Such an arbitrary limitation -- this should be enough to convince you to switch to a language that has a sane level of expressiveness.

cannot-do-dynamic-property-assignment.php

<?php

class WordProblem {

  /**
   * sorry, but this won't work
   */
   
  private $BINARY_OPERATORS = [
    'plus'          => function($l, $r) { return $l + $r; },
    'minus'         => function($l, $r) { return $l - $r; },
    'multiplied by' => function($l, $r) { return $l * $r; },
    'divided by'    => function($l, $r) { return $l / $r; }
  ];
    
  public function __construct($question) {}

}

constructor-init-only.php

<?php

class WordProblem
{

  private $BINARY_OPERATORS;

  public function __construct($question) {
    // you are forced to make the assignment here
    $this->BINARY_OPERATORS = [
      'plus'          => function($l, $r) { return $l + $r; },
      'minus'         => function($l, $r) { return $l - $r; },
      'multiplied by' => function($l, $r) { return $l * $r; },
      'divided by'    => function($l, $r) { return $l / $r; }
    ];
  }

}