Paris with its changing fashion trends, the world of education follows trends as well. Educators cringe when they hear “No Child Left Behind” some ten years beyond its advent. Now, the phrases “Common Core” and “Student Learning Objectives” have teachers seeing red. However, despite the latest and greatest trends to boost student achievement, the very same students in the United States continue to underperform on a global scale in Mathematics. In 2012, the Program for International Student Assessment (PISA) bore out results that “29 nations and jurisdictions outperformed the United States by a statistically significant margin,” (Heiten, 2013). In order for our students to rise to a position high on the performance scale of nations, students must master the basics in all subjects, but more specifically in the area of Mathematics.
In an effort to develop students with a deeper understanding of mathematical and language and reading concepts, forty-five states (my home state of Maryland being one of them) and the District of Columbia have adopted the Common Core Standards, a system of expected benchmarks for students in grades K-12. According to the Common Core State Standards Initiative website, the standards “define the knowledge and skills students should have within their K-12 education careers so that they will graduate high school able to succeed in entry-level, credit-bearing academic college courses and in workforce training programs,” (Common Core State Standards Initiative, 2014). The local statistics mirror the national data.
Both present conditions which are symptomatic of a larger systemic problem; American students are not mastering mathematical concepts at any level. The learning environment is a fourth grade inclusion classroom in a neighborhood school in the suburban Washington, D.C. (Maryland) area. Students in the class are differently abled. The class has students with Individualized Learning Plans (IEP) to accommodate varying needs from Asperger’s Syndrome to mild intellectual disabilities. There are also students who have been tested and identified as Talented and Gifted (TAG), as well as on grade level learners. Students are taught in whole group, differentiated small groups, and occasional pull out sessions with specialists. Current Conditions
There are twenty-one students in the fourth grade inclusion classroom. All students took a standardized unit test in October 2013 that tested the Common Core Standards taught in the first quarter of the 2013-2014 school year. Of these, Standard 4.OA.B – Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number.
Determine whether a given whole number in the range 1–100 is prime or composite, (Common Core State Standards Initiative, 2014), only 20% scored at a level of “proficient” on standardized (MUST Test Result Data, 2013). The lack of proficiency in this standard is symptomatic of the underlying condition I have encountered; students have not yet mastered basic multiplication facts. Without mastery of basic multiplication facts 0-12, students are unable to manipulate and perform operations on fractions and decimals and subsequent pre-algebra concepts in the latter half of fourth grade and continuing into following grades through high school.
The current conditions for the fourth grade class is at 20% of students who have performed at a “proficient” level of mastery in basic mathematical facts. This is equivalent to a grade of 80%, or a “B”, in traditional percentage and letter grading systems used in the US. The desired state of performance is the inverse of the current statistics; 80% should have mastery at a level of proficient or advanced and 20% performing at minimal or below grade level standards. After mastering basic facts, students will be able to not only identify multiples and factors of numbers 1-100, they will also be able to perform operations on fractions and later, algebraic statements. Data Collection Processes
Discussion of Data Collection Instruments
The designer developed a survey for teachers of grades three through five in order to help determine where problems or areas of deficiency are in current math. The first two questions asked the percentage of their students who are currently proficient in accuracy and automaticity in multiplication facts. In other questions, respondents ranked their responses using a Likert Scale, which helped to identify their attitude on the necessity of students mastering basic multiplication facts currently in order to develop a deeper understanding of current and future mathematical concepts. In the questionnaire, respondents were asked to rank what they believe to be their students’ biggest challenges in mastering this specific standard. Questions also asked the extent to which computer aided instruction is used in helping aid in mastery of multiplication facts. In getting answers to these questions, I will use the data to identify several factors; impact of teacher’s attitude toward remediating students in basic facts that should have been mastered in the previous grade, and time dedicated to instruction and practice in this particular standard. Discussion of Sources of Data
Six intermediate elementary (grades three through five) classroom teachers who instruct students in mathematics answered the survey and questionnaire. Students of these teachers range from those with special needs, general education needs, and also students identified as “Talented and Gifted” (TAG). Data Gathered Through Other Sources
Quantitative data was gathered from the Prince George’s County Public Schools Mandatory Unit Systems Test (MUST) in Mathematics administered countywide to fourth grade students in 146 elementary schools. Specific data used in this needs analysis was limited to one fourth grade inclusion classroom, Lake Arbor Elementary, where the designer is the teacher. The designer collected further quantitative data from the same inclusion class on timed multiplication tests where twenty-two students answered 100 multiplication facts (0-12) problems in five minutes.
Data Analysis Techniques Used
The survey and questionnaire were designed to gather data that would substantiate the need for students to master basic multiplication skills in intermediate elementary grades. The survey was used to gather both qualitative and quantitative data based on teachers giving percentage results of students’ current level of performance. Teachers also ranked what they believed would improve their teaching of mathematics in the classroom. The questionnaire was designed to gather data on teachers’ attitudes of the importance of student mastery of basic multiplication facts. The questionnaire also served as a tool to gain input on the challenges the believe limit their students from performing on grade level in mathematics, particularly in mastering basic multiplication facts. Finally, teachers were given the opportunity to answer an open-ended question, which gauged their attitude toward the importance of mastery of basic multiplication facts in the modern world and classroom.
Results of Analysis
Question one of the survey asked what percentage of your students can answer basic multiplication facts with accuracy on most occasions.
Findings of Needs Analysis
While a majority of respondents determined mastery of basic multiplication facts as “essential for success in their current grade,” it is of note that two teachers said mastery of basic facts are “desirable, but not as important as in past year.” This information would indicate teachers’ attitudes are moving away memorization of facts, possibly due to the widespread availability of technological applications that students can or will use in the classroom and later in life. The attitude towards the lowering of importance of rote memory skills for facts reflects the larger societal dependence on technology. Applications on smartphones and mobile devices are becoming increasingly used in place of mental math and are utilized both by the current generation of students in elementary school now, but also by the newer generation of teachers who instruct them.
To further deepen the understanding of the philosophical shift in importance of memorization of multiplication facts, teachers were asked if they administered timed multiplication tests in their classroom. Furthermore, teachers were asked if they encourage an atmosphere of healthy competition for mastery of the facts amongst their students. While all six respondents reported that they do administer timed multiplication tests, only one teacher stated that there was an atmosphere of “healthy competition” amongst her students where they challenge one another to higher levels of performance.
The information suggests that while teachers are still administering the tests as part of regular instruction, the instructors’ attitude of the importance of them as a way to aid in student mastery of facts is evidenced in the lack of encouragement by both teacher and students to achieve at higher levels. Finally in the questionnaire, teachers were asked to rank factors they believe to be the biggest challenge(s) their students face that prevent them from performing on grade level in their current math instruction. The two most common responses amongst all respondents cited both a lack of support from parents in practice of math facts and a lack of basic understanding and mastery of basic mathematical facts from addition and subtraction up to division and multiplication as the biggest barriers to student success. Goal of Instruction
Given practice in automaticity and accuracy, fourth grade students will be able to independently complete 100 multiplication problems of basic facts 0-12 in five minutes time with an increase in automaticity and accuracy of 50% over a ten-week period as measured by a pre-test and post-test assessments. Having this knowledge will enable students to manipulate and perform operations on fractions and mixed numbers, as well as deepen their knowledge of factors and multiples for future instruction.