Error array to string conversion

if ($_SERVER["REQUEST_METHOD"] == "POST" AND isset($_POST["save"])) {
    $validasi = false; $err = false;
    if ($update) {
        $sql = "UPDATE nilai SET kd_kriteria='$_POST[kd_kriteria]', nim='$_POST[nim]', nilai='$_POST[nilai]' WHERE kd_nilai='$_GET[key]'";
    } else {
        $query = "INSERT INTO nilai VALUES ";
        foreach ($_POST["nilai"] as $kd_kriteria => $nilai) {
            $query .= "(NULL, '$_POST[kd_beasiswa]', '$kd_kriteria', '$_POST[nim]', '$nilai'),";
        }
        $sql = rtrim($query, ',');
        $validasi = true;
    }

    if ($validasi) {
        foreach ($_POST["nilai"] as $kd_kriteria => $nilai) {
            $q = $connection->query("SELECT kd_nilai FROM nilai WHERE kd_beasiswa=$_POST[kd_beasiswa] AND kd_kriteria=$kd_kriteria AND nim=$_POST[nim] AND nilai LIKE '%$nilai%'");
            if ($q->num_rows) {
                echo alert("Nilai untuk ".$_POST["nim"]." sudah ada!", "?page=nilai");
                $err = true;
            }
        }
    }

  if (!$err AND $connection->query($sql)) {
        echo alert("Berhasil!", "?page=nilai");
    } else {
        echo alert("Gagal!", "?page=nilai");
    }