Teaching Sequences for Short-Term and Instant Interventions

At the beginning of Tuesday morning’s session for grades 3-5 mathematics, participants described conditions that they would want to have in place in their “ideal” teaching community. Answers included the no “blame” game, common language approaches, vertical and horizontal teaming, time for data driven instruction and an endless supply of manipulatives.The goal of the day was to continue discussing intervention methods, specifically short-term and instant intervention within a lesson, and how these methods could help the participants’ ideal community become a reality.

Short-term intervention is based on the same cycle as the extended intervention: assess, analyze, plan and teach. After assessing, the analysis focused on different types of questioning strategies that could be utilized to determine where the error occurred, where the last place that the student seemed successful was, and what gaps might exist that could make the next objective difficult. Questioning or “break it down” techniques included providing an example, providing a context, providing a rule, providing a missing or first step, the roll back, or narrowing/eliminating false choices. Teachers need to exercise restraint during the questioning so as not to take too much time out of the lesson and lose the focus.

Strong questioning techniques come from a solid knowledge of the content, not just at grade level, but across the board. Content knowledge is obtained through text study, collaborative planning, peer coaching and professional development. Participants discussed how to plan short-term interventions, which used the same process described in Monday’s post, but on a much smaller time scale. Teachers need to decide when a short-term intervention is more appropriate for supporting a student than extended intervention. Teachers also need to determine what they need to develop in themselves so that they can quickly craft effective short-term interventions.

The session concluded with reflection on a professional reading by T.R. Wang. This one quote seemed to summarize the objective of the presentation: “…one is to study whom you are teaching, the other thing is to study the knowledge you are teaching. If you can interweave the two things together nicely, you will succeed.”

Materials for this session are available here.

Supporting Students with Disabilities: The Modules and Beyond

In one of Tuesday’s sessions for grades 3-8 ELA, “Supporting Students with Disabilities: The Modules and Beyond,” participants were introduced to the four A’s of Intervention:

  • Anticipate – How do you anticipate student needs?
  • Assess – How do you assess the results of the instructional decisions that were made in a lesson?
  • Act – How do you plan to act to meet student needs?
  • Analyze – What do you do to analyze the results?

The teachers then saw the four A’s in action by watching videos of teachers in their classrooms and talking about how the teachers used the A’s with their students. Much time was spent on reflection and considering the information gained in Monday’s sessions regarding intervention strategies. The goal was to learn about how teachers can use these strategies to support all their students, not just students with disabilities.

The materials for this session are available here.

Crafting a Teaching Sequence for Extended Intervention

The focus of Monday’s session for grades 3-5 math was how to craft a teaching sequence for extended intervention. Participants worked through the entire process of developing a sequence of module lessons that could be utilized for remedial purposes, filling in learning gaps or supporting enrichment. The day started with examining three types of problems encountered in fourth grade. Participants were then asked to focus on just one of the problems and discuss/think of a sequence of related math problems that would lead to a student being successful at the problem at large. Discussions were centered on the idea of how teaching must be collaborative, not an isolated task. Teachers need to play off of the strengths of their fellow teachers in order to help solidify the vertical foundation being built through the Common Core standards. One highlighted belief was that ”A teacher’s pedagogical content knowledge of the grade levels preceding and following his or her own impacts students’ success daily and is the primary engine necessary to meet the needs of all students.” With that in mind, participants started learning how to build a ladder from a point of strength to the objective.

The process for developing the teaching sequence for intervention is based on a cycle that starts with assessing the student, analyzing, developing a plan, teaching and then re-assessing. After assessing the student (using the module assessment), teachers analyze student work using a mathematical practices protocol that helps identify strengths and weaknesses and also aids in developing questions that can be used to help identify the error or where the “lost” has occurred. In other words, teachers need to find where the crack in the foundation is located and where the last point of success is located. Once identified, teachers can read the corresponding module overview and find where in the overview of module topics and lesson objectives the breakdown occurred. At what lesson or lessons did the crack first appear? Once the crack is identified, teachers can now work on constructing a ladder of complexity, but keeping in mind that traveling up the ladder must be able to be done efficiently. Each rung of the ladder is intended for a 20 minute activity, with the top of the ladder being a task aligned to a final objective. Ladders or intervention plans should not exceed 3 weeks in length.

Strategies for finding the vertical links amongst grade levels included looking at the curriculum map, curriculum overview, foundational standards and the Common Core standards checklists found on EngageNY. Much time and energy was spent on researching within topics and lessons across grade levels to find activities or lessons that help aid in teaching the sequence more deeply. Groups made an illustrated poster to share the sequence and then spent time creating “second” chance assessment questions that allow students to experience and see their growth first hand.

