Where Is The Math In Science Olympiad? Aligning .

Table 1. continuedB Event TitleTowersWind PowerWright StuffWrite it/Do itScience Standards &Practices (SPs)SPs: 2-6SPs: 2-8SPs: 2-6SPs: 2, 5-8Mathematics Topics AddressedBuild a specified towerbefore competition.Build a blade assemblyto capture wind power.Design a free-flight,rubber-powered monoplaneto achieve maximumair time.Construct objects froma student’s description.MS CCSSM & Practices (MPs)7GB6: (See Crime Busters)Mathematics DOK*1, 27GA2: Draw geometric shapes with conditions.1, 2Design mathematical models4MPs: 1-86RPA3B: (See Optics)1, 27RPA3: (See Food Science)1, 2Design mathematical models4MPs: 1-86RPA3B: (See Optics)1, 27GB6: (See Crime Busters)1, 27GB5: (See Optics)1, 2Design mathematical models4MPs: 1-8Standards vary.3MPs: 2- 8*Due to multiple parts per event, more than one DOK rating may be listed.Prior studies of Science Olympiaddirect their focus toward student perceptions, preparation for SO events,and the impact their participation hadon their career choices (McGee-Brownet. al., 2003; Wirt, 2011; Christie, 2008).These studies found that students whoparticipated in SO events demonstrateda higher percentage of positive feelingstoward STEM content areas, gained anincrease of 21st century skills, and aremore likely to follow a STEM relatedcareer path (McGee-Brown et. al., 2003;Wirt, 2011; Christie, 2008).Although this research discussesSTEM careers and skills, there exists agap in the literature specifically aligningthe Science Olympiad events to DOKlevels, CCSSM, or the MathematicalPractices. While specific science contentstandards were identified on the ScienceOlympiad website, no record relatingthese events to mathematics or DOK levels existed in the review of the literature.As teachers seek to learn how to best106prepare their students for these events, itis helpful that connections between SOevents and the mathematical knowledgeare made explicit.MethodologyBoth a content analysis and alignmentof DOK levels were used in this studyas a means to determine the relationshipsbetween the Science Olympiad DivisionB and C events, the Next GenerationScience Standards and Practices, Webb’sDepth of Knowledge Framework, andthe Common Core State Standards forMathematics and Mathematical Practices.Results were used to support mathematics and science teachers, administrators,and school districts that participate in theScience Olympiad competitions.Procedures for Content AlignmentA quantitative content analysis wasused to determine which mathematical topics were addressed in the B andC events and how often they occurred(Krippendorff, 2012; Neuendorf, 2002).Data gathered from five resources provided by the Science Olympiad websiteincluded: rules of each event, powerpoints, event content wikis, released exams, and videos. After authors definedthe purpose of analysis and materials tobe analyzed, the identification of rulesthat constituted a “match” between thestandards and events was made. The establishment of the CCSSM and Mathematical Practice categories led theauthors to decide that in order for an eventto exhibit a particular standard (or fit ina category), the mathematics involvedmust be at or beyond grade levels forDivision B (6-8) or Division C (9-12).For example, many events required calculations but reviewers did not includeany mathematics standards lower thanfourth grade as evidence. However, if themathematics was an essential feature ofthe event, such as developing an experimental design where statistical/graphicalanalysis was necessary, then the mathematics was matched with the appropriateSCIENCE EDUCATOR

