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While many teachers recognize the value of inquiry-based learning, most find it a difficult approach to teaching mathematics. The traditional way of teaching math by figuring equations and plugging in numbers focuses only on computation. Teachers have taught math this way for years, and it has developed such a poor reputation that students may actively dislike the subject or find it intimidating. New ideas and perspectives on teaching math may help overcome this challenge.

In inquiry-based learning, teachers use questions, problems and scenarios to help students learn through individual thought and investigation. Instead of simply presenting facts, the teacher encourages students to talk about a problem and draw on their intuition to understand it. Inquiry-based learning also focuses on letting students ask their own questions - essentially providing their own inquiry. Student-led questions follow teacher-guided inquiry.

Instead of lecturing about learning goals, the teacher cultivates a learning environment and helps students explore it through questions and experiences.

1. Process focus
When students solve problems themselves, they internalize conceptual processes. Inquiry-based teaching prioritizes process over product.

2. Investigation
The teacher may pose a problem derived from the class content or students' questions. The students then investigate the issue to find an answer.

3. Group learning
Students may work in pairs or in small groups when exploring a problem. Students assist one another throughout the learning process, which enables them to share and build upon ideas as well as articulate how they arrived at a solution.

4. Discussion monitoring
As the students work together, the teacher can move from group to group, listening to their discussions. Teachers may ask questions to gauge students' understanding and correct any misconceptions.

5. Real-life application
Students solve math problems that have a meaningful life application. For example, a teacher may present a multiplication problem as an interesting story: "Brittany has 2 bags of candy. Each bag has 4 candies inside. How many candies does Brittany have altogether?"

Teachers may wish to focus less on math computation and more on helping students determine which pieces of information are useful and how this information applies to the real world. Teachers can develop students' understanding of the topic with guided inquiries.

Think about what you want your students to know or do before class.

Start with one or more overall guiding questions.

Inform students that there are multiple ways to solve a problem.

Model how students can develop their own questions.

Teaching students to ask higher-level questions is an important aspect of inquiry-based learning, but what kinds of questions work? Three ways that a teacher can successfully model questions to students include the following:

1. Ask big questions that have more than one answer.

2. Think about how to model questioning across a range of grade levels.

3. Phrase your questions in a way that fosters individual exploration.

The following example illustrates the use of an inquiry-based math strategy in the classroom:

An inquiry-based classroom discussion helps learners understand the concept of slope. The teacher draws a picture of two hills: one taller and one longer. The teacher asks, "Which hill is steeper?" The question may stimulate a lively discussion or a debate about the correct answer.

Inquiry-based learning involves guiding students by asking more in-depth questions - questions that encourage students to pose high-level questions themselves. This type of teacher-guided inquiry can motivate students to think critically and to appreciate learning.
Learn about the University of Texas at Arlington M.Ed. in Curriculum and Instruction - Math Education online program.
Sources:
Edutopia: Inquiry-Based Learning: From Teacher-Guided to Student-Driven Strategies for Teaching Elementary Mathematics: Inquiry Teaching: Models of Instruction KQED: How Can We Teach Math to Encourage 'Patient Problem Solving'? Have a question or concern about this article? Please contact us.

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How Inquiry-Based Learning Can Work in a Math Classroom

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While many teachers recognize the value of inquiry-based learning, most find it a difficult approach to teaching mathematics. The traditional way of teaching math by figuring equations and plugging in numbers focuses only on computation. Teachers have taught math this way for years, and it has developed such a poor reputation that students may actively dislike the subject or find it intimidating.

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Edutopia is a free source of information, inspiration, and practical strategies for learning and teaching in preK-12 education. We are published by the George Lucas Educational Foundation, a nonprofit, nonpartisan organization.

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At the heart of the IB is the Learner Profile, a long- term, holistic vision of education that underpins all three programmes and puts the student at the centre of teaching and learning.

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I met Greg Schwanbeck at Apple Distinguished Educator sleepaway camp last month. He teaches science. I teach math. We set those differences aside and found a connection. I use multimedia in my curriculum. Greg uses video for assessment in a way I found compelling.

