Correlated Science & Math: A New Model for Linking Two Disciplines Sandra S. West, Ph.D. Texas State University-San Marcos Sandra T. Browning, Ph.D. University of Houston – Clear Lake

Correlated Science & Math Origin 1998 Developed the 1st Correlated Science & Math chart 2001 published 1st article 2

Middle School Science Module for training under-prepared teachers Download lesson plans & PPts 3

2006 Used Middle School Science Module as basis to design syllabi Began implementing the Correlated Science & Math model with the Mix It Up project 4

Traditional “Integration” Mathematics Uses Science: Mathematics Uses Science: application of mathematics concept application of mathematics concept make mathematics concept interesting make mathematics concept interesting : Science Uses Mathematics Formulas: as a tool to work science problems as a tool to work science problems to teach or explain the science concept to teach or explain the science concept 5

Traditional “Integration” Recommended as Best Practice Recommended as Best Practice Science Science Benchmarks for Science Literacy Benchmarks for Science Literacy National Science Education Standards National Science Education Standards Mathematics Mathematics NCTM Principals and Standards NCTM Principals and Standards Research supports Science & Math Integration Research supports Science & Math Integration Prior to 2008 Prior to 2008 Few small, poorly designed studies Few small, poorly designed studies Improves math scores Improves math scores 6

Correlated Science & Math: A New Model of PD Science Science w/Math Integrated Science & Math Math w/ Science Integrated Math & Science Math Correlated Science & Math 7

Teaches Both Science and Mathematics Teaching conceptually Teaching conceptually Using the appropriate language of each discipline Using the appropriate language of each discipline Identifying language confusing to students Identifying language confusing to students Using Inquiry for concepts & Direct Instruction for skills Using Inquiry for concepts & Direct Instruction for skills Using natural links between the disciplines Using natural links between the disciplines ID parallel ideas (zero & no acceleration or slope) Aligned with state and national standards Aligned with state and national standards Co-taught to teams of Science and Math teachers together Co-taught to teams of Science and Math teachers together Builds a Community of Practice Builds a Community of Practice Teacher teams & their principals Teacher teams & their principals University teams University teams University & teachers University & teachers 8

Correlated Science & Math (CSM): Teacher Training Courses Science led CSM courses Correlated Physics & Math Correlated Chemistry & Math Correlated Geology & Math Correlated Space Science & Math Math led CMS courses Correlated Quantitative Reasoning & Science Correlated Algebraic Reasoning & Science 9

Correlated Science & Math (CSM): STEM Principal Institute Mix It Up Principals –2 days –During teacher training –Ate breakfast & lunch with their teachers –Ben Johnson, EduTec, former Assoc. Superintendent and science teacher –Reviewed STEM research & best practices –Analyzed school data 10

Correlated Science & Math (CSM): Teacher Testimonies “Through hands-on instruction, numerous investigations, and straight forward note-taking, I was able to work side-by- side with a fellow teacher to develop wonderful integrated lessons for our students. This team teaching approach to lesson planning and construction will help to keep my students' interest in mathematics and science alive.” "The material was taught in such a way as to make the learning process more complete. I know that there is still much more that I can and need to learn and would love to participate in any continued learning opportunities that might be offered through the Science and Math 'Mix It Up' program.” 11

Sample & Treatment, Data Sources 81 Science & Math teachers ’06-’09 Training –Summer - 70 hours, 2 weeks –AY – 30 hours, Saturdays Classroom observations Pre/posttests –Teachers –Students 12

Results: Teachers As a result of participating in the CSM training: 1. Content knowledge increased in science & math, p< Adopted an integrated Science & Math approach 3. Perceived CSM to be effective for learning the content & language of each discipline 4. Reported using more integrated lessons 13

Results: Teachers Reported –Discovered the limitation of their own conceptual understanding of the science & math content –Developed a new understanding of essential concepts in both science & math, –Visualized essential concepts due to hands on activities –Gained new understanding of similar concepts used in both science & math 14

Results: Teachers Classroom observations/interviews revealed –Use of integrated lessons –Lack of knowledge about fundamental concepts that were not taught in CSM (Ex. Gummy bear density) –Use of lessons from CSM training –Use of materials & books by CSM teachers and their colleagues for lesson planning and lessons –Changes to best practice instructional strategies 15

Results: Principals Better understanding of how to best support high quality STEM education What to look for in walk-throughs, lesson plans & formal observations Importance of focused collaborative planning time Importance of intense and sustained STEM content/pedagogy focused PD 16

Results: Students Increase in TAKS scores from previous year Increase in student performance with CSM pre/posttests, p<0.05 –Items from released national or state tests –Not TAKS 17

Correlated Geology & Math Syllabus Develop typical Geology S&S Japanese Lesson Study Science teacher teaches the concept to math teacher ID Math links ID order Math is taught 3 hrs. planning/1 hr instruction 18