Figure 2. Mathematics Content Standards by Grades Addressed in B Events. This figure illustratesthe frequency of math topics included within events.standard(s) and mathematical practices.The eight mathematical practices (MPs)describe the varieties of processes andproficiencies that mathematics educatorsseek to develop in their students (CCSSM,2010). Finally, the frequency of alignedstandards was documented with an effortto quantify the number of times each eventwas dependent on specific mathematicalcontent standards (Division B: grades 6-8and Division C: grades 9-12).Alignment Models for DOKResearchers have developed modelsto enable more sophisticated alignmentanalysis of standards (Case, Jorgensen, &Zucker, 2009). The most frequentlyused are Webb’s Model, Surveys ofEnacted Curriculum (SEC), and theAchieve Model. Norman Webb’s modelof alignment has been used frequentlyin the field of education (Ananda,2003; Impara, 2001; La Marca et al.,Figure 3. Middle and High School Content Areas Addressed in B Event. This figure illustrates thefrequency of specific content areas within event.WINTER 2018 VOL. 26, NO. 22000). Webb aligns programs along thelines of five dimensions of an assessment: (a) content focus, (b) categoricalconcurrence, (c) depth of knowledgeconsistency, (d) range of knowledgecorrespondence, and (e) balance ofrepresentation.Content focus concerns the development of student knowledge of the subject matter Categorical concurrenceexamines the similarity between thecategories of content in the standardsand assessments. Depth of knowledgeconsistency compares the content complexity required by the standards andmeasured by the assessments. Range ofknowledge correspondence comparesthe span of knowledge required by thestandards in a subject area to that ofthe assessments. Balance of representation compares the emphasis givento certain topics and objectives in thestandards to the assessment’s corresponding emphasis. To carry out analignment study using Webb’s model,a panel consisting of four to six educators and content specialists trainedto identify DOK levels and standardsare required. Each criterion is ratednumerically, allowing the results to beobjectively quantified, calculated, andreported.Andrew Porter developed the Surveysof Enacted Curriculum (SEC) Modelthat categorizes the standards and assessments according to content topicsand cognitive demand (CCSSO, 2002).Cognitive demand is described usingcategories that are specific to each specific discipline. In mathematics these include (a) memorization, (b) procedures,(c) understanding, (d) generalizations/proof, and (e) solutions of non-routineproblems. This categorization producesa matrix that enables a comparison ofthe standards and assessments (Porter,2002).The third model by Achieve, Inc., hasdeveloped an alignment model that canbe used to compare a state’s standards tothose of other states or nations, provideprofessional development to state educators and perform an audit of a state’seducation reform. The Achieve model107

Table 2. Alignment of C EventsC Event TitleEcologyHS Science Standards &Practices (SPs)LS1–2-3Mathematics Topics AddressedGrowth Curves of Populations,Exponentials, Logistics, NumberPyramids, Invasion Curves, andPredator-Prey Graphs.HSF CCSSM & Practices (MPs)IFB4: Interpret features (quantities)of graphed and give a verbaldescription of the relationship.Mathematics DOK*2, 3LEB5: Interpret parameters in alinear or exponential function.Invasive SpeciesLS4– 2Time series and Invasion Curves.Microbe MissionLS1–1, 3-7Exponential Growth Curve.IDB6a: Fit a function to data tosolve problems in context.IDA1: Interpret categorical andquantitative data. Summarize,represent, and interpret data on asingle count or measurementvariable.IDA1: (See Invasive Species).2, 31, 2, 36SP4: Summarize and describedistributions and display datain graphs.Anatomy and PhysiologyLS1–2-3Homeostasis-ActionPotential GraphDisease DetectivesESS3–4; ETS1–3Odds Ratio,Epidemic Curve,Identify types of error andstatistical analysis.SP: 2HovercraftSPs: 2-6MPs: 2,4,5Kinematic Equations,Projectile Motion,Momentum, Density, Pascal’s law,IFC7e: Analyze functions using differentrepresentations. Graph exponential,trigonometric, and logarithmic functions.Show key features by hand and usingtechnology.N-QA2: Reason quantitatively anduse units to solve problems.Define appropriate quantities for thepurpose of descriptive modeling.IDA2: Interpret Categorical andQuantitative Data.Summarize, represent, andinterpret datato compare center) and spread.REI.A1: Reasoning with Equations andInequalities by explaining steps andconstructing viable arguments.1, 21, 2, 31, 2N-Q2: (See Anatomy and Physiology).Wind PowerSPs: 2-8Materials SciencePS1–3; PS2–6SPs: 2-8108Power of Wind FormulaMultimeter ReadingsYoung’s ModulusStress/Strain Curve,Creep Rate, Viscosity,Surface Area/Volume, Ratios.MPs: 2-5, 7-8N-Q2: (See Anatomy and Physiology).7GB6: Solve problems involving area,volume and surface area.23, 4N-Q.1-3:1. Use units to understand problems2. Define appropriate quantities for modeling.3. Choose a level of accuracy whenreporting quantities.SCIENCE EDUCATOR