Let's say he wants to assess the impulse-momentum theorem, which is the theorem that explains why boxers roll with punches rather than against them. ie. If you double the duration of the impact, you halve its force. (Cut me some slack here, science-buds. Everybody knows I have no idea what I'm talking about.)

He gave me permission to share with you three versions of the same assessment of a student's understanding of the impulse-momentum theorem. Let me invite you to assess the assessments in the comments. List some advantages and disadvantages. Ask yourself, "What is each option really assessing?" Greg will be along shortly to offer his own commentary and to assess your assessment of the assessments.

An 80 kg stuntman jumps off of a platform high in the air and lands on an airbag. The stuntman hits the airbag with an initial velocity of 45 m/s downward. 0.1 s elapses between the moment the stuntman first touches the airbag and the moment the airbag completely deflates and he comes to rest. Assume that the maximum force that the stuntman can experience and survive is 39200 N. Does the stuntman survive the fall?

A stuntman jumps off of the top of a crane extended high up in the air. Below him is an airbag-a large inflatable cushion that has a thickness of 3 meters. When the stuntman comes into contact with the airbag, the impact deflates the airbag over a period of time, compressing the airbag from 3 meters thick to 0 meters thick while slowing him down to a stop. Explain, making reference to the impulse momentum theorem, why the stuntman is able to survive.

Explain, making reference to the impulse momentum theorem, why the stuntman is able to survive the jump.

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I met Greg Schwanbeck at Apple Distinguished Educator sleepaway camp last month. He teaches science. I teach math. We set those differences aside and found a connection. I use multimedia in my curriculum. Greg uses video for assessment in a way I found compelling.

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Conceptual understanding

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What is Inquiry-Based Science?

Dr. Robyn M. Gillies is a professor in the School of Education at The University of Queensland, Brisbane, Australia. For over 20 years, she has researched the effects of cooperative learning on students' learning in science, mathematics, and social science content areas at the elementary and secondary levels. She has researched inquiry-based science in the classroom and has published her findings in many international journals, including the International Journal of Educational Research, Pedagogies: An International Journal, and Teaching Education. The extent of Dr. Gillies work in education is far reaching; she is the author of over 80 journal articles, two books, and nearly 20 book chapters. The SSEC recently contacted Dr. Gillies in hopes that she could provide valuable insight for our LASER i3 teachers. Dr. Gillies graciously agreed. Thank you, Dr. Gillies!
First, can you explain your interest in education and in inquiry-based science, specifically?
For about 20 years I have been researching the effects of cooperative learning on students' learning in science, mathematics, and social science content areas in elementary and secondary schools, and the majority of the findings have indicated that cooperative learning where students work together to investigate a problem or solve a dilemma can be used successfully to promote student engagement, socialization, and learning. Parallel to this research has been my interest in science and my concerns that teachers often seem reluctant to teach it in a way that is problem-based where student have opportunities to work together to investigate a topic. I have also been concerned for some time in the relatively mediocre performances of many students in Australia, the USA, and the UK on standardized international tests such as PISA and TIMMS, particularly when I see how consistently successful Finland, Singapore, the Republic of Korea, Chinese Taipei, and Japan have been on these same tests. In a sense, I've realized that cooperative learning with its emphasis on group cooperation and investigation can be used as a tool to help teachers teach science in a way that taps into students' natural curiosity to explore their world.
What is inquiry-based science?
Inquiry-based science adopts an investigative approach to teaching and learning where students are provided with opportunities to investigate a problem, search for possible solutions, make observations, ask questions, test out ideas, and think creatively and use their intuition. In this sense, inquiry-based science involves students doing science where they have opportunities to explore possible solutions, develop explanations for the phenomena under investigation, elaborate on concepts and processes, and evaluate or assess their understandings in the light of available evidence. This approach to teaching relies on teachers recognizing the importance of presenting problems to students that will challenge their current conceptual understandings so they are forced to reconcile anomalous thinking and construct new understandings.
How does inquiry-based science help students?
Inquiry-based science challenges students' thinking by engaging them in investigating scientifically orientated questions where they learn to give priority to evidence, evaluate explanations in the light of alternative explanations and learn to communicate and justify their decisions. These are dispositions needed to promote and justify their decisions. In short, "Scientific inquiry requires the use of evidence, logic, and imagination in developing explanations about the natural world" (Newman et al., 2004, p.258).
How does a teacher know if he/she is successfully teaching science using an inquiry-based approach?
Teachers can gauge the success of their teaching through students' level of engagement with the topic and each other, the scientific language they use to communicate their ideas, and the quality of the work they produce. Subtle comments such as "Are we doing science today? I really liked the way we did...." Are typical of the types of comments students will make when they have enjoyed participating in science investigations.

