Success in Math with Let’s Go Learn

“Algebra  is  a  foundation  and  language  system  on  which  higher  order  mathematics,  science,  technology,  and  engineering  courses  are  built.”    

(A.  Evan,  2006)   Introduction Success in algebra is a key indicator of success in college. This is both good news and bad news: good news because it gives educators a concrete way to support students, bad news because algebra poses a significant obstacle for many students. In short:

o If students want to go to college or enter a STEM career, their chances increase significantly if they pass algebra in middle or high school (Hein et al., 2013).

o If they fail algebra and re-take it, chances are slim that they will pass it the second time around (WestEd, 2012).

o If they don’t master the concepts, system, or language of algebra, they’re going to have a difficult time getting into and/or passing other higher math and science classes (Adelman, 2006; Conley, 2007).

o “If you don’t prepare everyone, then essentially you only have the privileged kids who are prepared to take [advanced math] …. The disparities have turned access to algebra into a civil rights issue” (Garland, 2014).

What can you do to ensure that all your students succeed in algebra? Step 1: Start differentiating instruction in elementary school. The first step to success in algebra is to recognize that mastery of middle school and high school objectives depends on mastering math objectives for each grade level from K - Grade 5: “Just as students’ relative success in higher-level mathematics is closely linked to their success in middle-school math, so too does students’ relative success in middle school depend largely on the strength of academic foundations developed in earlier grades” (Finkelstein et al., 2012). We know the content and processes that students have to understand and practice in the elementary years. Content has to include numbers and operations, algebra, geometry, measurement, data analysis, and probability, and processes must include problem solving, reasoning and proof, communication, connections, and representation. But do we recognize that the path to success means accomplishing each segment of the journey? If students miss a chunk of skills or subskills in any content area, or if they miss the opportunity to practice the cognitive and metacognitive processes that guide mathematical thinking,

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chances are good that higher math will elude them. Why? Because if students who are enrolled in algebra are not prepared and do not pass, their chances of ever passing it are slim. Young students come to school with very different levels of math experience. By the time teachers realize that their students aren’t prepared for middle school or high school math, it’s almost too late. According to research by Jungjohann, Clarke, and Cary, “Long-term trajectories are established as early as kindergarten” (Morgan & Farkas, 2009; Jungjohann et al., 2009). To remediate the issues, the authors cite the recommendation of the National Advisory Panel in 2008: “a focused, coherent progression of mathematics learning with emphasis on proficiency with key topics” (Jungjohann et al., 2009). The key takeaway here is that while we know that algebra is the predictor of success in higher math, college, or career – algebra is just the tip of the iceberg. Math success for all students is possible when teachers have accurate, timely data about their pupils’ strengths and weaknesses in different domains and then use the data to differentiate instruction for each student until mastery is accomplished. Let’s Go Learn has created a system that provides the data, the reporting, and the instruction that make personalized learning possible. Its online computer-adaptive assessment ADAM evaluates the individual math skills of students in Kindergarten through Grade 8. Let’s Go Learn’s underlying assessment system then assigns students lessons that remediate the learning gaps that prevent students from reaching grade level and beyond. ADAM covers the subskills for Numbers and Operations, Measurement, Data Analysis, Geometry, and Algebra that follow. These subskills are the stair steps that students have to master to prepare for algebra. If students master grade-level skills and subskills year to year, their potential for success in algebra increases dramatically. Step 2: For upper elementary and older students with existing gaps, ensure that they have requisite pre-algebra skills BEFORE they are placed in algebra. Many schools place students into algebra because they are in 8th or 9th grade or because they have passed a prerequisite course. When students are placed in algebra without first determining if they have the foundation skills, the risk of failure outweighs early placement. According to Finkelstein et al. (2012), “When students take algebra 1 (that is, in which grade) is less important than whether students are ready to take it.” How can educators assess students’ current knowledge? The most effective way to determine if students are ready for algebra is to give them a truly granular diagnostic assessment. Let’s Go Learn’s pre-algebra computer-adaptive diagnostic assessment provides teachers with a valid and reliable measure of