Table 2. continuedC Event TitleOpticsHS Science Standards &Practices (SPs)PS4–1, 3-5Mathematics Topics AddressedAngles of reflection andrefraction and Snell’s Law.HSF CCSSM & Practices (MPs)8GA3: Describe the effect of dilations,translations, rotations, and reflectionsusing coordinates.Mathematics DOK*1, 2, 3TFB5: Choose trigonometric functionsto model phenomena.ForensicsSPs 2-8Angle of Impact of Blood Spatter.Chemistry LabPS1–2, 4-5, 7Stoichiometry.8EEA4: Perform operations inscientific notation.TFB7: Use inverse functionsto solve trigonometric equations.Evaluate and interpret solutionsusing technology.N-Q.A1-3: (See Materials Science).21, 2, 3SSE.A1b: Interpret expressions byviewing one or more of their partsas a single entity.CED.A1: Create equations and inequalitiesin one variable and use to solve problems.CED.A2: Create equations in two or morevariables to represent relationshipsbetween quantities; graph equations oncoordinate axes with labels and scales.HydrogeologyESS3–4, 6SPs: 2, 5-6, 8Game OnSPs: 2, 5Write It Do ItSPs: 2, 5-8Experimental DesignSPs: 1-8Algebraic Equations,Matrices, Mathematical Modeling,Estimation, andNumerical Modeling.Programming with Technology.Measurement, andPrecision in Description.Creating a graph from atable. GraphStatistics (Central Tendency,and Hypothesis Testing.REIB3: Solve linear equations andinequalities in one variable.N-Q.1-3: (See Materials Science).MPs: 2-5, 8N-Q.1-3: (See Materials Science).IC-B.3. Recognize purposes and differencesamong surveys, experiments, andobservational studies; explain howrandomization relates to each.IC-B4: Use survey data to estimatepopulation means or proportions;and develop a margin of error throughsimulation models.3, 431, 21, 2, 3IC-B5: Use data and simulationsfrom a randomized experimentto compare two treatments.Electric VehicleSPs: 2-8Motor cogging formulaRobot ArmSPs: 2-8TowersSP’s: 2-6Construction of a robotic armto grab, lift, and depositspecific items in prescribedlocations.Problem solving,Precision in Measurement, andGeometric Structures.WINTER 2018 VOL. 26, NO. 2IC-B6: Evaluate reports based on data.CEDA2: (See Chemistry lab).MPs: 1, 2, 4-6MPs: 1-822, 31, 2, 3109

Table 2. continuedC Event TitleHelicoptersRocks and MineralsRemote SensingDynamic PlanetAstronomyHS Science Standards &Practices (SPs)SPs: 2-6MS-PS1–1;MS-ESS2–1;ESS2–3PS4–1, 2, 5;ESS2–2, 4-5MS-ESS2–2-;ESS2–2-3ESS1–2-3Mathematics Topics AddressedPrecision in Measurement,Problem solving, Modeling, lookfor and expressing regularity inrepeated reasoning.Crystal structures of minerals.Image Interpretation,Radiation, and find surfacearea using graphs.Drift velocity and Magnitudeof Earthquakes.H-R Diagram,Distance modulus,Scientific Notation, andHubble’s Law.HSF CCSSM & Practices (MPs)MPs: 1-8Mathematics DOK*1, 2, 3,GMDB4: Identify shapes of two-andthree-dimensional cross-sectionsgenerated by rotations.7GB6: (See Materials Science).12, 3, 4N-Q1-3: (See Materials Science).1, 2N-Q1-3: (See Materials Science).1, 2*Due to multiple parts per event, more than one DOK rating may be listed.uses five criteria for alignment: content centrality, performance centrality,challenge, balance, and range (CCSSO, 2002; Resnick et al., 2003). Content centrality compares the contentof each test item to the correspondingstandard. Performance centrality compares the difficulty (cognitive demand)of each item to the difficulty requiredby the corresponding standard. Challenge examines whether a set of itemsconsidered together expresses the degree of proficiency required by thestandards. Balance and Range providea quantitative and qualitative evaluation of the emphasis placed on topicsin the assessment compared to the emphasis placed on the same topics in thestandard (Case, Jorgensen, & Zucker,2009).The authors selected Webb’s modelprimarily for the DOK criteria whichhad been used in previous publications aligning assessments with theCommon Core. The reliability withinWebb’s model has been well established by its use in alignment studiesfor more than 10 states (Council ofChief State School Officers [CCSSO],2002). Producers of standardized testsrely on Webb’s model to augmentnorm-referenced assessments for compliance. Webb’s model is adaptable to other purposes for which an110alignment study may be required(Impara, 2001).Reviewer Panel Participants andTrainingBecause this content alignment requires a panel of experts in particularmathematics and science content fields,six pre-service and two in-service mathematics and science teachers were askedto serve as reviewers. For this study, theWebb Alignment Tool was used, wherealignment analysis is a two-part process.Two training and work sessions (approx.3 hours each) with the mathematics andscience panelists were held. On day oneall participants were provided with copies of the CCSSM grades 5-12, NextGeneration Science Standards grades5-12, Webb’s Depth of Knowledge framework, Hess’s Model (2013), and the 2016Science Olympiad Event Guides and resources. Reviewers used these materialsfor their training on assigning DOK levelsto the mathematics embedded in the SOevents. On day 2, reviewers aligned an SOevent to the mathematics standards andidentified the DOK levels using Hess’smodel (see Figure 1).Interrater ReliabilityTo ensure that raters coded the itemsin a consistent manner, the authorsconducted two rounds of review. Theprocess involved coding randomly selected mathematics items from eachevent, with a total of 73 mathematicsitems selected for calibration. In the firstround reviewers rated items independently and reconvened to discuss ratings and resolve any discrepancies. Inthe second round, the authors rated theremaining items independently to checkthe interrater reliability. Results showedacceptable interrater reliability for thecontent analysis at an 81% percentagreement using CCSM and SO events.For DOK results, the weighted kappacoefficient, which is a measure of rateragreement that takes into account agreement of ordinal data due to chance, wasat 0.78 for mathematics.FindingsTable 1 illustrates the relationshipbetween science and mathematics topics behind the B events within middleschool Science Olympiad divisions. Thefirst two columns describe the individualevents and science standards addressed(Science Olympiad, 2017). The next twocolumns identify the middle school (MS)mathematics topics, corresponding standards, and practices that were alignedby reviewing documents shared on theSO website (i.e. power points, handouts,SCIENCE EDUCATOR

