Diagnostic Interview as a Tool in Math Instruction

When students are underperforming in math, teachers start the intervention process by asking them, “Why?”

Many teachers want feedback, formally or informally, from their students. And according to a new article in Teaching Children Mathematics, the role of diagnostic interviews as a form of math intervention has been shown to be effective.

One-on-one meetings between a student and a teacher can help to determine what teaching techniques work best. The article points out that this approach is not about evaluating the student or teacher, but an opportunity to let the student speak. While diagnostic interviews may include an assessment of a student’s academic level, the goal is to discover the deficiency and the reason for it.

For help developing a diagnostic program that can be applied in your classroom, refer to: How Do My Students Think: Diagnosing Student Thinking published by the American Psychological Association. Scholastic offers information about incorporating diagnostic Interviews into math assessment as part of the Math Reasoning Inventory.

Have diagnostic interviews worked in your experience? How can they best be implemented in schools where personalized lesson plans and individualized assessments are more challenging to create?

Share your thoughts below.

Professional Development for the Common Core

As the introduction of the new Common Core State Standards (CCSS) in math approaches, teachers must prepare to teach with these benchmarks in mind.

Fortunately, many resources are available. In Catherine Gewertz’s "Curriculum Matters" blog, she highlights the new Mathematics Common Core Coalition. The Coalition was formed in conjunction with several educational groups including the National Council of Teachers of Mathematics (NCTM) and the Association of Mathematics Teacher Educators (AMTE) among others. The NCTM has even set up a section on their website dedicated to the transition to the Common Core.

This new website offers resources about the curriculum and development of a Common Core assessment, as well as extensive professional development materials. These materials include webinars and e-seminars with videos, handouts, and demonstrations to provide ideas for implementing the Common Core State Standards. Becoming familiar with the content and format of the new standards will help teachers make the most of the Common Core.

As a new era begins in American math education, educators will take the opportunity to apply the best instructional practices to the material covered by the CCSS. The standards were designed by National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO) based on successful and effective models found around the country and the world.  Professional development resources like those offered on the NCTM website can help teachers make the Common Core a successful initiative.  

What about Differentiated Assessment?

It seems that every time I have a conversation with another educator about best practices, the words differentiated instruction come up. This term has certainly become a popular one in education and most teachers recognize the benefits of teaching to individual students' strengths. What follows from instruction, however, is assessment, and rarely have I heard (or used) the term differentiated assessment. In the urgency for educators to master the technique of differentiated instruction, there has been little focus on assessing students in a more individualized manner.

Douglas Reeves recently authored an article providing some suggestions for integrating differentiated assessment into classroom practices. At the heart of his suggestions is the idea of creating a “menu” from which students can choose. This idea is most easily started with homework assignments. Reeves suggests offering different levels of problems in 3 separate columns. Students have to choose a certain number of problems from any of the columns. In doing this, all of the students complete the same number of problems but not necessarily the same level of problems. Some students will start with easy problems and stick with them because they need more practice. Others will move on to more challenging problems at various points throughout the assignment. The idea is that students work to their ability level, and by seeing which problems students complete each evening the teacher gets a quick snapshot of each student’s comfort level.

Reeves extends this idea into other areas of assessment by suggesting that teachers offer different assignments with the same available point values. For example, one student may choose an assignment worth 100 points, while another student may choose to complete 2 smaller 50-point assignments. Students are completing the same amount of work but each student can choose an activity that is configured to best meet his or her needs.

These are just a few suggestions to get your brain churning about how to integrate differentiated assessment. Just as differentiated instruction took teachers years to research and master, it is likely that this skill will require the same amount of time. So, let’s get started…let’s take our instruction to the next level with powerful assessments that meet student needs.

Quantile® Knowledge Clusters in Mathematics Help Inform Instruction

Many thanks to our friends at MetaMetrics Inc. for contributing a useful guest blog entry about how teachers can match all students to the right instruction with the Quantile Framework for Mathematics.

The Quantile^® Framework for Mathematics is a tool teachers can use to make student test results useful at the classroom instruction level. A student’s Quantile measure (test score) provides information about which mathematical skills students are ready to learn in the classroom. These skills are called QTaxons. Once a teacher knows a student’s Quantile measure, the teacher knows which QTaxons the student is ready to be introduced to in the classroom. Underlying each QTaxon is a knowledge cluster that offers classroom teachers a wealth of information about the skills that come before the QTaxon skill and those that follow it. This information can be tremendously helpful in guiding decisions about instructional strategies.

A QTaxon is linked to prerequisite, supplemental and impending QTaxons that illustrate the developmental and inter-connective aspects that are so important in the study of mathematics. A prerequisite QTaxon includes the skills and concepts that should be addressed or mastered by the student before instruction on the focus QTaxon. A supplemental QTaxon includes skills that can enrich a topic or help teachers and students make connections across the spectrum of mathematical concepts. An impending QTaxon can provide insights into the levels of mathematics skills beyond the focus QTaxon.

Below is an example of a knowledge cluster in the Quantile Framework using a focus QTaxon about 'unit rates'.

QTaxon: “Calculate unit rates to make comparisons.”

This QTaxon has a Quantile measure of 830Q. (Each QTaxon has a Quantile measure that estimates its difficulty at the introductory level.) 