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student readiness. Because this assessment is computer-adaptive, students who do not yet have the foundation are not subjected to a series of questions that they don’t know how to solve, which can negatively impact their association with math – and specifically algebra – instruction. WestEd’s Center for the Future of Teaching and Learning studied students in 24 school districts. The study found that when students repeated Algebra I, “[O]nly 1 in 5 scored at a proficient level on standardized tests” (Tucker, 2012). LGL Pre-Algebra evaluates a student’s math foundation through an assessment of his or her strengths and weaknesses in integer operations, fraction operations, decimal operations, comparing and converting, estimating and rounding, evaluating exponents, ratios and proportions, simplifying expressions, coordinate graphing, linear functions, simple equations, geometry, interpreting data, and simple probability. LGL Pre-Algebra is composed of three parts. Part I is a pre-screener that presents students with one question from each of the 14 pre-algebra constructs. Based on the results, students may test out of a particular section of Part II. Part II tests each of the 14 pre-algebra constructs in detail. Part III assesses foundational skills; students take this part only if their errors demonstrate a possible deficit in multiplication math facts or reading comprehension. In addition, if performance in early, lower-level constructs indicates a possible deficiency, then LGL Pre-Algebra ceases testing and checks either math facts or English language proficiency to further identify the student’s strengths and weaknesses. If students demonstrate a lack of mastery, then Let’s Go Learn’s assessment system places them in the appropriate math or pre-algebra lessons to fill the learning gaps. Finkelstein et al. (2012) writes that “school systems are struggling to successfully teach, or reteach, mathematics to students who are not already performing well in math by the time they reach middle school." With Let’s Go Learn’s pre-algebra diagnostic assessment and online lessons, teachers can ensure that students are adequately prepared for algebra. According to Finkelstein (2012), “If students have the necessary math foundation when they first take algebra 1, whenever that is, they have a much better chance of becoming proficient in algebra 1 content. In turn, algebra 1 proficiency serves as the necessary foundation for being successful in the next higher level of math after algebra 1.” Step 3: Place students in algebra when they’re ready. “Algebra is considered a ‘gateway’ course for the sequence of mathematics and science courses that prepares students for success in later schooling (Matthews and Farmer, 2008)” (Walston & Carlivati McCarroll, 2010).

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With so much research indicating that “few repeaters achieve proficiency on their second attempt,” educators have to strive to ensure that students master algebra the first time around (Finkelstein et al, 2012). To accomplish this, schools would do well to assess student algebra skills in the months prior to student enrollment in algebra. Let’s Go Learn’s computer-adaptive diagnostic algebra assessment evaluates 11 different constructs of Algebra I. These constructs include: evaluating advanced exponents, solving linear equations, graphing and analyzing linear equations, relations and functions, solving and graphing inequalities, solving and graphing systems, polynomial equations, factoring polynomials, radical equations and expressions, quadratic equations, and rational expressions and equations. The assessment is divided into two parts. Part I, the pre-screener, presents students with two questions representing each of the 11 algebra constructs determined to encompass the essential knowledge of Algebra I. Based on pre-screening results, students may test out of constructs on which they have demonstrated mastery. Part II contains the detailed test items that make up each of the 11 algebra constructs. Full construct testing is based on the student’s performance. The assessment’s adaptive logic adjusts the number of questions given to a student in real-time, based on his or her error rate. This reduces student test frustration and increases the reliability of the overall assessment. The LGL assessment system places students who show learning gaps in the 11 algebra constructs into online lessons designed to provide direct instruction and practice in the areas of weakness. Using Let’s Go Learn’s online math diagnostic assessments and online math instruction, teachers can ensure that students stay on grade level year after year as they move toward the requirements of higher-level math. The ultimate goal? Success in college and career.

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LGL Process Flow for Successful Math Assessment and Placement Finkelstein et al. (2012) suggest that to support student success, educators should “improve course-placement criteria used to assign middle- and high-school students to the appropriate math courses based on their current mathematical knowledge.” Let’s Go Learn has created a Process Flow for Success in Math.