Sample Inquiry Lesson Correlated Physics & Math “Position” Physics, Position Engagement & Exploration: Insectum texanum Bug Exploration Explanation: Physics (Define distance, displacement) & Math (rectangular coordinate plane) Elaboration: Physics ( D iscuss point & frame of reference) & Math (distance formula, real number system & absolute value) Evaluation: Comprehensive problem involving Physics (position, distance & displacement, point & frame of reference) Math (coordinate plane, real number system & absolute value) 19

New Discoveries throughout the Journey During course planning Language issues Parallel Ideas Fun of being in a Community of Practice During classroom observations During course instruction Use of math “tricks” by math teachers that undermine student conceptual understanding 20

Correlated Science & Math Language Issues First evidence of Language Issues Planning “Correlated Physics & Math” course “Motion” lesson planning –Physics instructor teaching math instructor the motion lesson –Physics instructor asks math instructor what she means by “motion” –Math instructor waving her hand “You know - movement” –Physics instructor “That’s not what we mean in science by ‘movement.’ We mean moving from point A to point B” 21

Classroom observation of trained CSM 7th grade Science teacher Science Ed & Math Ed observers Density lab w/ Gummy bears –Teacher had students measure length & width to calculate the volume instead of using water displacement –A hazard in using web-based or commercial (other than approved Texas textbook) science lessons for teachers who lack sufficient content background 22

Classroom observation of trained CSM 7th grade Science teacher Language Issues Science ed observer remarked on the problem w/ using calculations for volume on an “irregular shaped object” –Science uses water displacement method to measure volume of an “irregular shaped object” –Science names the shape & calculates volume with formulas on “regular shaped objects” Math calls “regular objects” objects with congruent faces and angles, such as prisms, etc. 23

Correlated Science & Math Language Issues Same words, different meanings –Motion –Homonym? Synonyms: different words, same meanings CSM Dictionary 24

Same Words: Different Meaning = Homonyms Word/TermMathScience Arrow symbol (->)RayVector, Produces (chemistry) FormulaEquation, proportionRatio (H2O) Concretenumbers are considered concrete examples of the concepts applies only to things that can be physically experienced, numbers are considered abstract Constantvalue that doesn’t change, but can be represented by a letter variable that is kept the same throughout a type of investigation called an experiment 25

Same Words: Same Meaning = Synonyms MeaningMathScience Length & direction of a straight line drawn from the start to finish distancedisplacement Same on both sides of the process or equationbalancedEquilibrium There is no way to fold or rotate the object so that it overlays itself No symmetryasymmetry An object may be rotated such that it exactly overlays itself Rotational symmetry Radial symmetry 26

Correlated Science & Math Courses Differences Between Which Discipline was Primary Course development –Create a typical primary discipline syllabus –Identify links between the disciplines Science led courses very different from math led courses –Science led courses more coherent, perhaps due to the “purity” of math (math=math vs physics=biology) –Math led courses less coherent, perhaps due to the variety of sciences (physics, chemistry, Earth/space science, biology) that linked to the math concepts. 27

Parallel Concepts Concepts in Math and Science that have parallel relationships (i.e., ideas that “behave” the same) Acceleration & Slope  Acceleration is defined as the ratio of the change of velocity to the change in time  When the velocity is constant, acceleration is zero (slope of a horizontal line) When the acceleration is viewed at an instant, there is no acceleration (slope of a vertical line) 28

Misconnections Concepts in Math and Science that exemplify misconceptions, contradictions, or common errors (i.e., ideas that are connected, but not directly) Adding two fractions with like denominators – the quotient of the sum of the numerators and the denominator (i.e., (a/b)+(c/b)=(a+c)/b) Radiometric dating is used to determine the age of rocks. The age of rocks is estimated by the amount of a certain radiometric isotope contained in a specific rock. The formula to determine the age of a rock is (# of parent isotopes)/(# of parent isotopes + # of daughter isotopes) 29

Correlated Science & Math Courses Differences Between Which Discipline was Primary Linkages between the different science & math areas vary –Physics & Chemistry- algebra –Earth/Space Science - geometry –Biology - algebra Common math among all sciences –Measurement –Units –Ratio –Scale –Best estimate –Etc. 30

Obstacles Cited by Teachers Lack of adequate planning time Weak content knowledge/background of teacher Limited availability of integrated Model lessons Materials Lack of administrative support Training General materials Scheduling for collaborative planning $ for field trips 31

Correlated Science & Math Benefits Enhanced learning of Science & Math –Faculty –Teachers –Students ID language issues that may confuse students –Science “Reduce” vs Math “Simplify” Enhanced collaboration –Faculty –Students/Teachers Enhanced K-12 student performance? –Student pre/posttest scores (p=<.05) –’10 cohort has control classes –State test scores improve - only ID trends –No longitudinal student studies valid measure Texas Student Data access theoretically available 32

Correlated Science & Math: A New Model for Linking Two Disciplines Samples at –Correlated Science (Physics) Position & Math 5E Lesson plan –Correlated Science & Math Position PPt Questions ? Funded in part by: –Texas Higher Education Coordinating Board –Texas State University - San Marcos –Fund for the Improvement of Post Secondary Education –Texas Space Grant Consortium 33