# Alternative Assessments: Multiple-Choice Tests

Have you ever given a multiple-choice test and wondered whether restricting your students’ creativity to a small number of available options truly assessed their comprehension of a concept? I have, but I didn’t toss the multiple-choices out. Call me an optimist, but I always try to find the benefit of something.

I asked myself, “What could possibly be the benefit of giving a multiple-choice test?” The last time I created a multiple-choice test, I found it far more involved than creating other types of assessments. Once I typed out the question, I knew the correct answer and struggled to write three more false answers for a total of four possible answers.  So, I wondered if I could harness some of that critical thinking that went into creating the multiple-choice test. What if I could take a different approach to this type of test that required a higher level of critical thinking? I thought for a while about it and decided to create a complete multiple-choice test, but without the questions.

That’s right! I gave my students a multiple-choice test with four answer choices (with the correct answer marked) for each question, but without the questions. Using the answer choices provided, they had to figure out what the question could have been. The first time that I tried it, the students seemed extremely engaged in the different way of thinking. What I liked about it was that it really got them to critically think about the material before writing down a question.

What alternative assessments have you created to inspire critical thinking?

# Solving Multistep Percent Problems (Sample Lesson Plan)

In designing this lesson plan, I wanted to approach the concept of multi-step percent problems in the context of problem situations. According to the Common Core State Standards Initiative (2012), “Mathematically proficient students make sense of quantities and their relationships in problem situations.” This means that for students to be mathematically proficient, they need to be able to decontextualize and contextualize quantitative problems. By teaching students to decontextualize problem situations and represent them symbolically, students will develop their quantitative reasoning skills. The lesson explores ways of decontextualizing problem situations that relate to percentages (i.e. sales on merchandise). Students are then shown how to use different operations to compare sale prices during the Teacher Presentation and practice decontextualizing problem situations in collaborate multi-ability groups during Class Activities.

For English Learner students, the process of decontextualizing problem situations requires a certain level of English language proficiency that may be beyond their proficiency level. In order to facilitate their English language development while lowering their anxiety, I integrated the collaborative model into the Class Activities portion of the lesson. The collaborative model is beneficial not only for English Learner students, but for all students. As students interact and engage their peers in this model, they become active agents of their own learning and experience learning at a whole new level, “Educational experiences that are active, social, contextual, engaging, and student-owned lead to deeper learning” (Cornell University, 2013). For English Learner students and especially for Jonathan, the profiled English Learner student, collaborating offers an opportunity to interact with other students, allowing them to develop their English language proficiency through listening and speaking with other students. While developing their English language proficiency, English Learner students will also be able to engage in a model of learning that develops their critical thinking skills, “The fact that students are actively exchanging, debating and negotiating ideas within their groups increases students’ interest in learning. Importantly, by engaging in discussion and taking responsibility for their learning, students are encouraged to become critical thinkers” (Dooly, 2008, p. 2). In order to facilitate the active exchange of ideas within these collaborative groups, I integrated the use of posters, strategically placed around the room, with a list of discussion and sentence starters. John Larmer (2013) suggests the use of discussion and sentence starters as a way of helping English Learner students acquire 21st century learning skills and develop their English language proficiency, “Help English learners access the project by thinking carefully about the language functions called for in specific 21st century learning activities; place them in supportive teams; provide models such as sentence starters and graphic organizers to help with collaborative discussions.”

At the beginning of the lesson, I engaged the students in brainstorming as a way of activating background knowledge of the word “sales.” Exposing English Learner students to new concepts through vocabulary correlations facilitates their learning and their English language development. By activating background knowledge, the students will be able to make connections to the learning that are meaningful and personally engaging. It also helps to engage the students in activating background knowledge to ensure that students are approaching the new concept with a basic foundational understanding of the concepts necessary for learning the new concept. Using a Circle Map to record the students’ responses help graphically organize the responses for the students, especially the English Learner students, to visualize their relationships to the word. For Jonathan, the profiled English Leaner, the Circle Map will facilitate his acquisition of the meaning of the word “sales” and the relationships of the students’ responses, especially considering his interest in creating art. Individuals with spatial intelligence enjoy creating art and easily learn through visual presentations. Giles, Pitre, and Womack suggest that teachers utilize visual presentations to accommodate the learning needs of students with spatial intelligence, “Teachers can foster this intelligence by utilizing charts, graphs, diagrams, graphic organizers, videotapes, color, art activities, doodling, microscopes and computer graphics software.” I have also integrated PowerPoint in the Introduction and the Teacher Presentation as another way of visually presenting the concepts, example percent problems, and the steps for solving each problem.