Figure 4. B Event CCSSM per Grade Level. This figure illustrates number of standards per gradelevel.practice tests). The last column identifies the mathematics DOK levels usingWebb’s identification for mathematicsand science (Hess, 2013).Analysis of Group B EventsAs observed from Table 1, one eventmay contain multiple standards and/orpractices for math or science. Comparing the Mathematical DOK levelsamong all 23 events, 7 were categorized at a Mathematical DOK level of4, while 8 were at a level 3, 7 were at alevel 2 DOK and only 1 was at a level 1DOK. All of these events fell under oneof the following science strands: Life,Personal & Social Science, PhysicalScience & Chemistry, Inquiry & Natureof Science, Technology & Engineering, and Earth and Space Science. Thehighest DOK levels for Math (Level 4)Figure 5. Mathematics Content Standards Addressed in C Events. This figure illustrates mathematicstopics found in grades 6-12.WINTER 2018 VOL. 26, NO. 2were in the areas of: Technology & Engineering (4 out of 7), Physical Science &Chemistry (2 out of 7), and Inquiry &Nature of Science (1 out of 7). It maybe that these three content areas requirehigh scientific DOK demands for students that also transfer to high levelsof mathematics problem solving situations. Additional data of B events areillustrated in Figures 2 and 3.As illustrated in Figure 2, most standards addressed were within 7th grade(44%), with the highest categories in Geometry (17%), Ratios (11%), and Statistics (9%). Sixth grade was second highest(Figure 2) at 27%, with the highest topics in Ratios (13%) and Statistics (7%).With all grade levels combined (Figure2), most standards addressed were: Ratios(25%), Geometry (23%), and Statistics(21%). Similar findings within all middleand high school events identified the areas of Geometry, Ratios, and Statistics asrepresenting the majority of topics withinthe B events (Figure 3).Analysis of Group C EventsTable 2 illustrates the relationship between science and mathematics topicswithin the Division C high school SOevents. The first two columns describe theindividual events and science standardsaddressed (Science Olympiad, 2017). Thenext two columns identify the high school(HS) mathematics topics, correspondingstandards, and practices that were alignedby reviewing documents shared on theSO website (i.e. power points, handouts,practice tests). The last column identifiesthe mathematics DOK levels using Webb’sidentification for mathematics and science(Hess, 2013).As observed from Table 2, one eventmay contain multiple standards and/or practices for math or science. Comparing the Mathematical DOK levelsamong all 23 events, 3 were categorizedat a Mathematical DOK level of 4, while11 were at a level 3, 8 were at a level 2DOK and only 1 was at a level 1 DOK.All of these events fell under one of thefollowing science strands: Life, Personal &Social Science, Physical Science &Chemistry, Inquiry & Nature of Science,Technology & Engineering, and Earth111

Figure 6. Middle and High School Content Areas Addressed in C Event. This figure illustrates thenumber of high school standards addressed.and Space Science. The highest DOKlevels for Math (Level 4) were in the areas of: Technology & Engineering (2 outof 4), Physical Science & Chemistry (2out of 4), and Inquiry & Nature of Science (1 out of 4). There were the samethree areas

tional tournaments (Science Olympiad, 2017). Science Olympiad is broken into four divisions: A1 (grades K-3); A2 (grades 3-6), B (grades 6-9), and C (grades 9-12). Students may compete individually in an event, but the overwhelming major-ity of students compete in pairs or groups. National r