Does inquiry-based science look different in a lower-elementary classroom than in a middle-school classroom?
The principles are the same -- the need to excite and engage students' attention so they want to investigate the topic is critically important at any age. However, the way teachers actually teach it has to be more hands-on, directive or guided, and concrete for younger children.
What are some common misconceptions that teachers have regarding inquiry-based science?
... Teacher[s] often think they are 'doing inquiry' because they are out at the front of the classroom directing the inquiry or investigation or demonstrating how to do it. This is not inquiry science. Inquiry science requires teachers to be able to excite the students' interest in a topic and then provide them with opportunities to undertake the investigation either by themselves or preferably in collaboration with others. The teacher, though, needs to remain active in the lesson, guiding the students and asking questions to help them consolidate their understandings. Providing feedback is critically important to helping students understand how they are progressing.
You have observed many teachers over the years. Can you describe any teachers and/or students who exemplified inquiry-based science?
Good teachers engage students' interest through novelty, something unusual that spurs their curiosity and then they use language that is very dialogic or language that lets the student know that they are interested in what they think or want to say about the topic. Good teachers then carefully guide students as they begin to explore or investigate the topic, being careful not to dominate the conversation but allow student time to develop responses or think about the issue more carefully. In this sense they give students the time to reflect and think more carefully about the issue. However, good teachers are always careful to ensure that the inquiry-based science lesson moves forward and they do this be asking questions that probe and challenge students' thinking as well as giving them feedback that is meaningful and timely. Teachers who do inquiry well tend have a very good understanding of both the content they are teaching and the processes involved. They tend to use language that is very collaborative and friendly and take a genuine interest in what students are doing. They ask questions that challenge students' thinking and they acknowledge students' efforts.
What advice do you have for teachers who do not have a lot of time to teach science?
Recognize your limitations but try to optimize on what time you have. Be well prepared and try to ensure that science activities are interesting -- stimulate students' interest in science. If they are interested, they will continue to be interested even if they have not covered the full curriculum.
Can you provide an example of higher-level thinking and problem-solving questions that you may see with 7 and 8 year-old students?
Children will engage in higher-level thinking if teachers give them time to talk about a topic. Angela O'Donnell (Rutgers University) demonstrated how this can be achieved through her approach to Scripted Cooperation where two students work together on a topic. One then asks the other to recount as much as possible what they have learned while the listener asks the speaker questions. The students then switch roles and again they recount and ask each other questions. Over time, the questions become more complex so the respondent is compelled to provide more elaborate explanations.

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Dr. Robyn M. Gillies is a professor in the School of Education at The University of Queensland, Brisbane, Australia. For over 20 years, she has researched the effects of cooperative learning on students' learning in science, mathematics, and social science content areas at the elementary and secondary levels.

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Performance-based learning is when students participate in performing tasks or activities that are meaningful and engaging. The purpose of this kind of learning is to help students acquire and apply knowledge, practice skills, and develop independent and collaborative work habits. The culminating activity or product for performance-based learning is one that lets a student demonstrate evidence of understanding through a transfer of skills.

A performance-based assessment is open-ended and without a single, correct answer, and it should demonstrate authentic learning, such as the creation of a newspaper or class debate. The benefit of performance-based assessments is that students who are more actively involved in the learning process absorb and understand the material at a much deeper level. Other characteristics of performance-based assessments are that they are complex and time-bound.