During the Introduction, I emphasized the time (or extended time) necessary to wait on students to provide their responses to questions. It is crucial to allow students enough time to think about a question and develop a response that they are confident in sharing with the class. For English Learner students, sharing with the class may already be a high-anxiety situation. There is no need to exacerbate the situation by requiring speedy responses. In order to lower the students’ anxiety, I emphasized implementing a longer wait time. This not only provides the English Learner students and Jonathan, the profiled English Learner student, with extra time to process content, but also to linguistically plan their response.

The lesson incorporates a number of strategies, supporting the 1/3 Plus Model. The students are intentionally placed in collaborative multi-ability groups to allow the top third the opportunity to lead the collaborative discussion and provide support to his/her peers. During the Introduction, the top third may offer more advanced vocabulary when they think of the word “sales.” The middle third of the students will learn because they have a basic understanding of the concepts underlying percent problems and will be able to participate in the collaborative discussions. During discussions, they may respond on a voluntary basis or they may wait to hear another student respond first. By giving students extra time to respond after asking them a question, the middle third (and bottom third) will be more encouraged to participate in class discussions. The bottom third will be first engaged by the activation of background knowledge. This will facilitate their learning and help them make connections to any new vocabulary or concepts. Using graphic organizers, like the Circle Map, will help the bottom third visualize vocabulary and their relationship to the concept being taught. Including PowerPoint as a means of visually highlighting key aspects of translating percent problems and providing images for students to relate to facilitates the learning process. By collaborating in multi-ability group, the bottom third are able to work with other students, developing their mathematical and English language proficiency through observational learning and social contexts. The questions asked at the end of the lesson are progressively leveled according to Bloom’s taxonomy to encourage higher order thinking of all students. Having students participate in a think-pair-share to engage their learning and have them share their responses helps the bottom third and middle third take the time to reflect on their learning and hear other students’ responses. It helps the top third reflect and consider further investigations while sharing their ideas with other students.

PowerPoint Presentation Used with Lesson

# Rigor, Relevance, and Relationship

The emphasis in mathematics education is on shifting the classroom dynamic to promoting mathematical reasoning. Too much time has been placed on rote learning, particularly in mathematics. With the transition to the Common Core State Standards, we are beginning to integrate rigor, relevance, and relationship, in a way that enhances the students’ procedural knowledge while fostering greater conceptual understanding. For example, embracing the Standards for Mathematical Practice as a set of guiding principles that explore the many facets of mathematical reasoning allows students to become active and engaged learners.  Through rigor, they will exercise higher order thinking and develop their metacognitive skills. Through relevance, they will contextualize the abstract nature of mathematics by forming connections with real life experiences, personalizing their learning. Through relationship, we as teachers must know our students in order to create a highly engaging learning environment.

# Applying Bloom’s Revised Taxonomy to Mathematics

A few months ago, I designed a training on applying Bloom’s Taxonomy to create higher order thinking questions in mathematics.

I showed two figures: (1) A right triangle and (2) an equilateral triangle.

#### Equilateral Triangle

The following were questions that I developed to help the instructors think through the various levels of Bloom’s Revised Taxonomy in regards to mathematics.

• Knowledge – What can you tell me about the first triangle?
• The students provide any information they know about the mathematical concept.
• Comprehension – What makes the first triangle a right triangle?
• The students use the information they already know about triangles to rightly identify a specific triangle.
• Application – Based on what you know about right triangles, why is the second triangle not a right triangle?
• The students apply the information they already know about triangle to differentiating one triangle from another based on their characteristics.
• Analysis – How is the first triangle similar to a rectangle?
• The students compare the characteristics of a right triangle with those of a rectangle.
• Evaluation – How would you prove that all right triangles fit in a circle, with each vertex (or corner) of the triangle touching the circle?
• The students extend their understanding of triangles by proving a well-known theorem of geometry (see Thale’s Theorem)
• Synthesis – How could you use the right triangle to design our next engineering project?
• The students integrate information they know and understand about the right triangle into designing a new project.