Linked Learning: How does it Influence the Required Preparation of Mathematics Teachers in California? Agnes Tuska Department of Mathematics California State University, Fresno Abstract During the 2013-2014 academic year, a group of teacher educators at California State University, Fresno, has formed a learning community in order to study the implementation of Linked Learning in some pilot schools of California, and to align the university s teacher preparation program with the new demands of the Linked Learning approach. The learning community consisted of about ten active members from various disciplines. I was the sole mathematics educator of the group. This paper is the summary of my subject-specific reflections. Introduction The James Irvine Foundation in California has created ConnectEd : The California Center for College and Career in April 2006. ConnectEd works with educators, policymakers, industry, and other stakeholders in California to promote the development and implementation of multiple pathways to college and career. The multiple pathways approach has been renamed to linked learning in 2010. The four core components of Linked Learning are: (1) Rigorous academics; (2) Career-based learning in the classroom; (3) Work-based learning in professional settings; and (4) Integrated student supports (counseling, supplemental instruction, etc). The Linked Learning approach promises to improve school achievement, high school graduation rates, and access to higher education; increase the educational and work opportunities for vulnerable students; and prepare California s population of young people for responsible participation in public life. Done right, it could also respond effectively to demographic shifts and address future economic challenges. (Oakes & Saunders, 2010, p. 15). According to the Facts for Educators and Administrators sheet in the LinkedLearning.org website, the momentum is growing to expand the Linked Learning approach across California. There were 63 school districts and county offices of education involved in the pilot program, and the State of California has provided $250 million for the California Career Pathways Trust, a grant program to promote collaboration between schools and employers for
the development of work-based learning opportunities. Additional grant opportunities of $250 million are open in 2015 to promote district and community college partnerships. The evaluation of the first five years of Linked Learning pilot programs is very promising. For example, compared with their peers, Linked Learning students were more likely to report that high school prepares them for working with people in professional settings (+21 percentage point); they have improved presentation skills (+22 percentage point); they have support navigating decisions on what they plan to do after graduation (+12 percentage points); they are able to judge whether they can trust the results of an online search (+17 percentage points); they see connections between what they learned in class and the real world (+10 percentage points). Moreover, Linked Learning students on average have earned 6.9 more credits by the end of 10 th grade than similar peers at traditional high schools, and were 5.2 percentage points more likely to stay within their district through 12 th grade rather than transfer or drop out. (Guha et al., 2014) Highlights of the school visits through the lens of a mathematics educator A pathway or academy is a career-inspired subject that is infused into academics. Students who have chosen a pathway take courses from freshman year through their senior year, focusing on that subject. For example, students in a forensic science pathway (offered in a high school at Fresno Unified School District), may have a crime investigation as the main project for a semester. During that semester, students pay particular attention to the psychological profiles of characters in a drama or novel they read, write a crime scene report, or play roles as witnesses or investigators as part of their English class. Meanwhile, they learn about bullet trajectories, force, and acceleration by investigating the hypothetical crime scene. The mathematics component may include the analysis of testimonials, where student look for contradictions, and use logic to make a case for the conviction of a suspect, or use graphs and functions to represent the relationship among variables in the crime. They may also use statistical data in building their case for a conviction. Students typically work in teams, heavily use the internet as resource, and make written and oral presentation of their findings. Their studies are supplemented with help from regional employers and experts who donate their
time and expertise to regularly provide guest speaking, demonstrations, job shadowing, and paid and unpaid internships to the students. Our learning community of teacher educators have made two visits to Porterville Unified School District, where each high school of the district provides one or two of the following pathways: Academy of Digital Design & Communication; Academy of Law, Justice and Education; Academy of Engineering; Academy of Performing Arts; Multimedia and Technology Academy; Environmental Science Academy; Academy of Finance; Academy of Health Sciences; Alternative Energy Resource Occupations; Academy of Emerging Agricultural Technology. We were touring the schools with the help of trained student guides. One of our student guides has attended the Academy of Health Sciences because his main interest was to become a medical doctor. He has completed the Advanced Placement Calculus course since it was an expectation for application to medical school, and has also completed scientific projects that involved linear algebra and differential equations. He had self-confidence, work experience in a hospital, and felt morally committed to serve as a doctor in a rural area such as the place he has grown up because he has realized the negative effects of lack of adequate medical personnel in his locality. The class with the most mathematical content in that district dealt with conversions of units and mixture problems. Since students were aware of the dire implications of making mistakes with dosage of drugs or