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References  Cavanagh, S. (2008). Catching up on algebra. EdWeek. Retrieved from http://www.edweek.org/ew/articles/2008/04/23/34algebra_ep.h27.html Center for Public Education. (2012). High school rigor and good advice: Setting up students for success. Retrieved from http://www.centerforpubliceducation.org/Main-Menu/Staffingstudents/High- school-rigor-and-good-advice-Setting-up-students-to-succeed Conley, D. T. (2007). Redefining college readiness. Eugene, OR: Education Policy Improvement Center. Evans et al. (2006). The gateway to student success in mathematics and science. American Institutes for Research. Retrieved from http://www.microsoftmathpartnership.org/assests/gateway_document.pdf Finkelstein et al. (2012). College bound in middle school & high school? How math course sequences matter. The Center for the Future of Teaching & Learning at WestEd. Retrieved from http://www.wested.org/wp- content/files_mf/139931976631921CFTL_MathPatterns_Main_Report.pdf Garland, S. (2013). The math standards: Content and controversy. The Hechinger Report. Retrieved from http://hechingerreport.org/content/the- math-standards-content-and-controversy_13325/ Hein, V., et al. (2013, November). Predictors of post-secondary success. College & Career Readiness & Success Center at American Institutes for Research. Jungjohann, K., et al. (2009). “Early learning in mathematics: A formula for

success.” Pacific Institutes for Research, Institute of Education Sciences. Musen, L. (2010). Pre-algebra and algebra: Enrollment and achievement. Annenberg School Institute for School Reform. Noguchi, S. (2013, February 2). California abandons algebra requirement for eighth-graders. San Jose Mercury News. Retrieved from http://www.mercurynews.com/ci_22509069/california-abandons-algebra- requirement-eighth-graders Soave, R. (2013, February 8). California no longer requiring eighth graders to take algebra. Daily Caller. Retrieved from http://dailycaller.com/2013/02/08/california-no-longer-requiring-eighth- graders-to-take-algebra/#ixzz3BT3xVxRc

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Tucker, J. (2012, November 30). Students failing algebra rarely recover. SF Gate. Retrieved from http://www.sfgate.com/education/article/Students- failing- algebra-rarely-recover-4082741.php Walston, J. & Carlivati McCarroll, J. (2010, October). Eighth-grade algebra: Findings from the eighth grade round of the Early Childhood Longitude Study, Kindergarten Class of 1998-99 (ECLS-K). Statistics in Brief. National Center for Statistics, IES.

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Appendix: ADAM Scope & Sequence  Numbers and Operations

o Rounding (10s, 100s, 1,000s), comma & place holder, counting (by 1s, 2s, 3s, 5, 10s, 100s, and 1000s), text and numerals, numerals (2-digit), cardinal and ordinal numbers, counting backwards

o Place value: decimals (thousand, ten-thousand, hundred-thousand, millions), expanded form

o Comparing and ordering: decimals, money, symbols (2-digit and 3-digit), numbers

o Addition of whole numbers: multiple digits, regrouping, non-regrouping, 2-digit plus 1-digit, to 10, equivalent forms, modeling with objects

o Subtraction of whole numbers: regrouping, non-regrouping, subtracting from 10

o Multiplication of whole numbers: commutative, associative, distributive, 2-digit and 3-digit by 2-digit, 3-digit by 1-digit, 2-digit by 1-digit, powers of ten, factors 2 to 10, factors 0 and 1, grouping, and repeated addition

o Division of whole numbers: 4-digit, whole numbers, facts, 1-digit divisors and remainders, division as inverse of multiplication

o Fractions: adding and subtracting with unlike denominators, converting fractions, least common multiple & greatest common factor, multiplying and dividing, solving problems, multiplying patterns, adding with like denominators, adding, proper/improper/mixed, multiplying by whole number, comparing and ordering, as decimals and place value tenth and hundredth, equivalent with lowest terms, as parts of sets, partitioning objects into parts

