JSFiddle - React, Tailwind, and code Playground

HTML

<form class="form-inline left" method="POST">
    <div class="form-group">
        <label for="listar">Listar por</label>
        <select id="filtro" name="filtro" class="form-control">
            <option value="">Escolha algo:</option>
            <option value="professor">Professor</option>
            <option value="assunto">Assunto</option>
        </select>
    </div>
</form>

JavaScript

document.getElementById('filtro').addEventListener('change', function() {
    this.form.submit();
});