Also, there are learning standards in each discipline that set academic expectations and define what is proficient in meeting that standard. Performance-based activities can integrate two or more subjects and should also meet 21st Century expectations whenever possible:

There are also Information Literacy standards and Media Literacy standards that require performance-based learning.

Clear Expectations

Performance-based activities can be challenging for students to complete. They need to understand from the beginning exactly what is being asked of them and how they will be assessed.

Examples and models may help, but it is more important to provide detailed criteria that will be used to assess the performance-based assessment. All criteria should be addressed in a scoring rubric.

Observations are an important component and can be used to provide students with feedback to improve performance. Teachers and students can both use observations. There may be peer to peer student feedback. There could be a checklist or a tally to record student achievement.

The goal of performance-based learning should be to enhance what the students have learned, not just have them recall facts. The following six types of activities provide good starting points for assessments in performance-based learning.

Presentations

One easy way to have students complete a performance-based activity is to have them do a presentation or report of some kind. This activity could be done by students, which takes time, or in collaborative groups.

The basis for the presentation may be one of the following:

Providing information

Teaching a skill

Reporting progress

Persuading others

Students may choose to add in visual aids or a PowerPoint presentation or Google Slides to help illustrate elements in their speech. Presentations work well across the curriculum as long as there is a clear set of expectations for students to work with from the beginning.

Portfolios

Student portfolios can include items that students have created and collected over a period. Art portfolios are for students who want to apply to art programs in college.

Another example is when students create a portfolio of their written work that shows how they have progressed from the beginning to the end of class. The writing in a portfolio can be from any discipline or a combination of disciplines.

Some teachers have students select those items they feel represents their best work to be included in a portfolio. The benefit of an activity like this is that it is something that grows over time and is therefore not just completed and forgotten. A portfolio can provide students with a lasting selection of artifacts that they can use later in their academic career.

Reflections may be included in student portfolios in which students may make a note of their growth based on the materials in the portfolio.

Performances

Dramatic performances are one kind of collaborative activities that can be used as a performance-based assessment. Students can create, perform, and/or provide a critical response. Examples include dance, recital, dramatic enactment. There may be prose or poetry interpretation.

This form of performance-based assessment can take time, so there must be a clear pacing guide.

Students must be provided time to address the demands of the activity; resources must be readily available and meet all safety standards. Students should have opportunities to draft stage work and practice.

Developing the criteria and the rubric and sharing these with students before evaluating a dramatic performance is critical.

Projects are commonly used by teachers as performance-based activities. They can include everything from research papers to artistic representations of information learned. Projects may require students to apply their knowledge and skills while completing the assigned task. They can be aligned with the higher levels of creativity, analysis, and synthesis.

Students might be asked to complete reports, diagrams, and maps. Teachers can also choose to have students work individually or in groups.

Journals may be part of a performance-based assessment. Journals can be used to record student reflections. Teachers may require students to complete journal entries. Some teachers may use journals as a way to record participation.

Exhibits and Fairs

Teachers can expand the idea of performance-based activities by creating exhibits or fairs for students to display their work. Examples include things like history fairs to art exhibitions. Students work on a product or item that will be exhibited publicly.

Exhibitions show in-depth learning and may include feedback from viewers.

In some cases, students might be required to explain or defend their work to those attending the exhibition.

Some fairs like science fairs could include the possibility of prizes and awards.

A debate in the classroom is one form of performance-based learning that teaches students about varied viewpoints and opinions. Skills associated with debate include research, media and argument literacy, reading comprehension, evidence evaluation, public speaking, and civic skills.

There are many different formats for debate. One is the fishbowl debate in which a handful of students form a half circle facing the other students and debate a topic. The rest of the classmates may pose questions to the panel.

Another form is a mock trial where teams representing the prosecution and defense take on the roles of attorneys and witnesses. A judge, or judging panel, oversees the courtroom presentation.

Middle school and high schools can use debates in the classroom, with increased levels of sophistication by grade level.

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Great Ideas for Performance-Based Activities

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These six kinds of authentic performance-based activities allow students to apply knowledge, practice skills, and develop independent work habits.

