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Published byDevon Hope Modified over 3 years ago

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**Integrated (International) Math Pathway vs Traditional Math Pathway**

The math department has spent the last year adjusting our curriculum to meet the common core standards. There are two basics claims for the transition to the CCSS and they are: students tend to learn more with student centered learning rather than teacher lectures; and that “less is more”. The latter meaning that fewer topics are covered but are attacked with more depth and rigor. While attempting to adjust traditional math courses (Alg 1, Geom, and Alg 2) to the new standards we have found it very difficult to narrow the topics in addition to adding some geometry, and quite a bit of statistics to the curriculum. It has also been a challenge to accelerate students to the newer higher level without also creating greater conceptual gaps than may already exist.

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**What Do They Look Like? INTEGRATED TRADITIONAL REGULAR HONORS**

8th Grade 8th Grade Math H. Math I Freshmen Math I H. Math II Sophomores Math II H. Math III Juniors Math III H.PreCalc Seniors PreCalc AP Calculus (Stats) AP Stats (Comp.Science) (Applied-Financial Algebra) (Math IV) TRADITIONAL REGULAR HONORS 8th Grade 8th Grade Math Algebra I Freshmen Algebra I H.Algebra II Sophomores Algebra II H.Geom Juniors Geometry H.PreCalc Seniors PreCalc AP Calculus (Stats) AP Stats (Comp.Science) (Applied-Financial Algebra)

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**How Do They Differ? TRADITIONAL INTERGRATED**

Objectives presented as separate concepts Taught via rules, procedures, and memorization Lecture based, teacher directed Continuous practice of procedures INTERGRATED Objectives from algebra, geometry, functions, math modeling, and probability and statistics, are interwoven Real world problems are investigated via lab-type experiences Teacher serves as facilitator and coach Collaborative learning Practice with a purpose The key here are the procedures used in the math instructional strategies. The integrated pathway focuses on student centered learning and investigations while the traditional is lecture/teacher directed.

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**How Do Those Attributes Align with CCSS?**

Common Core Attributes Focus and coherence Balance of Concepts and Skills College and Career Readiness Mathematical Practices Mathematical Practices Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning Hopefully it is clear that the integrated pathway is more closely aligned with the CCSS than the traditional pathway both in curricular content and instructional presentation.

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FACTS TO CONSIDER Although the percentage of US high school students enrolled in integrated mathematics courses is pretty small, the worldwide percentage of students enrolled in integrated mathematics courses would be about 99%. In the US K-8 mathematics is integrated, and in the rest of the world, K-12 mathematics is integrated. So about 12 million US students in Algebra I, Geometry, or Algebra II would be about 1% of more than 1 billion school-aged children worldwide. In college, in the workplace, and in everyday life, problems do not come labeled “Algebra” or “Geometry”. Thus, for success in college and careers, high school graduates need opportunities to bring together their understandings of number, algebra, geometry, and statistics. In other words, whatever the names of the courses, mathematics curriculum and instruction should provide opportunities for integrated learning. Our students are often compared to students across the globe and criticized for not measuring up. I have always felt the comparison has been unfair. The comparisons of students tested and content tested are like comparing apples and oranges. We can close the content gap through integrating our math curriculum as is done by 99% of the rest of worlds best scoring countries. Integrated mathematics also just makes logical sense. What problem in the real world clearly states before you solve it, “use Algebra or Geometry or Trigonometry”? I recall a real world problem recently presented our custodial staff at the stadium. The IHSA had changed to throwing sector to match that of colleges requirements. Our custodians at the stadium were unsure to make this adjustment. It took the assistance of a math teacher to solve this dilemma with involved geometry/algebra/and trigonometry.

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DATA POINTS From a paper prepared for the National Academies Board on Science Education and Board on Testing and Assessment for “Highly Successful STEM Schools”… COSMIC Study Results (Comparing Options in Secondary Mathematics :Investigating Curriculum) Tarr, Ross, McNaught, Chavez, Grouws, Reys, Sears and Taylan, 2010 Results as measured on three tests – two created specifically for the study and one standardized – measuring content, reasoning and problem solving

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Gain Scores (Posttest – Pretest) were positively correlated on three tests in favor of integrated curricula compared to traditional curricula. When controlling for %FRL (Free and Reduced Lunch), the magnitude of the correlation between Curriculum Type and student outcomes become significantly different than 0 in favor of the integrated curricula. Opportunity to Learn (OTL) was significantly and positively correlated with higher performance on all three outcome measures. OTL and %FRL are closely related. In other words, the findings suggest that using integrated math with students of poverty is a promising option.

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**Advanced Functions and Modeling**

Much has been written about how to close the achievement gap. Most educational gurus agree that students who take more rigorous coursework learn more, perform better on tests, and reach higher levels of post-secondary education. Advanced math enrollment (beyond three years) in one north carolina school after instituting integrated math curriculum Prob/Stats 39 Discrete 40 108 54 Stat/Disc 110 111 77 AFM Advanced Functions and Modeling 103 Precalc 188 193 171 170 131 IM4 Integrated Math 4 16 75 69 147 166 AP Stats 61 62 81 104 88 80 AP Calc 63 74 84 97 TOTALS 391 455 499 504 510 631 Shown here are the enrollment in courses beyond Math I II and III in one NC high school over a 6-year period.

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**Most Recent Information from PARCC December 21st, 2012**

PARCC high school assessments will include course-based tests in Algebra I, Algebra II and Geometry as well as equivalent integrated courses Mathematics I, II, and III. For the first three years of testing, the math will be based on an enhanced version of the final mathematics assessment (Algebra II or Math III) that include two additional performance based tests that draw on students’ knowledge of key concepts and skills from earlier high school math courses. Since Integrated Math series incorporate all topics of math content each year, at progressively high levels; it stands to reason that students might have better retention of previously learned material than in isolated content curriculum of traditional pathways. PARCC information released December 21st, 2012

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**Math Common Core Pathway Update December 18th, 2012**

Public Act that was passed in June of 2012, charged ISBE to “…coordinate the acquisition, adaptation, and development of middle and high school mathematics curriculum models to aid school districts and teachers in implementing standards for all students.” Public Act Model to be presented by March 1, 2013 “We have recently confirmed with the group of stakeholders that is creating the model mathematics curriculum that the curriculum will follow the INTEGRATED PATHWAY at the secondary level (which will also impact middle school math curriculum for those who offer a compressed or accelerated math trajectory for 6-8th grade students.” (Anji Garza – Director of Professional Development Lee/Ogle ROE#47) Illinois has decided that districts will have this INTEGRATED model curriculum that they can either adopt or adapt. “It has been our understanding, however, that the developed “model curriculum” will drive the assessment that will be ordered from the PARCC assessment consortium”. (Anji Garza) The most recent information conveyed in an from Anji Garza, Director of Professional Development at the ROE #47 As recently as Monday of this week, I was able to speak with Dr. Robert Mann, Professor of Mathematics at WIU, who is also a member of the State Model Curriculum Committee, charged with writing the new integrated curriculum that is to be presented by March 1st of this year for state approval. He concurred that it would be in our students best interest to forge ahead with a transition to an Integrated Math Pathway. His rational is: Although it remains to be seen whether or not the state will actually mandate the new curriculum, it is more closely aligned to the CCSS and PARCC tests will be available for both Traditional and Integrated programs.

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