Time and pacing came up as an area of concern. Most agreed that the process presented would work well in aiding AIS instruction. The point was really driven home that teachers need to utilize the strengths of their other grade level teachers on where to find foundational lessons in the modules that directly link to the final objective.

Materials for this session are available here.

Meeting Students’ Needs; Grades 3-8 ELA Module Updates

During today’s 3-8 ELA sessions, Expeditionary Learning focused on meeting students’ needs by providing participants with transcripts of actual moments observed in classrooms where the modules are being used. The transcripts included exchanges between teachers and their students of various levels of language acquisition. Groups discussed the intervention strategies used by the teachers in the transcripts. They also talked about other interventions the teachers could have used to help more students be successful. Discussions resulted in a great exchange of ideas and the sharing of strategies that have been successful for some and not so successful for others. Teachers reflected on the day’s learning about teachers’ questioning, probing and responding habits in the classroom.

Expeditionary Learning also provided an update on some of the ELA modules currently in revision:

  • Grade 4 Module 1A (previously Module 1) is under revision by NYSED and will be posted this summer. This module will still focus on The Iroquois, but it will include Eagle Song as an optional independent read. A new addition will be The Keeping Quilt which will be used as a read aloud and will only require a teacher copy.
  • A new option for teachers will be Grade 4 Module 1B, a module with a focus on poetry. Texts will include A River of Words: The Story by Jen Bryant (teacher copy only) and Love That Dog by Sharon Creech (one per student).
  • Grade 5 Module 4 is also undergoing some revisions. The text Eight Days will remain, but Dark Water Rising has been removed. Unit 2 will be revised during the 2014-15 school year, with no new texts being required.

Modeling with Equations and Functions

In today’s Algebra I session, participants explored the lessons in Module 5 of Algebra I, “A Synthesis of Modeling with Equations and Functions.” The module is packed with experiences that pull together the cohesiveness of the topics covered throughout the year and is loaded with application problems that develop fluency, but not computational fluency alone. This module drives home the fact that students need to be fluent in pulling their prior knowledge to the forefront in a variety of settings. This can be a challenging and interesting task to incorporate into the design of a lesson. Some key problems/exercises that participants looked at were the following:

Lesson 1, Exercise 2:
Students examine a graph of a function and recognize the function type and state the parent function. Students then need to be able to identify what transformation took place to the parent function to produce the graph, a more challenging task and perhaps one that students will struggle with. Lastly, students need to write the equation of the function. Lesson 2, exercise 2 had some concrete examples of the same nature.

Lesson 2, Exercise 4:
This exercise was an excellent example of allowing students the opportunity to communicate their conceptual understanding and critique the reasoning of others.  This problem is highly recommended and generated great discussion amongst the crowd.

Lessons progressed through problems that had students analyzing data sets, verbal descriptions and graphs.

Lesson 4, Exercise 2:
This exercise provided an opportunity for students to determine what type of function best models the data displayed in a graph. The graph appears to be a quadratic, but as participants learned at the last NTI, looks can be deceiving. As it turned out, the graph was quadratic and it provided an opportunity for the sharing of great techniques of solution. These strategies included solving a system of equations, using the second differences (common theme of the day) to find the leading coefficient for the quadratic, and estimating the other root and working backwards to find the quadratic. This problem was well received because of the opportunity it presented for students to be successful.

Another good example of a modeling problem was the opening exercise discussed for Lesson 5 that involved exercise time and rest time for interval training. We quickly learned as a group that part of the modeling process is learning how to handle any assumptions that are made and determining how those assumptions will affect the desired outcome.

Finally, participants looked at problems that involved modeling exercises from sequences and investigated the question: should we believe in patterns? Participants examined an interesting example that involved the appearance of a pattern from points on a circle that crashes after the 6th term. The example reinforced that a pattern can disappear.

One of the biggest takeaways of the session is that students need to be able to recognize whether they have enough information to be sure that the function they have created is an accurate representation of the data being described.

The presenters touched briefly on how to support learning throughout this module and any other module. They shared three key points:

  1. Be attentive to language. Teachers need to be clear with their mathematical vocabulary. They need to accurate and precise with the mathematical language being used in the classroom, so this can transfer to the students.
  2. Teachers need to remember that conceptual knowledge precedes fluency.
  3. Conceptual understanding is achieved through strong questioning techniques, progressing from the concrete-pictorial-abstract, and knowing and showing the progression of the content.

The materials for this session are available here: