Thank you for watching our video presentation. This is an early stage design and development project in its second year; we are continually revising and improving our newly developed K-2 materials based on what we are learning from field testing in urban, suburban, and rural school districts across the country. We are most interested in discussion about the use of formative assessment, learning trajectories, and visual representations to improve mathematics teaching and learning. We look forward to hearing from you!

We hope you will enjoy this small look into the work we are doing around formative assessment and learning progressions. It is really exciting to have the opportunity to extend the OGAP work to K-2. 

 This work is so powerful and truly impacts teachers understanding of the learning progressions in additive reasoning. It has been the most powerful professional development my system has ever done!! 

This video is just a brief overview of OGAP additive and how it can be used to impact instruction. I first learned about OGAP in the fall of 2017 when I attended a local four day intensive professional development. I am a special education teacher for grades 1 and 2. I can honestly say that OGAP additive is the one process and prodcedural training that all teachers in younger grades need, especially interventionists and resource teachers. Since the training, I have been able to see the specifics areas of weakness that are prohibiting my students from making progress within the general education curriculum. These are areas and gaps that don’t just go away and have to be addressed for students to truly grasp and have conceptual understanding of numerical operations and math problem solving along the mathematical development required to attain mastery of grade level skills. 

This work has completely changed K-2 math instruction at my school.  Teachers have developed a deeper understanding of the mathematical content they are teaching in addition to the importance of early numeracy as the foundation for all other mathematics.  Teachers are able to move beyond identifying student work as right or wrong and are looking for the strengths in all student work so that they can work to move students forward in their mathematical reasoning.  Every teacher who attends OGAP comments that this is the information they have always wanted and that it is the college class they wish they would have had before beginning their teaching.  It is truly life changing.  

Thank you all for your comments about the impact this work has had in your schools and districts. One thing we hear a lot is that elementary teachers have not had access to this information on how young children learn mathematics and develop understanding of counting, number, addition and subtraction. Professional learning takes time and resources. There is a lot of pressure to bypass that and just give teachers and students the right curriculum materials or technology-based programs to use, rather than investing in teachers and supporting them in developing their own understanding so they can make more informed instructional decisions. 

OGAP has been the game changer in teacher content knowledge in mathematics for lower elementary.  This formative teaching and learning process has helped teachers become reflective instructional facilitators in their classrooms.  School administrators have been enthusiastic about the change in the learning environment in the school after the teachers have given OGAP the commitment and proper implementation.  OGAP has also changed my mathematical thinking in my daily life. There is now knowledge about numbers that can not be taken away from the daily life of teachers, students, school leaders, and adults. 

The videographer has done a very professional job in taking and editing the work.  The subject is clearly and concisely portrayed so that teachers can learn of useful strategies in teaching children critical subjects of interest. 

I am a huge OGAP supporter.  I have used many of the strategies to help my students progress through their math understanding.  It is a great resource and program.  It helps teachers understand the framework of additive strategies and ways to be more deliberate  during instruction.   

This work is extraordinarily powerful and has limitless potential to help us develop that deep number sense that will stay with our students for their entire lives. The focus is on high quality instruction with an emphasis on supporting teachers' understanding of both the mathematics and their students' work. Thank you for the brilliant contribution to our profession. 

Our school system has used OGAP for approximately four years.  The way in which students are able to think about problem solving and their fluency in strategies is amazing.  As an adult, it has changed my teaching.  The process is methodical and thorough.  The assessments are so helpful in guiding students to greater mathematical understanding. 

The testimonials for this project speak to the success that teachers feel they have both in their own mathematical development and the mathematical development of their students.  Seeing a small snippet of what you are doing for early ages and hearing you say that you have worked with older students, I wonder if you can talk a bit about the early development of algebraic thinking and how and when that occurs in your program.  Thank you.

OGAP has had a tremendously positive impact on teaching ad learning in our district!  The investment has paid significant dividends.  

Great video! OGAP sounds like a powerful tool for increasing teacher capacity and improving instruction. From the video and your summary, it seems like much of your focus is on supporting teachers to use LTs as a lens for analyzing students' strategies on assessment tasks. In your PD (or through features of the tool), how do you support teachers to act on their analyses (e.g. adapting instruction or guiding classroom discourse)? What does that support look like and how quickly do teachers in your program understand and embrace LTs for use in instruction? Have you experienced any challenges in this regard? Thanks and great work on your video!

