What Makes a Pre-AP Math Course Pre-AP?

By Sharri Zachary, RME Mathematics Research Coordinator

Pre-AP courses are designed to prepare students for college. According to The College Board (2014), Pre-AP courses are based on the following premises:

• All students can perform at rigorous academic levels
• Every student can engage in higher levels of learning when they are prepared as early as possible

As we transition into implementation of the revised Texas Essentials of Knowledge and Skills (TEKS), we have to ensure that Pre-AP courses still fulfill the purpose for which they are intended. The revised TEKS have added a level of academic rigor for ALL students in the general education classroom. Students are expected to deepen their conceptual understanding of math concepts, including reasoning and justifying their solution. This means that students in Pre-AP courses have to be met with challenges that expand their knowledge and skills and push them a notch above, toward the next level. We have to be cautious to avoid students receiving Pre-AP credit for course work that is not Pre-AP.

Pre-AP Math Course Goals:

• Teach on grade level but at a higher level of academic rigor
• Assess students at a level similar to what is offered in an AP course (rigorous multiple-choice and free-response formats)
• Promote student development in skills, habits, and concepts necessary for college success
• Encourage students to develop their communication skills in mathematics to interpret problem situations and explain solutions both orally and written
• Incorporate technology as a tool for help in solving problems, experimenting, interpreting results, and verifying solutions

This is just a small list of goals for Pre-AP math courses. The College Board has official Pre-AP courses in mathematics (and English language arts) for middle and high school students offered through their SpringBoard program (The College Board, 2014). These courses offer rigorous curriculum and formative assessments consistent with their beliefs and expectations.

The College Board. (2014). Pre-AP. Retrieved from http://apcentral.collegeboard.com/apc/public/preap/index.html

Open-ended Assessments: Part 1

By Brea Ratliff, Secondary Mathematics Research Coordinator

As schools prepare for standardized testing this spring, many educators often wonder which instructional strategies will be most effective in terms of ensuring student success.

Beyond the scope of content, state mathematics assessments are measuring students’ ability to problem solve, recognize appropriate conjectures, communicate and analyze knowledge, and understand how mathematical ideas connect.

In short, these tests evaluate whether or not students are able to demonstrate the appropriate processing skills necessary for mathematics at each grade level.

On the STAAR Mathematics assessment for grades 3-8, mathematical processing skills are “incorporated into at least 75% of the test questions…and [are] identified along with content standards” (TEA, 2013). In order for students to perform well on an assessment designed this way, they should show success on formative assessments where they are challenged to apply their content knowledge while confidently using these skills. Over the next several weeks, we will explore a variety of open-ended formative assessments for students in grades 5 and 8, and students who are taking Algebra 1. These assessments can be implemented in a variety of ways. Depending on the makeup of your classroom, they could be a bell ringer, or the performance indicator during or following direct instruction. Many teachers also use them to start meaningful discussions with their students, as well as for an exit ticket or homework assignment. The possibilities are endless.

This week, let’s begin by looking at a few open-ended assessment ideas for 5th grade – all of which build upon student expectation 5.10(C) from the TEKS:

5.10(C) – The student is expected to select and use appropriate units and formulas to measure length, perimeter, area, and volume.

Level 1 – Assessments designed to develop proficiency in one student expectation. Assessments build around one particular skill are often helpful after when introducing a concept, or providing targeted intervention.

 Level 2 – Assessments designed to develop proficiency in two or more student expectations. The assessments for this level can vary in degree. While some may be designed to assess a combination of content skills, others may be written to include process skills. In this next example, we continue to look at 5.10(C), but also student expectations 5.3(A) and 5.3(B):

5.3(A) – The student is expected to use addition and subtraction to solve problems involving whole numbers and decimals.

5.3(B) – The student is expected to use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology).

For this next example, we assess students’ logical reasoning while addressing student expectation 5.16(A):

5.16(A) – The student is expected to make generalizations from patterns or sets of examples and nonexamples.

This assessment covers two content standards we have already addressed [5.3(A), 5.10(C)], and introduces two standards from Probability and Statistics and Underlying Processes and Mathematical Tools:

5.13(B) – The student is expected to describe characteristics of data presented in tables and graphs including median, mode, and range.

5.14(B) – The student is expected to solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

These are just a few examples to use with your students, but they are guaranteed to challenge your students to apply what they know about length, perimeter, area and volume in a new way.

Texas Education Agency. (2013). STAAR Assessed Curriculum, Grade 5. Retrieved from http://www.tea.state.tx.us/WorkArea/linkit.aspx?LinkIdentifier=id&ItemID=2147488330&libID=2147488329

Success With Elapsed Time: Part 2

By Cassandra Hatfield, RME Assessment Coordinator

Using the number line to facilitate students understanding of elapsed time can support understanding because it is a familiar model they have used with the base 10 system. Initially, in Success with Elapsed Time: Part 1 I discussed ways to support students in thinking about elapsed time out of context and support the transition to thinking about the base 60 system of time. In this part, I will focus on three basic underlying types of contextual situations that student’s encounter with elapsed time and how to use the structure of those problems to facilitate further use of the number line.

Read through these three problems, and consider what the problems have in common and what is different about them.

1	Sam’s school starts at 7:50 am. He goes to lunch is at 12:20 pm. How much time elapses between when school starts and when he goes to lunch?
2	Jessie has soccer practice at 4:15pm. Practice lasts for 1 hour and 30 minutes. What time will practice end?
3	Michelle’s mom needs her turkey to be done for dinner at 6:30 pm. It will take the turkey 4 hours and 15 minutes to bake. What time does the need to put the turkey in the oven?

Using this model, it is clear to see that each problem has 2 of the 3 pieces of information:

Basic Structure of Elapsed Time Problems

1
2
3

In working in classrooms on this topic, I found that it was effective to give students the opportunity to brainstorm in groups and then discuss the similarities and differences between the problems as a class. The students were able to realize the structure of the problems and that one part was missing without me providing the overarching model. By giving the students the opportunity to develop the model, I became the facilitator of the learning.

As you are planning for lessons on elapsed time, plan to give students a variety of different problem types. Many traditional textbooks only offer problems with a start time and an elapsed time.

Dixon, J. (2008). Tracking time: Representing elapsed time on an open timeline. Teaching Children Mathematics, 15(1), 18-24.