Hi Wendy,

Thanks for making the first post! :)

The teachers participating in the project receive professional development during the year (one day program overview during the summer, and approximately once a month during the academic year). The professional development focuses on reviewing implemented lessons and previewing upcoming lessons as well as on student thinking associated with the lessons. The teachers also have access to project team leaders if they have additional questions.

The LEAP materials are implemented as a replacement to the mathematics that would normally be planned for a particular day. Note that our data also show that the "loss" of the normal lessons that are replaced by LEAP lessons does not effect student achievement on state standardized assessments.

We are collecting assessment data each year using both a LEAP-designed assessment and state-mandated standardized (end of year) assessments. We designed the LEAP assessment given that state standardized assessments typically are not designed to measure early algebra learning.

We do not have any parent or community materials available, but that is an excellent idea. As we move forward with the LEAP materials, that will be something that we will plan to include.

Again, thanks for viewing and for your thoughtful questions. 

Thanks Miriam for visiting and for your comments.

By comprehensive, we mean an approach that considers the "entire" domain of early algebra; for example, there has been a lot of prior research on specific aspects of early algebra that has provided important results about children's algebraic thinking (equal sign - Carpenter and colleagues; generalized arithmetic - Schifter and colleagues; symbolic representations - Carraher and colleagues, to name a few); however, few, if any, studies have considered the entire domain. We also view comprehensive as meaning a long term view - spanning grades rather than a single grade. By business-as-usual, we mean elementary curricula that are primarily arithmetic-focused, with perhaps some early algebra content appearing here and there.

Our project website provides some examples of tasks and lessons as well as concepts that we have found to be particularly productive in fostering children's algebraic thinking. As an example, we have found work with open number sentences (e.g., 3+4=_+5; 7=2+_) to be examples of tasks that help promote a relational view of the equal sign and that provide students experience with number sentences in non-typical formats (3+4=_ versus 8=8 or 3+4=1+_+3).

Given we are now entering the fourth and final year of our large-scale study, and are bringing our small-scale study to a close, we hope the challenges at this point are not too unexpected! :)

Our fidelity of implementation data show differences in teachers' implementation of our early algebra intervention (and subsequently, their students' performance), thus one challenge we face moving forward is trying to understand how to better support teachers in their efforts to implement our early algebra materials with fidelity.

Hi, Eric and Maria.

Following up on one part of your research, namely measuring fidelity of implementation:

Can you share a bit about how you are measuring fidelity in your research?

And, based on what you have measured, what differences in teachers' implementation seem particularly important in terms of students' opportunities to learn (or students' performance)? 

Hi Dan,

We are assessing fidelity using multiple measures. We utilize self-report measures, specifically teacher logs and interviews, as well as classroom observations. Teacher implementation logs are completed by teachers in our experimental group after each lesson, while regular classroom logs are completed monthly by all teachers (both experimental and control). Interviews are conducted by a researcher on our team three times a year with a subset of teachers. Observations are also conducted with a randomly selected subset of teachers, typically around 50 per year. We observe each classroom twice and code the observations on a variety of variables.

To date we have primarily used the self-report measures as descriptive data. However, we have run analyses looking at the relationship between measures of FOI within the observation and student performance on both a standardized assessment and an assessment created by the project. While analysis is currently ongoing, we are seeing some impact of teacher implementation on student performance. For example, in one analysis we found that teachers' efficiency, their handling of student difficulty, and their inclusion of student ideas was positively related to student performance on the LEAP assessment.

We are in the beginning stages of analyzing the Grade 5 data, and so will have more to say about both student performance (looking across Grades 3-5) and teacher implementation, as well as links between the two in the near future.

Thanks for "stopping by" Jeremy!

If a teacher or school is interested, they can learn more about Project LEAP, its early algebra curricular materials, and LEAP Professional Development, by reviewing our project brochure: Project LEAP

Excellent question Gladys. We are not examining teacher knowledge as part of our research, however, anecdotally, it does seem that to some extent the PD and their implementation of the LEAP lessons are enhancing teachers' knowledge. 

With regard to your second question, the short answer is yes. The lesson materials have gone through multiple revisions as we have taken into account both student and teacher experiences with the materials since Project LEAP's inception (almost 8 years ago). And in the current work (our large-scale study), teachers are expected to teach the concepts and practices targeted in each lesson, and we provide suggestions on ways in which to engage students in the lessons, however, we are not requiring that teachers follow a "lock-step" script of implementation. Much like the implementation of any curricular materials, teachers often use their professional experience and knowledge to adapt for their particular contexts.

Hi Sybilla,

Many students start with drawing on many of the tasks in our lesson materials and, for some students, this seems to provide the scaffolding that often leads to a generalization (expressed oftentimes with words, and then symbolically). Teachers often find that the diagrams help students to articulate a relationship in words, and expressing the relationship in words can then lead to the development of symbolic notation to represent the relationship.

Perhaps I did not provide enough explanation regarding the results: At baseline (i.e., Grade 3 pre-test) there was no statistically significant difference between the two students groups, and in each subsequent year of the intervention (end of Grade 3, end of Grade 4, and end of Grade 5), the intervention students significantly outperformed the comparison students.