Hi Michael. Thank you for your questions. Yes, supporting teachers to use LTs as a lens to analyze and respond to student thinking is the focus--not only through assessment tasks, but throughout instruction. There are 3 parts to the formative assessment cycle-- assessing, analyzing, and responding--and the instructional response is definitely the most challenging for teachers. However, the progression (LT) not only serves as a tool for analysis, but also for response. Once teachers identify the level of student thinking represented in the student work, the progression provides guidance as to the appropriate next step. For example, if a student is counting on by ones to solve an additive problem, the next step is not to teach the  standard algorithm (which is at the top of the progression). Rather the next step might be to use a model that incorporates groups of ten ones (like the bead strings shown in the video) to support the student in unitizing and developing a counting by tens strategy. If a student is jumping by tens on the number line, then the next step would be to help them jump by multiples of ten (as you see a teacher highlighting in the classroom clip). Teachers find that the progression give them this guidance but they also need to have the autonomy and confidence to make those decisions, sometimes against the recommendations of the curricular materials or pacing guides that they are using. This can be a challenge. Maybe some of the teachers who have posted here could also respond to this!

We are also currently studying how teachers are understanding and making sense of the LT in sorting and responding to their own student work, and while that research is very much in progress, we are seeing that there is a progression of their own understanding. This has been very useful for us in thinking about how to improve the LT progression and the PD, and also in better understanding how teachers take this up in practice, often in ways we didn't anticipate.

OGAP seems to be as much a tool to support student understanding and learning as it is to supporting teacher learning - such an important combination for the teaching and learning of mathematics.  I'm curious about whether on not you can envision OGAP being utilized in pre-service education? 

Thanks for the comments and question Karen. When we first began the OGAP work we didn't fully appreciate the importance of the teacher PD and thought the OGAP tools could stand alone. We learned quickly that using the tools for both teacher and student knowledge was vital to impacting classroom practice. 

We do have some pre-service instructors who are using the OGAP progressions and other materials in their courses. They have found them to be very effective with pre-service to expand content knowledge and strategies and thinking about student work in planning for instruction. 

We really try to emphasize the idea that the progressions help you design instruction and provide access to the content for all students and this is an important message for pre-service teachers to understand.

I am interested to hear more about how your additive LT integrates strategies with problem structures and problem situations. Can you share how the framework was developed and whether it is available to share?

This work sounds really powerful!

Thanks for sharing more. I can see how your tools and training would support teachers in formative assessment. I appreciate how your additive progression includes number concepts that are necessary to support using procedures with understanding.

I also appreciate your comment that the progression helps categorize children's strategies, not the children. In my work with teachers, we are always trying to move away from thinking in terms of "my low kids" and "my high kids" to thinking about what student work reveals about their understanding.

Hello Caroline, Nicole, and Beth,

This program sounds wonderful!  I teach 8^th grade pre-algebra, algebra, and geometry in bucks county and graduated with my undergrad in secondary ed, math from Penn State University.  I often think about the extensive methods courses that our elementary school teachers have gone through in order to prepare them to effectively teach multiple disciplines.  However, I also know that there are times when our elementary school teachers may not feel as confident in the ways to formatively assess math and to ensure that our students are learning at a level that promotes deep understanding. I think that OGAP sounds like a great opportunity to help teachers focus strictly on ways to analyze student thinking and move forward with instruction.

Do you have a program that currently exists for grades 3 through 6? Does this program look similar to the one that is implemented at the K through 2 level?

I am also interested in knowing if the teachers that participate in OGAP are supplied with the materials to implement the items from the online item bank.  It looks like there are a lot of manipulatives being used within the classroom to help students create an understanding.  Does the additive reasoning framework help show teachers how to utilize the manipulatives effectively in the classroom?

Being a secondary math teacher, it is important for us  to understand how our students are being taught the mathematical concepts at the elementary school level. Creating a deep foundation of number sense is crucial for our students to be successful at the secondary level.

Hi Nicole...Thanks for all your questions. Yes we do have OGAP Multiplicative Reasoning and Fractional Reasoning for grades 3-5/6. We also have proportional reasoning for grades 6-8. You can see more about all of these at ogapmathllc.com. You can also find contact information for me and I would be happy to answer all your questions and describe our program. Our original development work was in these other content areas and then we partnered with Penn and Caroline to expand our work to the K-2. Teachers do have access to all the materials as part of the training. The item bank is one of the core components of our work along with the progressions and the PD. I look forward to hearing from you.