Algebra I in 7th Grade?

Understanding Implications for Teachers

and Schools

Terrie McLaughlin Galanti

PhD Candidate, Mathematics Education Leadership

George Mason University

and Students!

Sequencing Our Session!

What are the policies behind broad acceleration of Algebra I to 8th Grade or earlier?◦ What is driving the demand?◦ What happens to accelerated students in college mathematics?

What does acceleration look like in our schools?◦ Who is sitting in these classrooms?◦ What are their opportunities to learn?

What are the stories of acceleration in one Northern Virginia high school?

Where do we go from here?

Opening Question

What does it mean to

be “smart” in

mathematics?

Foreshadowing Challenges of Acceleration

Algebra I is the “new civil right”

(Moses, 1993)

How do we ensure that

“algebra for all” is not “dumbing

down” algebra?

The Algebra Initiative Colloquium

(Lacampagne et al., 1995)

Increasing Access to Algebra I

Percentage of U.S. students studying Algebra I in 8th grade or earlier

(Loveless, 2016)

16%

1990

47%

2011

44%

2015

What are the implications for mathematical opportunities to learn?

• More advanced mathematics course

taking (Gamoran & Hannigan, 2000;

Loveless, 2016)

• Higher mathematics achievement on

standardized tests (Smith, 1996;

Rickles, 2013)

• Increased likelihood of college

attendance (Spielhagen, 2006)

• “Statistically significant harmful effects”

for up to at least the 60th percentile of

mathematics readiness (Clotfelter, Ladd,

& Vigdor, 2015)

• 50% of all HS graduates entering 4-year

institutions have already studied calculus

(Carlson, Madison, & West, 2015)

• Only 20% of the 2015 high school

graduating class met the ACT STEM

readiness benchmark

Impact on Readiness for College

Mathematics

• Potential for reduced mathematical rigor and foundational proficiencies with broad access to Algebra I in Grade 8

(Nomi, 2012; Stein, Kaufman, Sherman, & Hillen, 2011)

• Accelerated students are struggling in college mathematics

– 44.5% of students who studied calculus in high school place into precalculus or lower in college (Bressoud, 2013)

– 67% of students entering Calculus I have already studied calculus (Bressoud, 2015)

– 33% of Calculus I course leave the course or fail

Comparing Beliefs of

College Professors

and High School Teachers

(Wade, 2011)

Data from Factors Influencing College Success in Mathematics (FICSMath) project

Preparing Students for College Calculus

NCEE (2013)What mathematics proficiencies do students in community colleges need?

What are the unintended consequences?

• High-achieving students and parents may idealize the fastest course trajectories at the expense of opportunities for reasoning and sense making

– Increasing numbers of students are accelerating the study of Algebra to 7th grade or earlier (Simzar, Domina, & Tran, 2016)

– Teachers may feel obligated to adjust advanced mathematics curricula to accommodate lack of readiness

– Students may be more likely to define success as speed and correctness

What do professional organizations say?

Three past NCTM presidents (Gojack, 2013; Larson, 2017a, 2017b; Seeley, 2005) have encouraged school divisions to emphasize powerful middle school mathematics curricula with algebraic thinking and proportional reasoning

Increasing acceleration of traditional secondary mathematics courses is not only “ineffective” but “counterproductive” (Bressoud, Camp, & Teague; 2013)

Curricula should not compacted before Grade 7 and that “placing students into tracks too early should be avoided at all costs” (Common Core State Standards Achieve Working Group, 2012)

The appropriateness of acceleration of secondary mathematics by more than one year for gifted students is a “dangerous myth” (p. 21) and “not beneficial for a majority of top students” (p. 22). (Sheffield, 2017)

An Emergent Phenomenon Hyper-acceleration of Algebra I to Grade 7There is a real danger in separating out children at a young age for active acceleration. They might handle the extra challenges in the 6th grade, but if they end up in a situation in which they are hitting Precalculus in the tenth grade, they are often not ready for the cognitive demands of the class. And all a school has succeeded in doing in this case is accelerating a child to a place of frustration. These students often report that they “loved math when they were little” but that “they no longer do now.” That can’t be our goal as parents or as educators.

Rachel Chou, Math Department Chair at Menlo School in Silicon Valley

Initiating Critical Conversations

Does your school sort students at a specific grade level on the basis of their perceived mathematical ability?

How do students’ mathematical experiences vary across programs for general, special, and gifted education?

How do groupings position students as more mathematically capable than others?

Huinker, 2019

Algebra I in Grade 7What does research say…1. My analysis of a national study

◦ (Characteristics of Successful Programs in College Calculus)

2. My qualitative pilot study◦ Focus group of 5 men who studies Algebra 1 in Grade 7 at the

same high school and are now majoring in STEM

3. My dissertation study◦ Five focus groups of 15 students who studies Algebra 1 in

Grade 7

From High School to College CalculusNational Survey Question: Does the level of acceleration of secondary mathematics courses predict end-of-course attitudes toward mathematics in first-semester college calculus?

Participants

◦ Freshman Calculus I Students (n = 2111)

◦ 62.5% of students (Grade 8 Algebra I and HS Calculus)

◦ 9.8 % of students (Grade 7 Algebra and HS Calculus)

◦ 27.7% (No HS Calculus)

Findings

◦ Overall decline in attitude in students from beginning to end of course

◦ Acceleration of Algebra I to Grade 8 had a positive impact on end-of course attitudes (b = 0.10), while acceleration to Grade 7 had no effect.