mixing acids or intravenous fluids, most of them have paid attention and persevered to find and justify the correctness of their answers. Communication, collaboration, and the enjoyment of successful teamwork were evident in most of the other classes we have visited in other sites, too. For example, in a high school in Sacramento, where the district has chosen only one particular high school to be the Linked Learning site, but the student demographics of the school remained the same as of the district, we have observed a class working on their senior engineering project: preparation for a nationwide robotics competition. The students have chosen a project manager, and have worked on various aspects of a complex task. Some students were using a 3D laser printer to create a required piece of the robot, while others were running state-of-the-art computer simulations to optimize the robot s performance. Two female students stayed in the school lab till 3 a.m. the previous night (with parental approval and cell phone contact) to generate the data required for some other members of the team for further progress. This kind of enthusiasm and commitment was hardly ever heard of
in high schools, outside of possibly some sports teams before a big game in a championship. Implications for the preparation of mathematics teachers The teachers in Linked Learning schools have been expected to intensively collaborate on designing main projects for their students across disciplines. As the principal of the school in Sacramento stated, his teachers have earned almost double of the typical district teacher salaries, but, in return, these teachers were expected to work long hours, including weekends, on school projects. Many teachers left because they did not fit into this hard working, demanding environment, but the teachers who remained there became totally committed and enthusiastic about their creative work. Our visiting team of teacher educators was very impressed by the financial resources of the schools, too. Unfortunately, the funding of public education in California has been severely cut many times. Our university has much less freedom and opportunity to fund any kind of student project, and faculty would be rarely compensated for any kind of extra expense or extra time and effort put into student projects. We also noted, that many of the teachers were career changers, such as aerospace engineer poet who became English teacher, computer scientist from the Silicon Valley who became engineering lab teacher, researcher chemist who became science teacher, just to name a few. They could make the career change with minimal or no pay cut to Linked Learning schools, but would not have been able to go to other schools without substantial financial sacrifice. Therefore, implications for teacher preparation in general include the request for better funding of our teacher preparation programs, and the demand of higher pay for attracting committed, creative educators at all levels. Implications for mathematics teacher preparation include the need for more collaborative, project-based learning during the subject matter preparation program. Active- and inquiry based-learning, and oral and written presentations of mathematical investigations should replace many of the lectures by professors. As California became committed to the Common Core State Standards in mathematics, the teacher preparation had to focus on instilling, as habits of mind, into prospective teachers the standards for mathematical practice for K- 12 education (California Department of Education, 2010, revised in 2013). The 8 Standards for Mathematical Practice are as follows: 1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Fortunately, the Linked Learning practices are directly aligned with these mathematical practice standards. Project-based learning and team work promotes sense making, perseverance, reasoning, and critiquing the reasoning of others. The use of appropriate tools, precision, use of structure, and the realization of repeated reasoning is part of collective problem solving. One of the most challenging practices for mathematics teachers in traditional schools is modeling with mathematics: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Modeling is hard for mathematics teachers who teach mathematics in isolation, but it comes naturally for mathematics teachers who work on real life projects with colleagues across disciplines and with outside professionals on educating students who are attending internships, participate in job shadowing, and are highly motivated and engaged in the societal and working issues of a career pathway. The professional development opportunities and requirements in the process of implementing the Common Core Standards in all subject areas will require intensive school-wide collaboration. The collaborative environment of Linked Learning schools will put teachers of those schools into advantage over the teachers of traditional schools. In conclusion, it seems that the best preparation for effective work at a Linked Learning environment for a prospective mathematics teacher is the same as the best preparation for effective Common Core Standard-based instruction at any school for a mathematics teacher: Learning rigorous content via challenging assignments and projects that require clear communication, collaboration, team work, and individual responsibility, in a supportive and inspiring learning environment. References California Department of Education. (2010, revised in 2013). California Common Core State Standards: Mathematics. Electronic version. Retrieved from http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf
Guha, R., Caspary, K., Stites, R., Padilla, C., Arshan, N., Park, C., Tse, V., Astudillo, S., Black, A., & Adelman, N. (2014). Taking stock of the California Linked Learning District Initiative. Fifth-year evaluation report. Menlo Park, CA: SRI International. Retrieved from http://www.sri.com/work/publications/taking-stock-california-linkedlearning-district-initiative-fifth-year-evaluation Oakes, Jeannie and Saunders, Marisa (Eds.). (2008, second printing 2010). Beyond Tracking: Multiple Pathways to College, Career, and Civic Participation. Harvard Education Press, Cambridge, MA.