o Number theory: divisibility rules, common greatest factors, prime factors, prime/composite numbers, multiples, factors

o Decimal operations: terminating and repeating decimals, division, multiplication and money notation, adding and subtracting

o Percentages: discounts and markups, increases and decreases, calculator percentages, estimating and calculating, proportions, ratios, percents and decimals, percents and fractions

o Ratios and proportions: using proportions to solve problems, interpreting and using ratios

o Positive and negative integers: multiplying and dividing negative numbers, adding and subtracting negative numbers, absolute value, solving problems with integer operations, ordering rational numbers, positive and negative numbers

o Exponents: rational numbers and exponent numbers, square roots, negative whole number exponents, irrational numbers, rational integer operations and powers, scientific notation

Measurement

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o Money: values, recognition o Time: calendar in weeks, elapsed time, calendar in months, reading a

clock o Temperature: reading, concept o Length: converting units, comparing metric lengths, converting units of

length, length, customary and metric units, concepts, number line, measuring by object, comparative vocabulary

o Weight: converting and comparing units and concepts of weight, units of measure, customary

o Capacity and volume: comparing metric capacity/volume, units of capacity/volume, units of measure, metric and customary capacity

o Rate: solving rate problems, scale, comparing rates, understanding rate

Data Analysis o Patterns and solving: linear patterns, extending linear patterns, extending

patterns, sorting by common attributes, simple patterns o Data representation: problem solving, features of data sets, multiple

representations of the same data, simple data representation o Simple probability: probability of multiple events, representing

probabilities, estimating future events, simple probability, likelihood o Outcomes: representing possible outcomes, representing

outcomes/results, recording outcomes o Displaying data: scatterplots, data representation, comparing data

(fractions and percents), displaying date, interpreting graphs o Measures of central tendency: data set quartiles, use of measures of

central tendency, outliers, changing central tendency, computing measures of central tendency, mean/median/mode

o Ordered pairs: writing ordered pairs, identifying ordered pairs o Samples: independent and dependent events, sampling errors, selecting

samples

Geometry o Location and direction: vocabulary o 2D shapes: solving problems of congruence, translations and reflections,

elements of geometric figures, symmetry, identifying congruent figures, polygons, forming polygons, describing shapes, attributes, naming by name and shape, comparing

o 3D shapes: geometric elements, patterns, qualities, composing, faces, shapes

o Triangles: Pythagorean theorem, solving for unknown angles, definitions, right angles, attributes

o Quadrilaterals: definitions, attributes o Area and perimeter: complex figures, perimeter/area/volume, area of

triangles/parallelograms, 2D and 3D units of measure, word problems, solving for area vs. perimeter, area with square units, dividing rectangles into squares

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o Lines: parallel and perpendicular, vertical line segment length, horizontal line segment length, plotting points of linear equation

o Circles: calculating using Pi, Pi, qualities o Angles: types, sum of angles, angles and angle measurement o Volume and surface area: surface area and volume of complex solids,

volume of triangular prisms and cylinders, volume, surface area o Geometric relationships: changes of scale, expressing geometric

relationships, using variables in geometric equations

Algebra o Relationships: equivalent multiplication, equivalent addition, rules of linear

patterns, commutative and associative properties of multiplication, symbolic unit conversion, relationships of quantities, sorting by unlike objects

o Expressions and problem solving: multiplying and dividing monomials, positive whole number powers, simplifying expressions, using order of operations to evaluate expressions, writing expressions, solving problems using order of operations, applying order of operations, equivalent expressions, writing algebraic expressions, using distributive property, order of operations (with parentheses), selecting operations, problem solving using data (addition and subtraction), number sentences and problems, symbols

o Equations: solving multi-step rate problems, solving two-step linear equations, algebraic terminology, solving 1-step inequalities, solving 1-step linear equations, solving linear functions, solving by substitution, problem solving and data, simple equations, formulas, concepts of variables, functional relationships, problem solving with equations/inequalities

o Graphing algebraic relationships: plotting set ratios, slope, graphing functions, graphic representations, coordinate plane