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How to assess student performance in science

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How to assess student performance in science

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Giving students free time each week to pursue a passion project can deepen engagement and learning.

As the past school year drew to a close, I found some yet-to-be-scheduled time with my seventh-grade English language arts classes-a rarity-and I wanted to take full advantage of it. Over the past few years, I've worked to offer my students more inquiry-based learning -having them develop their own questions to answer, research the questions in class, present their findings, and reflect on the process as a whole.

After researching some options, I landed on the concept of the Genius Hour, also known as 20 percent time. The process offers students time to work independently on a project of their choosing. It was my hope that incorporating an open-ended activity would spark enthusiasm and motivation in my students to wrap up the school year. I modified the concept to best meet my middle school students' needs and timeline using teacher Laura Randazzo's expertise. Instead of a daily time, I allocated six Friday class periods before the school year ended.

Defining the Project

I started by asking students to determine the individual questions and topics that they would research. Students presented these ideas to three peers before submitting to me for final approval. The students gained perspective on their classmates' interests, which helped further community in the classroom. The collaborative process also allowed them to offer support or assistance to others as they worked through their individual projects.

Some students started with a skill they already possessed, like singing or web design, and set out to improve on it. Others chose areas of interest where they had some knowledge but wanted to gain more. For example, a student who plays volleyball chose to research a position she did not yet know.

When it came time to conference with my students about their proposed learning, I was astounded with the questions they wanted to tackle when they were given time to allow their passions guide their learning. Students' project ideas ranged from creating a prototype for a self-filtering water bottle for places with little access to clean drinking water to organizing kindness boxes for the community so anyone could be cheered up with a prewritten message of hope. Other projects included learning to sign "The Star-Spangled Banner" and developing a website to help others learn how to use sign language.

Providing Parameters

It's important to determine how to assess the success of a project and convey those expectations at the outset. I reminded my students at the start of class that their grades would be based on their process, not on their final product. Most found this concept to be freeing in comparison to much of the work they typically complete in their classes. Assessments are designed to have students create something: a written essay, a lab report, a reading log, or an art project. Devising a system where the grade is process-based allows students more space to explore their needs and learning.

Each scheduled work day started with a reminder about the timeline and where students should be in the process. Because they started with research, several class periods included reminders about credible sources and the necessity of having a variety of different sources.

As the class neared the last few periods before presentations, the focus of the allocated time shifted to ideas surrounding how to best present findings based on students' learning. If you do this, remind those who struggle in the process that the final product is only part of the goal. Even if students don't get to the point of creating something that matches the magnitude of their aspirations, they still have plenty of learning to share with their peers at the conclusion of the project.

Assessing and Reflecting

Students presented their final projects to the class, which provided them with another opportunity to reflect on their learning. I asked them to spend three to five minutes sharing why they selected their chosen project, their process, and how they organized their time. Many used digital tools like websites to showcase what they learned. The digital element offered the flexibility to include videos, ways to donate to a cause, and links to support their research.

Some students gave in-class demonstrations of their project. For example, one student tackled overcoming a fear of public speaking by performing a memorized poem for the class.

Individual project assessment is valuable, but I also wanted to reflect with students on the process as a whole. I solicited their feedback by asking questions such as:

Was it a worthwhile way to spend our final Fridays of the marking period?

Did you feel well supported throughout the process?

How did you feel about the learning you accomplished?

Most students were surprised at how much they learned and how well they used the time provided. Many were surprised at their own abilities to find solutions for obstacles without my help. Some discovered the need to narrow down their project topics into more manageable chunks.

All of my students felt the time was beneficial because it developed their independent inquiry skills and motivated them at the end of the school year. Because the projects were process-based instead of outcome-based, students had the freedom to explore many facets of a concept. Every student told me they hoped my future students would have the same opportunity to learn about something that fed their individual curiosity and passion.

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Inquiry-Based Projects Feed Student Curiosity

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Giving students free time each week to pursue a passion project can deepen engagement and learning. As the past school year drew to a close, I found some yet-to-be-scheduled time with my seventh-grade English language arts classes-a rarity-and I wanted to take full advantage of it.