Prerequisite QTaxons:

1. Use proportional reasoning to solve problems. (530Q)
2. Identify equivalent decimals and fractions at the symbolic level, including simplifying fractions. Explain the equivalence. (710Q)
3. Write a ratio to compare two quantities. (210Q)

Supplemental QTaxons:

1. Convert measures of length, area, capacity, weight, and time expressed in a given unit to other units in the same measurement system. (820Q)
2. Describe the probability of an event using a fraction or ratio. (440Q)
3. Determine the ratio or rate of change of a relation given a table or graph. (810Q)

Impending QTaxons:

1. Use dimensional analysis to rename quantities or rates. (950Q)
2. Use scale factors to reduce and enlarge drawings on grids. (990Q)

With some Quantile information – the student’s Quantile measure, the Quantile measure of the focus QTaxon, and the Quantile measures of the prerequisite, supplemental and impending QTaxons – the classroom teacher can use assessment results to target instruction that addresses the needs of various populations of students in the classroom.

Consider the possibilities! By identifying the level of mathematics ability for students, educators can differentiate instruction, forecast performance on new material or assessments and benchmark progress throughout the year. The supplemental QTaxons in the knowledge cluster provide instructional tips on making connections across content strands and enriching instruction. The knowledge clusters found on the Quantile website at www.quantiles.com are one aspect of the free materials available to teachers, students and families.

The 2009 PISA Results for Mathematics

Every few years, the Programme for International Student Assessment (PISA) measures the academic achievement of countries around the world. In 2009, students from 65 different countries and economies participated – 34 OECD (Organisation for Economic Co-operation and Development) countries and 31 partner countries.

The top 5 performers were Shanghai-China, Singapore, Hong Kong-China, Korea and Finland, with scores of 600, 562, 555, 546 and 541, respectively. The United States’ score was 487, 17th of OECD countries (31st overall), and 9 points below the OECD average. 

The results also showed that among OECD countries, boys outperformed girls by an average 12 points in math (whereas girls outperformed boys by 39 points in reading). Countries overall showed little change in math performance since the 2003 testing, with 6 OECD countries and 2 partner countries having significant gains. For the other 28 OECD countries, the percentage of top math performers decreased slightly.

Read the executive summary of the PISA 2009 Results

 

Photo credit: www.oecd.org

Math Performance in the US: How ARE We Doing?

 The release of the 2009 PISA (Programme for International Student Assessment) results last month prompted another round of hand-wringing over the United States' mediocre performance. Shanghai (China), South Korea, Finland, and Singapore topped the charts in math. The United States ranked 17th, slightly above the average of other advanced OECD (Organization for Economic Cooperation and Development) members. The latest PISA results followed the publication of the report U.S. Math Performance in Global Perspective, which summarized the importance of creating a population of high mathematical performers to feed a growing STEM-based economy. Sadly, the report concluded that the U.S. is lacking compared to its international peers. There’s an accessible article articulating the findings of the report at Education Next.

However, not everyone thinks the situation is so dire. The National Education Policy Center (NEPC) at the University of Colorado has challenged the methodology of the Harvard and Education Next report. The NEPC review calls the report’s comparison across countries and tests (PISA versus NAEP) “deceptive”, offering “essentially no assistance to U.S. educators seeking to improve students’ performance in mathematics.” Those sound like fighting words to me. Noted economist Robert Samuelson joined the fray with a recent article in The Washington Post, where he suggested that schools in the United States aren’t as bad as they are often depicted. Of course, that piece prompted a response in Education Next.

What’s the story? Are American schools short-changing us in the competition for top mathematical talent or not? Well, we can certainly do better, and we should seek to learn from countries like Singapore that have turned a largely illiterate population at the time of its independence in the 1960s into one of the world’s top academic and economic performers. And one area where everyone agrees (I think) is the need to remedy the performance gap among sub-groups in the United States. Blacks and Hispanics continue to lag behind whites. While some may argue that a focus on raising the bottom has taken resources from elevating the top, I certainly wouldn’t want the reverse.

 

http://www.flickr.com/photos/maaorg/ / CC BY 2.0

A New Initiative for Preparing Students for State Math Tests

Now that school has started, I'm working on new tasks and initiatives to ensure that our students have the best year possible. For many of us, success is measured by mandatory state assessments. If we had it our way, this would not be the case, but due to state and federal mandates our administrators, teachers and students are often judged by those pesky test scores.

When I taught high school, I didn't understand the pressure that elementary and middle school teachers are under to prepare students for the test. The words "teach to the test" frustrated me tremendously. If you're teaching the standards successfully, shouldn't the kids pass the test? I've learned that it's not that simple. Preparing students for the test isn't just about covering the standards, it's about covering the standards before the test in early May – our schools don't close until late June – and it's about preparing students for the various types of questions on the test.

Ideally, all of this is done without spending the entire month of April on test-prep activities, but this is a challenge due to pressure on teachers to increase scores. This year, I'm starting a new initiative titled ASK Aerobics (NJ's test is titled Assessment of Skills and Knowledge, or NJ ASK). All teachers in Grades 3-8 will assign a daily warm-up based on one of the four major mathematical strands, along with an open-ended question for the fifth day of the week. The goal is for students to complete one test-prep question each day for the entire year. As the math specialist, I will gather the work, compile data, and return to teachers a simple report showing students' strengths and weaknesses. Although it will be a lot of work, I feel that the data we collect can really inform instruction while consistently presenting students with a variety of NJ ASK-like problems. We're all keeping our fingers crossed that this will eliminate some of that last-minute pressure that teachers and students feel in the month before the test.

I'd love to hear about the pressures you feel with standardized tests and how you help students and teachers meet this challenge. Please share.

 

http://www.flickr.com/photos/rzganoza/ / CC BY 2.0