Dissertation Study ContextWest Valley High School

All participants

studied Algebra I in

Grade 7 and

Geometry in Grade 8

They contributed to

focus groups as

college students

“Coasting and Crashing”Stories of 5 Male STEM majors

Identities are “the dispositions and deeply held beliefs that students develop about their ability to participate and perform effectively in mathematical contexts and to use mathematics in powerful ways across the contexts of their lives”

(Aguirre, Mayfield-Ingram, and Martin 2013, p. 14)

For hyper-accelerated students, their identities of smartness in mathematics are malleable and evolve with exposure to more advanced mathematics and with time.

“Coasting and Crashing”Stories of Elementary/Middle School

I remember sort of the mentality just like going through elementary and middle school and it started when I was in the gifted program. It was like this expectation that if you don’t get like if you’re not in Algebra I (in Grade 7) than you are a dumbass.(Kevin)

If you weren’t going into Algebra I you would just be reviewing what you did in elementary school. I think almost a 1/3 of our class got 95% or higher percentile for that. A lot of people got 99. (Matthew)

Me and Adam Martinez we were the only ones who didn’t get a 500 (on the Algebra I SOL test) in our class, and I got ripped a lot.(Liam)

“Coasting and Crashing”Matthew’s story…

Most of us were just like coasting. We don’t like care that much. We’re just ready for the next thing.

You can kind of see where people stop coasting even in high school. As far as there were like people in Algebra II who were like all that accelerated up until Algebra II and Algebra II hit and something just clicked off for them. And they just crashed.

I think it is you kind of underestimate things as far as you kind of just like forget to study or you’re like, “I don’t need to study. I haven’t studied up to this point.”

“Coasting and Crashing”Collin’s story…

Everyone I had been with since middle school – the HL students – we were like coasting. HL1 your sophomore year, HL2 your junior year. I would just follow that, like I was the best of the best. I’m supposed to be, so I just take everything I must so that I could stay on top.

That partly comes from being the guy everyone says, “He’s just smart anyways”

When things got hard, I didn’t know how to deal with that. I’ll figure it out sooner or later, right? And then, you get the first “F” and you’re like OK maybe we you know should pump the brakes a bit.

“Coasting and Crashing”Kevin’s Story…

I am coasting when I don’t care about learning concepts.

Very often especially if you’re coasting, you’ll hit like a point and you won’t understand it and you will try to get an explanation, but the explanation makes no sense because in reality, there is some other concept from like a year or two back you just never learned you were able to coast without knowing it. You just knew the formula or whatever, but then that trips you up in the future.

At the end of the day, even if you are getting problems right, does that necessarily you are good at math if you don’t understand the concepts themselves? So, it’s hard to say exactly what being good at math means.

Identities of smartness…and their consequencesKevin: It’s hard to ask for help.

Matthew: Especially when you’re in this group like you don’t need to study like you don’t need help.

Liam: When you think everyone around you is getting an easy “A” and you are just sort of like uh it’s embarrassing.

Matthew: I also knew a lot of people who went to tutors were terrified to tell anyone that. I’m also here, I won’t tell anyone, don’t worry, I think people were like terrified to not be the best. I think it probably is like the biggest thing that our education is. Like you have to be the best all the time.

Edgar: Yeah. That was part of growing up for me. Learning to ask for help.

Back to our Opening Question

What does it mean to

be “smart” in

mathematics?

How can we reimagine opportunity to learn for our highly-accelerated students?

What mathematics are our accelerated

students learning?

Why do our accelerated students learn

mathematics?

How do our accelerated students learn

mathematics in our classrooms?

How do our accelerated students learn

mathematics in our schools?

Thank you for being here!

Please reach out if your would

like to talk more Algebra I

acceleration and mathematics

identities!

tgalanti@gmu.edu

ReferencesACT, Inc. (2017). The Condition of STEM 2017. Retrieved from https://www.act.org/content/dam/act/unsecured/documents/STEM/2017/STEM-Education-in-the-US-2017.pdf

Bressoud, D. M. (2013). Attracting and Retaining Students to Complete two-Year and Four-Year Undergraduate Degrees in STEM. The Role of Undergraduate Education. Retrieved from http://sites.nationalacademies.org/cs/groups/dbassesite/documents/webpage/dbasse_088835.pdf

BressBressoud, D. M. (2015). Insights from the MAA national study of college calculus. Mathematics Teacher, 109(3), 178–185. Carlson, M. P., Madison, B., & West, R. D. (2015). A Study of Students’ Readiness to Learn Calculus. International Journal of Research in Undergraduate Mathematics Education, 1(2)Clotfelter, C. T., Ladd, H. F., & Vigdor, J. L. (2015). The aftermath of accelerating algebra. Journal of Human Resources, 50(1), 159–188.Domina, T., McEachin, A., Penner, A., & Penner, E. (2015). Aiming high and falling short: California’s eighth-grade algebra-for-all effort. Educational Evaluation and Policy Analysis, 37(3), 275–295. Lacampagne, C. B. (1995). Introduction. In C. B. Lacampagne (Ed.), The Algebra Initiative Colloquium. Volume 2: Working Group Papers. Washington, DC: U.S. Government Printing Office. Loveless, T. (2013). Advanced math in eighth grade. Washington, DC: Brown Center on Education Policy, The Brookings Institution.Rickles, J. H. (2013). Examining heterogeneity in the effect of taking algebra in eighth grade. Journal of Educational Research, 106(4), 251–268. Simzar, R., Domina, T., & Tran, C. (2016). Eighth-Grade Algebra Course Placement and Student Motivation for Mathematics. AERA Open, 2(1), 2332858415625227. Smith, J. B. (1996) Does an extra year make any difference? The impact of early access to algebra on long-term gains in mathematics attainment. Educational Evaluation and Policy Analysis 18(2), 141-53.